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Meskine O, Descamps E, Keller A, Lemaître A, Baboux F, Ducci S, Milman P. Approaching Maximal Precision of Hong-Ou-Mandel Interferometry with Nonperfect Visibility. PHYSICAL REVIEW LETTERS 2024; 132:193603. [PMID: 38804918 DOI: 10.1103/physrevlett.132.193603] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/20/2023] [Accepted: 04/08/2024] [Indexed: 05/29/2024]
Abstract
In quantum mechanics, the precision achieved in parameter estimation using a quantum state as a probe is determined by the measurement strategy employed. The quantum limit of precision is bounded by a value set by the state and its dynamics. Theoretical results have revealed that in interference measurements with two possible outcomes, this limit can be reached under ideal conditions of perfect visibility and zero losses. However, in practice, these conditions cannot be achieved, so precision never reaches the quantum limit. But how do experimental setups approach precision limits under realistic circumstances? In this Letter, we provide a model for precision limits in two-photon Hong-Ou-Mandel interferometry using coincidence statistics for nonperfect visibility and temporally unresolved measurements. We show that the scaling of precision with visibility depends on the effective area in time-frequency phase space occupied by the state used as a probe, and we find that an optimal scaling exists. We demonstrate our results experimentally for different states in a setup where the visibility can be controlled and reaches up to 99.5%. In the optimal scenario, a ratio of 0.97 is observed between the experimental precision and the quantum limit, establishing a new benchmark in the field.
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Affiliation(s)
- O Meskine
- Laboratoire Matériaux et Phénomènes Quantiques, Université Paris Cité, CNRS UMR 7162, 75013 Paris, France
| | - E Descamps
- Laboratoire Matériaux et Phénomènes Quantiques, Université Paris Cité, CNRS UMR 7162, 75013 Paris, France
- Département de Physique de l'Ecole Normale Supérieure - PSL, 45 rue d'Ulm, 75230 Paris Cedex 05, France
| | - A Keller
- Laboratoire Matériaux et Phénomènes Quantiques, Université Paris Cité, CNRS UMR 7162, 75013 Paris, France
- Department de Physique, Université Paris-Saclay, 91405 Orsay Cedex, France
| | - A Lemaître
- Univ. Paris-Saclay, CNRS, Centre de Nanosciences et de Nanotechnologies, 91120 Palaiseau, France
| | - F Baboux
- Laboratoire Matériaux et Phénomènes Quantiques, Université Paris Cité, CNRS UMR 7162, 75013 Paris, France
| | - S Ducci
- Laboratoire Matériaux et Phénomènes Quantiques, Université Paris Cité, CNRS UMR 7162, 75013 Paris, France
| | - P Milman
- Laboratoire Matériaux et Phénomènes Quantiques, Université Paris Cité, CNRS UMR 7162, 75013 Paris, France
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2
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Gouzien É, Ruiz D, Le Régent FM, Guillaud J, Sangouard N. Performance Analysis of a Repetition Cat Code Architecture: Computing 256-bit Elliptic Curve Logarithm in 9 Hours with 126 133 Cat Qubits. PHYSICAL REVIEW LETTERS 2023; 131:040602. [PMID: 37566837 DOI: 10.1103/physrevlett.131.040602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/26/2023] [Accepted: 06/05/2023] [Indexed: 08/13/2023]
Abstract
Cat qubits provide appealing building blocks for quantum computing. They exhibit a tunable noise bias yielding an exponential suppression of bit flips with the average photon number and a protection against the remaining phase errors can be ensured by a simple repetition code. We here quantify the cost of a repetition code and provide valuable guidance for the choice of a large scale architecture using cat qubits by realizing a performance analysis based on the computation of discrete logarithms on an elliptic curve with Shor's algorithm. By focusing on a 2D grid of cat qubits with neighboring connectivity, we propose to implement 2-qubit gates via lattice surgery and Toffoli gates with off-line fault-tolerant preparation of magic states through projective measurements and subsequent gate teleportations. All-to-all connectivity between logical qubits is ensured by routing qubits. Assuming a ratio between single- and two-photon losses of 10^{-5} and a cycle time of 500 ns, we show concretely that such an architecture can compute a 256-bit elliptic curve logarithm in 9 h with 126 133 cat qubits and on average 19 photons by cat state. We give the details of the realization of Shor's algorithm so that the proposed performance analysis can be easily reused to guide the choice of architecture for others platforms.
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Affiliation(s)
- Élie Gouzien
- Université Paris-Saclay, CNRS, CEA, Institut de physique théorique, 91191 Gif-sur-Yvette, France
| | - Diego Ruiz
- Alice & Bob, 53 boulevard du Général Martial Valin, 75015 Paris, France
- Laboratoire de Physique de l'École normale supérieure, École normale supérieure, Mines Paris, Université PSL, Sorbonne Université, CNRS, Inria, 75005 Paris, France
| | - Francois-Marie Le Régent
- Alice & Bob, 53 boulevard du Général Martial Valin, 75015 Paris, France
- Laboratoire de Physique de l'École normale supérieure, École normale supérieure, Mines Paris, Université PSL, Sorbonne Université, CNRS, Inria, 75005 Paris, France
| | - Jérémie Guillaud
- Alice & Bob, 53 boulevard du Général Martial Valin, 75015 Paris, France
| | - Nicolas Sangouard
- Université Paris-Saclay, CNRS, CEA, Institut de physique théorique, 91191 Gif-sur-Yvette, France
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3
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Wu YD, Zhu Y, Bai G, Wang Y, Chiribella G. Quantum Similarity Testing with Convolutional Neural Networks. PHYSICAL REVIEW LETTERS 2023; 130:210601. [PMID: 37295121 DOI: 10.1103/physrevlett.130.210601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/04/2022] [Revised: 04/08/2023] [Accepted: 04/25/2023] [Indexed: 06/12/2023]
Abstract
The task of testing whether two uncharacterized quantum devices behave in the same way is crucial for benchmarking near-term quantum computers and quantum simulators, but has so far remained open for continuous variable quantum systems. In this Letter, we develop a machine learning algorithm for comparing unknown continuous variable states using limited and noisy data. The algorithm works on non-Gaussian quantum states for which similarity testing could not be achieved with previous techniques. Our approach is based on a convolutional neural network that assesses the similarity of quantum states based on a lower-dimensional state representation built from measurement data. The network can be trained off-line with classically simulated data from a fiducial set of states sharing structural similarities with the states to be tested, with experimental data generated by measurements on the fiducial states, or with a combination of simulated and experimental data. We test the performance of the model on noisy cat states and states generated by arbitrary selective number-dependent phase gates. Our network can also be applied to the problem of comparing continuous variable states across different experimental platforms, with different sets of achievable measurements, and to the problem of experimentally testing whether two states are equivalent up to Gaussian unitary transformations.
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Affiliation(s)
- Ya-Dong Wu
- Department of Computer Science, QICI Quantum Information and Computation Initiative, The University of Hong Kong, Pokfulam Road, Hong Kong
| | - Yan Zhu
- Department of Computer Science, QICI Quantum Information and Computation Initiative, The University of Hong Kong, Pokfulam Road, Hong Kong
| | - Ge Bai
- Centre for Quantum Technologies, National University of Singapore, Block S15, 3 Science Drive 2, 117543, Singapore
| | - Yuexuan Wang
- Department of Computer Science, AI Technology Laboratory, The University of Hong Kong, Pokfulam Road, Hong Kong
- College of Computer Science and Technology, Zhejiang University, Zhejiang Province 310058, China
| | - Giulio Chiribella
- Department of Computer Science, QICI Quantum Information and Computation Initiative, The University of Hong Kong, Pokfulam Road, Hong Kong
- Department of Computer Science, Parks Road, Oxford OX1 3QD, United Kingdom
- Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada
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4
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Grygar J, Hloušek J, Fiurášek J, Ježek M. Quantum non-Gaussianity certification of photon number-resolving detectors. OPTICS EXPRESS 2022; 30:33097-33111. [PMID: 36242357 DOI: 10.1364/oe.463786] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/17/2022] [Accepted: 08/03/2022] [Indexed: 06/16/2023]
Abstract
We report on direct experimental certification of the quantum non-Gaussian character of a photon number-resolving detector. The certification protocol is based on an adaptation of the existing quantum non-Gaussianity criteria for quantum states to quantum measurements. In our approach, it suffices to probe the detector with a vacuum state and two different thermal states to test its quantum non-Gaussianity. The certification is experimentally demonstrated for the detector formed by a spatially multiplexed array of ten single-photon avalanche photodiodes. We confirm the quantum non-Gaussianity of POVM elements Π^m associated with the m-fold coincidence counts, up to m = 7. The experimental ability to certify from the first principles the quantum non-Gaussian character of Π^m is for large m limited by low probability of the measurement outcomes, especially for vacuum input state. We find that the injection of independent Gaussian background noise into the detector can be helpful and may reduce the measurement time required for reliable confirmation of quantum non-Gaussianity. In addition, we modified and experimentally verified the quantum non-Gaussianity certification protocol employing a third thermal state instead of a vacuum to speed up the whole measurement. Our findings demonstrate the existence of efficient tools for the practical characterization of fundamental non-classical properties and benchmarking of complex optical quantum detectors.
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5
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Quantum state preparation and tomography of entangled mechanical resonators. Nature 2022; 604:463-467. [PMID: 35444325 DOI: 10.1038/s41586-022-04500-y] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/14/2021] [Accepted: 02/01/2022] [Indexed: 11/08/2022]
Abstract
Precisely engineered mechanical oscillators keep time, filter signals and sense motion, making them an indispensable part of the technological landscape of today. These unique capabilities motivate bringing mechanical devices into the quantum domain by interfacing them with engineered quantum circuits. Proposals to combine microwave-frequency mechanical resonators with superconducting devices suggest the possibility of powerful quantum acoustic processors1-3. Meanwhile, experiments in several mechanical systems have demonstrated quantum state control and readout4,5, phonon number resolution6,7 and phonon-mediated qubit-qubit interactions8,9. At present, these acoustic platforms lack processors capable of controlling the quantum states of several mechanical oscillators with a single qubit and the rapid quantum non-demolition measurements of mechanical states needed for error correction. Here we use a superconducting qubit to control and read out the quantum state of a pair of nanomechanical resonators. Our device is capable of fast qubit-mechanics swap operations, which we use to deterministically manipulate the mechanical states. By placing the qubit into the strong dispersive regime with both mechanical resonators simultaneously, we determine the phonon number distributions of the resonators by means of Ramsey measurements. Finally, we present quantum tomography of the prepared nonclassical and entangled mechanical states. Our result represents a concrete step towards feedback-based operation of a quantum acoustic processor.
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6
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Chakraborty A, Sensarma R. Nonequilibrium Dynamics of Renyi Entropy for Bosonic Many-Particle Systems. PHYSICAL REVIEW LETTERS 2021; 127:200603. [PMID: 34860062 DOI: 10.1103/physrevlett.127.200603] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/18/2018] [Revised: 05/10/2021] [Accepted: 10/04/2021] [Indexed: 06/13/2023]
Abstract
We propose a new field theoretic method for calculating Renyi entropy of a subsystem of many interacting bosons without using replica methods. This method is applicable to dynamics of both open and closed quantum systems starting from arbitrary initial conditions. Our method identifies the Wigner characteristic of a reduced density matrix with the partition function of the whole system with a set of linear sources turned on only in the subsystem, and uses this to calculate the subsystem's Renyi entropy. We use this method to study the evolution of Renyi entropy in a noninteracting open quantum system starting from an initial Fock state. We find a relation between the initial state and final density matrix which determines whether the entropy shows nonmonotonic behavior in time. For non-Markovian dynamics, we show that the entropy approaches its steady-state value as a power law with exponents governed by nonanalyticities of the bath. We illustrate that this field-theoretic method can be used to study large bosonic open quantum systems.
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Affiliation(s)
- Ahana Chakraborty
- Department of Theoretical Physics, Tata Institute of Fundamental Research, Mumbai 400005, India
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzerstrasse 38, 01187 Dresden, Germany
| | - Rajdeep Sensarma
- Department of Theoretical Physics, Tata Institute of Fundamental Research, Mumbai 400005, India
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7
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Ben Hayun A, Reinhardt O, Nemirovsky J, Karnieli A, Rivera N, Kaminer I. Shaping quantum photonic states using free electrons. SCIENCE ADVANCES 2021; 7:eabe4270. [PMID: 33692108 PMCID: PMC7946371 DOI: 10.1126/sciadv.abe4270] [Citation(s) in RCA: 17] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/21/2020] [Accepted: 01/25/2021] [Indexed: 05/29/2023]
Abstract
It is a long-standing goal to create light with unique quantum properties such as squeezing and entanglement. We propose the generation of quantum light using free-electron interactions, going beyond their already ubiquitous use in generating classical light. This concept is motivated by developments in electron microscopy, which recently demonstrated quantum free-electron interactions with light in photonic cavities. Such electron microscopes provide platforms for shaping quantum states of light through a judicious choice of the input light and electron states. Specifically, we show how electron energy combs implement photon displacement operations, creating displaced-Fock and displaced-squeezed states. We develop the theory for consecutive electron-cavity interactions with a common cavity and show how to generate any target Fock state. Looking forward, exploiting the degrees of freedom of electrons, light, and their interaction may achieve complete control over the quantum state of the generated light, leading to novel light statistics and correlations.
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Affiliation(s)
- A Ben Hayun
- Department of Electrical Engineering and Solid State Institute, Technion, Israel Institute of Technology, Haifa 32000, Israel
| | - O Reinhardt
- Department of Electrical Engineering and Solid State Institute, Technion, Israel Institute of Technology, Haifa 32000, Israel
| | - J Nemirovsky
- Department of Electrical Engineering and Solid State Institute, Technion, Israel Institute of Technology, Haifa 32000, Israel
| | - A Karnieli
- Sackler School of Physics, Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978, Israel
| | - N Rivera
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - I Kaminer
- Department of Electrical Engineering and Solid State Institute, Technion, Israel Institute of Technology, Haifa 32000, Israel.
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8
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Hloušek J, Ježek M, Fiurášek J. Direct Experimental Certification of Quantum Non-Gaussian Character and Wigner Function Negativity of Single-Photon Detectors. PHYSICAL REVIEW LETTERS 2021; 126:043601. [PMID: 33576686 DOI: 10.1103/physrevlett.126.043601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/15/2020] [Accepted: 01/06/2021] [Indexed: 06/12/2023]
Abstract
Highly nonclassical character of optical quantum detectors, such as single-photon detectors, is essential for preparation of quantum states of light and a vast majority of applications in quantum metrology and quantum information processing. Therefore, it is both fundamentally interesting and practically relevant to investigate the nonclassical features of optical quantum measurements. Here we propose and experimentally demonstrate a procedure for direct certification of quantum non-Gaussianity and Wigner function negativity, two crucial nonclassicality levels, of photonic quantum detectors. Remarkably, we characterize the highly nonclassical properties of the detector by probing it with only two classical thermal states and a vacuum state. We experimentally demonstrate the quantum non-Gaussianity of a single-photon avalanche diode even under the presence of background noise, and we also certify the negativity of the Wigner function of this detector. Our results open the way for direct benchmarking of photonic quantum detectors with a few measurements on classical states.
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Affiliation(s)
- Josef Hloušek
- Department of Optics, Palacký University, 17. listopadu 1192/12, 77146 Olomouc, Czech Republic
| | - Miroslav Ježek
- Department of Optics, Palacký University, 17. listopadu 1192/12, 77146 Olomouc, Czech Republic
| | - Jaromír Fiurášek
- Department of Optics, Palacký University, 17. listopadu 1192/12, 77146 Olomouc, Czech Republic
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9
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Ma Y, Pan X, Cai W, Mu X, Xu Y, Hu L, Wang W, Wang H, Song YP, Yang ZB, Zheng SB, Sun L. Manipulating Complex Hybrid Entanglement and Testing Multipartite Bell Inequalities in a Superconducting Circuit. PHYSICAL REVIEW LETTERS 2020; 125:180503. [PMID: 33196232 DOI: 10.1103/physrevlett.125.180503] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/16/2020] [Accepted: 09/23/2020] [Indexed: 06/11/2023]
Abstract
Quantum correlations in observables of multiple systems not only are of fundamental interest, but also play a key role in quantum information processing. As a signature of these correlations, the violation of Bell inequalities has not been demonstrated with multipartite hybrid entanglement involving both continuous and discrete variables. Here we create a five-partite entangled state with three superconducting transmon qubits and two photonic qubits, each encoded in the mesoscopic field of a microwave cavity. We reveal the quantum correlations among these distinct elements by joint Wigner tomography of the two cavity fields conditional on the detection of the qubits and by test of a five-partite Bell inequality. The measured Bell signal is 8.381±0.038, surpassing the bound of 8 for a four-partite entanglement imposed by quantum correlations by 10 standard deviations, demonstrating the genuine five-partite entanglement in a hybrid quantum system.
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Affiliation(s)
- Y Ma
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - X Pan
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - W Cai
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - X Mu
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - Y Xu
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - L Hu
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - W Wang
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - H Wang
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - Y P Song
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - Zhen-Biao Yang
- Fujian Key Laboratory of Quantum Information and Quantum Optics, College of Physics and Information Engineering, Fuzhou University, Fuzhou, Fujian 350108, China
| | - Shi-Biao Zheng
- Fujian Key Laboratory of Quantum Information and Quantum Optics, College of Physics and Information Engineering, Fuzhou University, Fuzhou, Fujian 350108, China
| | - L Sun
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
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10
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Flühmann C, Home JP. Direct Characteristic-Function Tomography of Quantum States of the Trapped-Ion Motional Oscillator. PHYSICAL REVIEW LETTERS 2020; 125:043602. [PMID: 32794777 DOI: 10.1103/physrevlett.125.043602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/21/2019] [Accepted: 06/26/2020] [Indexed: 06/11/2023]
Abstract
We implement direct readout of the symmetric characteristic function of quantum states of the motional oscillation of a trapped calcium ion. Suitably chosen internal state rotations combined with internal state-dependent displacements, based on bichromatic laser fields, map the expectation value of the real or imaginary part of the displacement operator to the internal states, which are subsequently read out. Combining these results provides full information about the symmetric characteristic function. We characterize the technique by applying it to a range of archetypal quantum oscillator states, including displaced and squeezed Gaussian states as well as two and three component superpositions of displaced squeezed states. For each, we discuss relevant features of the characteristic function and Wigner phase-space quasiprobability distribution. The direct reconstruction of these highly nonclassical oscillator states using a reduced number of measurements is an essential tool for understanding and optimizing the control of oscillator systems for quantum sensing and quantum information applications.
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Affiliation(s)
- C Flühmann
- Institute for Quantum Electronics, ETH Zürich, Otto-Stern-Weg 1, 8093 Zürich, Switzerland
| | - J P Home
- Institute for Quantum Electronics, ETH Zürich, Otto-Stern-Weg 1, 8093 Zürich, Switzerland
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11
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Lewis-Swan RJ, Barberena D, Muniz JA, Cline JRK, Young D, Thompson JK, Rey AM. Protocol for Precise Field Sensing in the Optical Domain with Cold Atoms in a Cavity. PHYSICAL REVIEW LETTERS 2020; 124:193602. [PMID: 32469538 DOI: 10.1103/physrevlett.124.193602] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/07/2019] [Accepted: 04/08/2020] [Indexed: 06/11/2023]
Abstract
In the context of quantum metrology, optical cavity-QED platforms have primarily been focused on the generation of entangled atomic spin states useful for next-generation frequency and time standards. Here, we report a complementary application: the use of optical cavities to generate nonclassical states of light for electric field sensing below the standard quantum limit. We show that cooperative atom-light interactions in the strong collective coupling regime can be used to engineer generalized atom-light cat states which enable quantum enhanced sensing of small displacements of the cavity field even in the presence of photon loss. We demonstrate that metrological gains of 10-20 dB below the standard quantum limit are within reach for current cavity-QED systems operating with long-lived alkaline-earth atoms.
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Affiliation(s)
- Robert J Lewis-Swan
- JILA, NIST, Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
- Center for Theory of Quantum Matter, University of Colorado, Boulder, Colorado 80309, USA
| | - Diego Barberena
- JILA, NIST, Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
- Center for Theory of Quantum Matter, University of Colorado, Boulder, Colorado 80309, USA
| | - Juan A Muniz
- JILA, NIST, Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
| | - Julia R K Cline
- JILA, NIST, Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
| | - Dylan Young
- JILA, NIST, Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
| | - James K Thompson
- JILA, NIST, Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
| | - Ana Maria Rey
- JILA, NIST, Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
- Center for Theory of Quantum Matter, University of Colorado, Boulder, Colorado 80309, USA
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12
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Peronnin T, Marković D, Ficheux Q, Huard B. Sequential Dispersive Measurement of a Superconducting Qubit. PHYSICAL REVIEW LETTERS 2020; 124:180502. [PMID: 32441960 DOI: 10.1103/physrevlett.124.180502] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/09/2019] [Accepted: 04/13/2020] [Indexed: 06/11/2023]
Abstract
We present a superconducting device that realizes the sequential measurement of a transmon qubit. The device disables common limitations of dispersive readout such as Purcell effect or transients in the cavity mode by turning on and off the coupling to the measurement channel on demand. The qubit measurement begins by loading a readout resonator that is coupled to the qubit. After an optimal interaction time with negligible loss, a microwave pump releases the content of the readout mode by upconversion into a measurement line in a characteristic time as low as 10 ns, which is 400 times shorter than the lifetime of the readout resonator. A direct measurement of the released field quadratures demonstrates a readout fidelity of 97.5% in a total measurement time of 220 ns. The Wigner tomography of the readout mode allows us to characterize the non-Gaussian nature of the readout mode and its dynamics.
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Affiliation(s)
- T Peronnin
- Université Lyon, ENS de Lyon, Université Claude Bernard Lyon 1, CNRS, Laboratoire de Physique, F-69342 Lyon, France
| | - D Marković
- Unité Mixte de Physique, CNRS, Thales, Université Paris-Sud, Université Paris-Saclay, 91767 Palaiseau, France
| | - Q Ficheux
- Université Lyon, ENS de Lyon, Université Claude Bernard Lyon 1, CNRS, Laboratoire de Physique, F-69342 Lyon, France
| | - B Huard
- Université Lyon, ENS de Lyon, Université Claude Bernard Lyon 1, CNRS, Laboratoire de Physique, F-69342 Lyon, France
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13
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Gan HCJ, Maslennikov G, Tseng KW, Nguyen C, Matsukevich D. Hybrid Quantum Computing with Conditional Beam Splitter Gate in Trapped Ion System. PHYSICAL REVIEW LETTERS 2020; 124:170502. [PMID: 32412255 DOI: 10.1103/physrevlett.124.170502] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/23/2019] [Accepted: 03/25/2020] [Indexed: 06/11/2023]
Abstract
The hybrid approach to quantum computation simultaneously utilizes both discrete and continuous variables, which offers the advantage of higher density encoding and processing powers for the same physical resources. Trapped ions, with discrete internal states and motional modes that can be described by continuous variables in an infinite-dimensional Hilbert space, offer a natural platform for this approach. A nonlinear gate for universal quantum computing can be implemented with the conditional beam splitter Hamiltonian |e⟩⟨e|(a[over ^]^{†}b[over ^]+a[over ^]b[over ^]^{†}) that swaps the quantum states of two motional modes, depending on the ion's internal state. We realize such a gate and demonstrate its applications for quantum state overlap measurements, single-shot parity measurement, and generation of NOON states.
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Affiliation(s)
- H C J Gan
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543 Singapore, Singapore
| | - Gleb Maslennikov
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543 Singapore, Singapore
| | - Ko-Wei Tseng
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543 Singapore, Singapore
| | - Chihuan Nguyen
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543 Singapore, Singapore
| | - Dzmitry Matsukevich
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543 Singapore, Singapore
- Department of Physics, National University of Singapore, 2 Science Drive 3, 117551 Singapore, Singapore
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14
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Dutta S, Cooper NR. Critical Response of a Quantum van der Pol Oscillator. PHYSICAL REVIEW LETTERS 2019; 123:250401. [PMID: 31922802 DOI: 10.1103/physrevlett.123.250401] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/07/2019] [Indexed: 06/10/2023]
Abstract
Classical dynamical systems close to a critical point are known to act as efficient sensors due to a strongly nonlinear response. We explore such systems in the quantum regime by modeling a quantum version of a driven van der Pol oscillator. We find the classical response survives down to one excitation quantum. At very weak drives, genuine quantum features arise, including diverging and negative susceptibilities. Further, the linear response is greatly enhanced by using a strong incoherent pump. These results are largely generic and can be probed in current experimental platforms suited for quantum sensing.
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Affiliation(s)
- Shovan Dutta
- T.C.M. Group, Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - Nigel R Cooper
- T.C.M. Group, Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, Cambridge CB3 0HE, United Kingdom
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15
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Wang W, Han J, Yadin B, Ma Y, Ma J, Cai W, Xu Y, Hu L, Wang H, Song YP, Gu M, Sun L. Witnessing Quantum Resource Conversion within Deterministic Quantum Computation Using One Pure Superconducting Qubit. PHYSICAL REVIEW LETTERS 2019; 123:220501. [PMID: 31868406 DOI: 10.1103/physrevlett.123.220501] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/19/2018] [Revised: 10/22/2019] [Indexed: 06/10/2023]
Abstract
Deterministic quantum computation with one qubit (DQC1) is iconic in highlighting that exponential quantum speedup may be achieved with negligible entanglement. Its discovery catalyzed a heated study of general quantum resources, and various conjectures regarding their role in DQC1's performance advantage. Coherence and discord are prominent candidates, respectively, characterizing nonclassicality within localized and correlated systems. Here we realize DQC1 within a superconducting system, engineered such that the dynamics of coherence and discord can be tracked throughout its execution. We experimentally confirm that DQC1 acts as a resource converter, consuming coherence to generate discord during its operation. Our results highlight superconducting circuits as a promising platform for both realizing DQC1 and related algorithms, and experimentally characterizing resource dynamics within quantum protocols.
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Affiliation(s)
- W Wang
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - J Han
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - B Yadin
- Atomic and Laser Physics, Clarendon Laboratory, University of Oxford, Parks Road, Oxford, OX1 3PU, United Kingdom
| | - Y Ma
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - J Ma
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - W Cai
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - Y Xu
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - L Hu
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - H Wang
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - Y P Song
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - Mile Gu
- School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 639673, Republic of Singapore
- Complexity Institute, Nanyang Technological University, Singapore 639673, Republic of Singapore
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, Republic of Singapore
| | - L Sun
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
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16
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Arrangoiz-Arriola P, Wollack EA, Wang Z, Pechal M, Jiang W, McKenna TP, Witmer JD, Van Laer R, Safavi-Naeini AH. Resolving the energy levels of a nanomechanical oscillator. Nature 2019; 571:537-540. [PMID: 31341303 DOI: 10.1038/s41586-019-1386-x] [Citation(s) in RCA: 27] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/12/2019] [Accepted: 06/04/2019] [Indexed: 11/09/2022]
Abstract
The quantum nature of an oscillating mechanical object is anything but apparent. The coherent states that describe the classical motion of a mechanical oscillator do not have a well defined energy, but are quantum superpositions of equally spaced energy eigenstates. Revealing this quantized structure is only possible with an apparatus that measures energy with a precision greater than the energy of a single phonon. One way to achieve this sensitivity is by engineering a strong but nonresonant interaction between the oscillator and an atom. In a system with sufficient quantum coherence, this interaction allows one to distinguish different energy eigenstates using resolvable differences in the atom's transition frequency. For photons, such dispersive measurements have been performed in cavity1,2 and circuit quantum electrodynamics3. Here we report an experiment in which an artificial atom senses the motional energy of a driven nanomechanical oscillator with sufficient sensitivity to resolve the quantization of its energy. To realize this, we build a hybrid platform that integrates nanomechanical piezoelectric resonators with a microwave superconducting qubit on the same chip. We excite phonons with resonant pulses and probe the resulting excitation spectrum of the qubit to observe phonon-number-dependent frequency shifts that are about five times larger than the qubit linewidth. Our result demonstrates a fully integrated platform for quantum acoustics that combines large couplings, considerable coherence times and excellent control over the mechanical mode structure. With modest experimental improvements, we expect that our approach will enable quantum nondemolition measurements of phonons4 and will lead to quantum sensors and information-processing approaches5 that use chip-scale nanomechanical devices.
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Affiliation(s)
- Patricio Arrangoiz-Arriola
- Department of Applied Physics, Stanford University, Stanford, CA, USA.,E. L. Ginzton Laboratory, Stanford University, Stanford, CA, USA
| | - E Alex Wollack
- Department of Applied Physics, Stanford University, Stanford, CA, USA.,E. L. Ginzton Laboratory, Stanford University, Stanford, CA, USA
| | - Zhaoyou Wang
- Department of Applied Physics, Stanford University, Stanford, CA, USA.,E. L. Ginzton Laboratory, Stanford University, Stanford, CA, USA
| | - Marek Pechal
- Department of Applied Physics, Stanford University, Stanford, CA, USA.,E. L. Ginzton Laboratory, Stanford University, Stanford, CA, USA
| | - Wentao Jiang
- Department of Applied Physics, Stanford University, Stanford, CA, USA.,E. L. Ginzton Laboratory, Stanford University, Stanford, CA, USA
| | - Timothy P McKenna
- Department of Applied Physics, Stanford University, Stanford, CA, USA.,E. L. Ginzton Laboratory, Stanford University, Stanford, CA, USA
| | - Jeremy D Witmer
- Department of Applied Physics, Stanford University, Stanford, CA, USA.,E. L. Ginzton Laboratory, Stanford University, Stanford, CA, USA
| | - Raphaël Van Laer
- Department of Applied Physics, Stanford University, Stanford, CA, USA.,E. L. Ginzton Laboratory, Stanford University, Stanford, CA, USA
| | - Amir H Safavi-Naeini
- Department of Applied Physics, Stanford University, Stanford, CA, USA. .,E. L. Ginzton Laboratory, Stanford University, Stanford, CA, USA.
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17
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Lee M, Friebe K, Fioretto DA, Schüppert K, Ong FR, Plankensteiner D, Torggler V, Ritsch H, Blatt R, Northup TE. Ion-Based Quantum Sensor for Optical Cavity Photon Numbers. PHYSICAL REVIEW LETTERS 2019; 122:153603. [PMID: 31050508 DOI: 10.1103/physrevlett.122.153603] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/31/2018] [Indexed: 06/09/2023]
Abstract
We dispersively couple a single trapped ion to an optical cavity to extract information about the cavity photon-number distribution in a nondestructive way. The photon-number-dependent ac Stark shift experienced by the ion is measured via Ramsey spectroscopy. We use these measurements first to obtain the ion-cavity interaction strength. Next, we reconstruct the cavity photon-number distribution for coherent states and for a state with mixed thermal-coherent statistics, finding overlaps above 99% with the calibrated states.
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Affiliation(s)
- Moonjoo Lee
- Institut für Experimentalphysik, Universität Innsbruck, Technikerstraße 25, 6020 Innsbruck, Austria
| | - Konstantin Friebe
- Institut für Experimentalphysik, Universität Innsbruck, Technikerstraße 25, 6020 Innsbruck, Austria
| | - Dario A Fioretto
- Institut für Experimentalphysik, Universität Innsbruck, Technikerstraße 25, 6020 Innsbruck, Austria
| | - Klemens Schüppert
- Institut für Experimentalphysik, Universität Innsbruck, Technikerstraße 25, 6020 Innsbruck, Austria
| | - Florian R Ong
- Institut für Experimentalphysik, Universität Innsbruck, Technikerstraße 25, 6020 Innsbruck, Austria
| | - David Plankensteiner
- Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 21 a, 6020 Innsbruck, Austria
| | - Valentin Torggler
- Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 21 a, 6020 Innsbruck, Austria
| | - Helmut Ritsch
- Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 21 a, 6020 Innsbruck, Austria
| | - Rainer Blatt
- Institut für Experimentalphysik, Universität Innsbruck, Technikerstraße 25, 6020 Innsbruck, Austria
- Institut für Quantenoptik und Quanteninformation, Österreichische Akademie der Wissenschaften, Technikerstraße 21a, 6020 Innsbruck, Austria
| | - Tracy E Northup
- Institut für Experimentalphysik, Universität Innsbruck, Technikerstraße 25, 6020 Innsbruck, Austria
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18
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Liu Y, Tian J, Betzholz R, Cai J. Pulsed Quantum-State Reconstruction of Dark Systems. PHYSICAL REVIEW LETTERS 2019; 122:110406. [PMID: 30951349 DOI: 10.1103/physrevlett.122.110406] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/29/2019] [Indexed: 06/09/2023]
Abstract
We propose a novel strategy to reconstruct the quantum state of dark systems, i.e., degrees of freedom that are not directly accessible for measurement or control. Our scheme relies on the quantum control of a two-level probe that exerts a state-dependent potential on the dark system. Using a sequence of control pulses applied to the probe makes it possible to tailor the information one can obtain and, for example, allows us to reconstruct the density operator of a dark spin as well as the Wigner characteristic function of a harmonic oscillator. Because of the symmetry of the applied pulse sequence, this scheme is robust against slow noise on the probe. The proof-of-principle experiments are readily feasible in solid-state spins and trapped ions.
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Affiliation(s)
- Yu Liu
- School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China
- International Joint Laboratory on Quantum Sensing and Quantum Metrology, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Jiazhao Tian
- School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China
- International Joint Laboratory on Quantum Sensing and Quantum Metrology, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Ralf Betzholz
- School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China
- International Joint Laboratory on Quantum Sensing and Quantum Metrology, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Jianming Cai
- School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China
- International Joint Laboratory on Quantum Sensing and Quantum Metrology, Huazhong University of Science and Technology, Wuhan 430074, China
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19
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Abstract
We show, in a formal way, how a class of complex quasiprobability distribution functions may be introduced by using the fractional Fourier transform. This leads to the Fresnel transform of a characteristic function instead of the usual Fourier transform. We end the manuscript by showing a way in which the distribution we are introducing may be reconstructed by using atom-field interactions.
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20
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Anaya-Contreras JA, Moya-Cessa HM, Zúñiga-Segundo A. The von Neumann Entropy for Mixed States. ENTROPY 2019; 21:e21010049. [PMID: 33266765 PMCID: PMC7514141 DOI: 10.3390/e21010049] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/27/2018] [Revised: 12/18/2018] [Accepted: 12/31/2018] [Indexed: 11/20/2022]
Abstract
The Araki–Lieb inequality is commonly used to calculate the entropy of subsystems when they are initially in pure states, as this forces the entropy of the two subsystems to be equal after the complete system evolves. Then, it is easy to calculate the entropy of a large subsystem by finding the entropy of the small one. To the best of our knowledge, there does not exist a way of calculating the entropy when one of the subsystems is initially in a mixed state. For the case of a two-level atom interacting with a quantized field, we show that it is possible to use the Araki–Lieb inequality and find the von Neumann entropy for the large (infinite) system. We show this in the two-level atom-field interaction.
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Affiliation(s)
- Jorge A. Anaya-Contreras
- Instituto Politécnico Nacional, ESFM Departamento de Física, Edificio 9 Unidad Profesional Adolfo López Mateos, 07738 México D.F., Mexico
| | - Héctor M. Moya-Cessa
- Instituto Nacional de Astrofísica, Óptica y Electrónica, Calle Luis Enrique Erro No. 1, 72840 Sta. María Tonantzintla, Pue., Mexico
- Correspondence: ; Tel.: +52-222-266-3100
| | - Arturo Zúñiga-Segundo
- Instituto Politécnico Nacional, ESFM Departamento de Física, Edificio 9 Unidad Profesional Adolfo López Mateos, 07738 México D.F., Mexico
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21
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Quantum control of surface acoustic-wave phonons. Nature 2018; 563:661-665. [DOI: 10.1038/s41586-018-0719-5] [Citation(s) in RCA: 184] [Impact Index Per Article: 30.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/19/2018] [Accepted: 09/10/2018] [Indexed: 11/08/2022]
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22
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Qin L, Wang Z, Zhang C, Li XQ. Direct measurement of the quantum state of photons in a cavity. OPTICS EXPRESS 2018; 26:7034-7042. [PMID: 29609389 DOI: 10.1364/oe.26.007034] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/28/2017] [Accepted: 12/18/2017] [Indexed: 06/08/2023]
Abstract
We propose a scheme to measure the quantum state of photons in a cavity. The proposal is based on the concept of quantum weak values and applies equally well to both the solid-state circuit and atomic cavity quantum electrodynamics (QED) systems. The proposed scheme allows us to access directly the superposition components in Fock state basis, rather than the Wigner function as usual in phase space. Moreover, the separate access feature held in the direct scheme does not require a global reconstruction for the quantum state, which provides a particular advantage beyond the conventional method of quantum state tomography.
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23
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Leroux C, Govia LCG, Clerk AA. Enhancing Cavity Quantum Electrodynamics via Antisqueezing: Synthetic Ultrastrong Coupling. PHYSICAL REVIEW LETTERS 2018; 120:093602. [PMID: 29547301 DOI: 10.1103/physrevlett.120.093602] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/28/2017] [Revised: 12/01/2017] [Indexed: 06/08/2023]
Abstract
We present and analyze a method where parametric (two-photon) driving of a cavity is used to exponentially enhance the light-matter coupling in a generic cavity QED setup, with time-dependent control. Our method allows one to enhance weak-coupling systems, such that they enter the strong coupling regime (where the coupling exceeds dissipative rates) and even the ultrastrong coupling regime (where the coupling is comparable to the cavity frequency). As an example, we show how the scheme allows one to use a weak-coupling system to adiabatically prepare the highly entangled ground state of the ultrastrong coupling system. The resulting state could be used for remote entanglement applications.
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Affiliation(s)
- C Leroux
- Department of Physics, McGill University, 3600 rue University, Montréal, Québec, Canada H3A 2T8
| | - L C G Govia
- Institute for Molecular Engineering, University of Chicago, 5640 South Ellis Avenue, Chicago, Illinois 60637, USA
| | - A A Clerk
- Institute for Molecular Engineering, University of Chicago, 5640 South Ellis Avenue, Chicago, Illinois 60637, USA
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24
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Landon-Cardinal O, Govia LCG, Clerk AA. Quantitative Tomography for Continuous Variable Quantum Systems. PHYSICAL REVIEW LETTERS 2018; 120:090501. [PMID: 29547319 DOI: 10.1103/physrevlett.120.090501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/07/2017] [Indexed: 06/08/2023]
Abstract
We present a continuous variable tomography scheme that reconstructs the Husimi Q function (Wigner function) by Lagrange interpolation, using measurements of the Q function (Wigner function) at the Padua points, conjectured to be optimal sampling points for two dimensional reconstruction. Our approach drastically reduces the number of measurements required compared to using equidistant points on a regular grid, although reanalysis of such experiments is possible. The reconstruction algorithm produces a reconstructed function with exponentially decreasing error and quasilinear runtime in the number of Padua points. Moreover, using the interpolating polynomial of the Q function, we present a technique to directly estimate the density matrix elements of the continuous variable state, with only a linear propagation of input measurement error. Furthermore, we derive a state-independent analytical bound on this error, such that our estimate of the density matrix is accompanied by a measure of its uncertainty.
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Affiliation(s)
- Olivier Landon-Cardinal
- Department of Physics, McGill University, 3600 rue University, Montréal, Québec, Canada H3A 2T8
| | - Luke C G Govia
- Department of Physics, McGill University, 3600 rue University, Montréal, Québec, Canada H3A 2T8
- Institute for Molecular Engineering, University of Chicago, 5640 S. Ellis Avenue, Chicago, IL 60637, USA
| | - Aashish A Clerk
- Department of Physics, McGill University, 3600 rue University, Montréal, Québec, Canada H3A 2T8
- Institute for Molecular Engineering, University of Chicago, 5640 S. Ellis Avenue, Chicago, IL 60637, USA
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25
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Experimentally simulating the dynamics of quantum light and matter at deep-strong coupling. Nat Commun 2017; 8:1715. [PMID: 29167425 PMCID: PMC5700074 DOI: 10.1038/s41467-017-01061-x] [Citation(s) in RCA: 124] [Impact Index Per Article: 17.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/23/2017] [Accepted: 08/15/2017] [Indexed: 11/08/2022] Open
Abstract
The quantum Rabi model describing the fundamental interaction between light and matter is a cornerstone of quantum physics. It predicts exotic phenomena like quantum phase transitions and ground-state entanglement in ultrastrong and deep-strong coupling regimes, where coupling strengths are comparable to or larger than subsystem energies. Demonstrating dynamics remains an outstanding challenge, the few experiments reaching these regimes being limited to spectroscopy. Here, we employ a circuit quantum electrodynamics chip with moderate coupling between a resonator and transmon qubit to realise accurate digital quantum simulation of deep-strong coupling dynamics. We advance the state of the art in solid-state digital quantum simulation by using up to 90 second-order Trotter steps and probing both subsystems in a combined Hilbert space dimension of ∼80, demonstrating characteristic Schrödinger-cat-like entanglement and large photon build-up. Our approach will enable exploration of extreme coupling regimes and quantum phase transitions, and demonstrates a clear first step towards larger complexities such as in the Dicke model.
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26
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Ding S, Maslennikov G, Hablützel R, Matsukevich D. Cross-Kerr Nonlinearity for Phonon Counting. PHYSICAL REVIEW LETTERS 2017; 119:193602. [PMID: 29219528 DOI: 10.1103/physrevlett.119.193602] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/01/2017] [Indexed: 06/07/2023]
Abstract
State measurement of a quantum harmonic oscillator is essential in quantum optics and quantum information processing. In a system of trapped ions, we experimentally demonstrate the projective measurement of the state of the ions' motional mode via an effective cross-Kerr coupling to another motional mode. This coupling is induced by the intrinsic nonlinearity of the Coulomb interaction between the ions. We spectroscopically resolve the frequency shift of the motional sideband of the first mode due to the presence of single phonons in the second mode and use it to reconstruct the phonon number distribution of the second mode.
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Affiliation(s)
- Shiqian Ding
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543 Singapore, Singapore
| | - Gleb Maslennikov
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543 Singapore, Singapore
| | - Roland Hablützel
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543 Singapore, Singapore
| | - Dzmitry Matsukevich
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543 Singapore, Singapore
- Department of Physics, National University of Singapore, 2 Science Drive 3, 117551 Singapore, Singapore
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27
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Ding S, Maslennikov G, Hablützel R, Loh H, Matsukevich D. Quantum Parametric Oscillator with Trapped Ions. PHYSICAL REVIEW LETTERS 2017; 119:150404. [PMID: 29077472 DOI: 10.1103/physrevlett.119.150404] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/20/2016] [Indexed: 06/07/2023]
Abstract
A strong nonlinear coupling between harmonic oscillators is highly desirable for quantum information processing and quantum simulation, but is difficult to achieve in many physical systems. Here, we exploit the Coulomb interaction between two trapped ions to achieve strong nonlinear coupling between normal modes of motion at the single-phonon level. We experimentally demonstrate phonon up- and down-conversion and apply this coupling to directly measure the parity and Wigner functions of the ions' motional states. Our results represent the fully quantum operation of a degenerate parametric oscillator and hold promise for quantum computation schemes that involve continuous variables.
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Affiliation(s)
- Shiqian Ding
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543 Singapore, Singapore
| | - Gleb Maslennikov
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543 Singapore, Singapore
| | - Roland Hablützel
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543 Singapore, Singapore
| | - Huanqian Loh
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543 Singapore, Singapore
| | - Dzmitry Matsukevich
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543 Singapore, Singapore
- Department of Physics, National University of Singapore, 2 Science Drive 3, 117551 Singapore, Singapore
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28
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Chen TY, Zhang WZ, Fang RZ, Hang CZ, Zhou L. Multi-path photon-phonon converter in optomechanical system at single-quantum level. OPTICS EXPRESS 2017; 25:10779-10790. [PMID: 28788767 DOI: 10.1364/oe.25.010779] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Based on photon-phonon nonlinear interaction, a scheme of controllable photon-phonon converters is proposed at single-quantum level in a composed quadratically coupled optomechanical system. With the assistance of the mechanical oscillator, the Kerr nonlinear effect between photon and phonon is enhanced so that the single-photon state can be converted into the phonon state with high fidelity even under the current experimental condition that the single-photon coupling rate is much smaller than mechanical frequency (g ≪ ωm). The state transfer protocols and their transfer fidelity are discussed analytically and numerically. A multi-path photon-phonon converter is designed by combining the optomechanical system with low frequency resonators, which can be controlled by experimentally adjustable parameters. This work provides us a potential platform for quantum state transfer and quantum information.
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29
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Liu K, Xu Y, Wang W, Zheng SB, Roy T, Kundu S, Chand M, Ranadive A, Vijay R, Song Y, Duan L, Sun L. A twofold quantum delayed-choice experiment in a superconducting circuit. SCIENCE ADVANCES 2017; 3:e1603159. [PMID: 28508079 PMCID: PMC5419705 DOI: 10.1126/sciadv.1603159] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 12/13/2016] [Accepted: 03/03/2017] [Indexed: 06/07/2023]
Abstract
Wave-particle complementarity lies at the heart of quantum mechanics. To illustrate this mysterious feature, Wheeler proposed the delayed-choice experiment, where a quantum system manifests the wave- or particle-like attribute, depending on the experimental arrangement, which is made after the system has entered the interferometer. In recent quantum delayed-choice experiments, these two complementary behaviors were simultaneously observed with a quantum interferometer in a superposition of being closed and open. We suggest and implement a conceptually different quantum delayed-choice experiment by introducing a which-path detector (WPD) that can simultaneously record and neglect the system's path information, but where the interferometer itself is classical. Our experiment is realized with a superconducting circuit, where a cavity acts as the WPD for an interfering qubit. Using this setup, we implement the first twofold delayed-choice experiment, which demonstrates that the system's behavior depends not only on the measuring device's configuration that can be chosen even after the system has been detected but also on whether we a posteriori erase or mark the which-path information, the latter of which cannot be revealed by previous quantum delayed-choice experiments. Our results represent the first demonstration of both counterintuitive features with the same experimental setup, significantly extending the concept of quantum delayed-choice experiment.
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Affiliation(s)
- Ke Liu
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - Yuan Xu
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - Weiting Wang
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - Shi-Biao Zheng
- Fujian Key Laboratory of Quantum Information and Quantum Optics, College of Physics and Information Engineering, Fuzhou University, Fuzhou, Fujian 350116, China
| | - Tanay Roy
- Department of Condensed Matter Physics and Materials Science, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India
| | - Suman Kundu
- Department of Condensed Matter Physics and Materials Science, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India
| | - Madhavi Chand
- Department of Condensed Matter Physics and Materials Science, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India
| | - Arpit Ranadive
- Department of Condensed Matter Physics and Materials Science, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India
| | - Rajamani Vijay
- Department of Condensed Matter Physics and Materials Science, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India
| | - Yipu Song
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - Luming Duan
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
- Department of Physics, University of Michigan, Ann Arbor, MI 48109, USA
| | - Luyan Sun
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
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30
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Hou Q, Yang W, Chen C, Yin Z. Generation of macroscopic Schrödinger cat state in diamond mechanical resonator. Sci Rep 2016; 6:37542. [PMID: 27876846 PMCID: PMC5120327 DOI: 10.1038/srep37542] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/18/2016] [Accepted: 10/27/2016] [Indexed: 12/03/2022] Open
Abstract
We propose a scheme to generate macroscopic Schrödinger cat state (SCS) in diamond mechanical resonator (DMR) via the dynamical strain-mediated coupling mechanism. In our model, the direct coupling between the nitrogen-vacancy (NV) center and lattice strain field enables coherent spin–phonon interactions in the quantum regime. Based on a cyclic Δ-type transition structure of the NV center constructed by combining the quantized mechanical strain field and a pair of external microwave fields, the populations of the different energy levels can be selectively transferred by controlling microwave fields, and the SCS can be created by adjusting the controllable parameters of the system. Furthermore, we demonstrate the nonclassicality of the mechanical SCS both in non-dissipative case and dissipative case. The experimental feasibility and challenge are justified using currently available technology.
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Affiliation(s)
- Qizhe Hou
- National Laboratory of Solid State Microstructures and School of Physics, Nanjing University, Nanjing 210093, China
| | - Wanli Yang
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China
| | - Changyong Chen
- Department of Physics, Shaoguan University, Shaoguan, Guangdong 512005, China
| | - Zhangqi Yin
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
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31
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Ofek N, Petrenko A, Heeres R, Reinhold P, Leghtas Z, Vlastakis B, Liu Y, Frunzio L, Girvin SM, Jiang L, Mirrahimi M, Devoret MH, Schoelkopf RJ. Extending the lifetime of a quantum bit with error correction in superconducting circuits. Nature 2016; 536:441-5. [DOI: 10.1038/nature18949] [Citation(s) in RCA: 469] [Impact Index Per Article: 58.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/12/2016] [Accepted: 06/08/2016] [Indexed: 12/18/2022]
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32
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Wang C, Gao YY, Reinhold P, Heeres RW, Ofek N, Chou K, Axline C, Reagor M, Blumoff J, Sliwa KM, Frunzio L, Girvin SM, Jiang L, Mirrahimi M, Devoret MH, Schoelkopf RJ. A Schrödinger cat living in two boxes. Science 2016; 352:1087-91. [DOI: 10.1126/science.aaf2941] [Citation(s) in RCA: 189] [Impact Index Per Article: 23.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/20/2016] [Accepted: 04/14/2016] [Indexed: 11/02/2022]
Affiliation(s)
- Chen Wang
- Department of Applied Physics and Physics, Yale University, New Haven, CT 06511, USA
| | - Yvonne Y. Gao
- Department of Applied Physics and Physics, Yale University, New Haven, CT 06511, USA
| | - Philip Reinhold
- Department of Applied Physics and Physics, Yale University, New Haven, CT 06511, USA
| | - R. W. Heeres
- Department of Applied Physics and Physics, Yale University, New Haven, CT 06511, USA
| | - Nissim Ofek
- Department of Applied Physics and Physics, Yale University, New Haven, CT 06511, USA
| | - Kevin Chou
- Department of Applied Physics and Physics, Yale University, New Haven, CT 06511, USA
| | - Christopher Axline
- Department of Applied Physics and Physics, Yale University, New Haven, CT 06511, USA
| | - Matthew Reagor
- Department of Applied Physics and Physics, Yale University, New Haven, CT 06511, USA
| | - Jacob Blumoff
- Department of Applied Physics and Physics, Yale University, New Haven, CT 06511, USA
| | - K. M. Sliwa
- Department of Applied Physics and Physics, Yale University, New Haven, CT 06511, USA
| | - L. Frunzio
- Department of Applied Physics and Physics, Yale University, New Haven, CT 06511, USA
| | - S. M. Girvin
- Department of Applied Physics and Physics, Yale University, New Haven, CT 06511, USA
| | - Liang Jiang
- Department of Applied Physics and Physics, Yale University, New Haven, CT 06511, USA
| | - M. Mirrahimi
- Department of Applied Physics and Physics, Yale University, New Haven, CT 06511, USA
- INRIA Paris-Rocquencourt, Domaine de Voluceau, B.P. 105, 78153 Le Chesnay Cedex, France
| | - M. H. Devoret
- Department of Applied Physics and Physics, Yale University, New Haven, CT 06511, USA
| | - R. J. Schoelkopf
- Department of Applied Physics and Physics, Yale University, New Haven, CT 06511, USA
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33
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Harder G, Silberhorn C, Rehacek J, Hradil Z, Motka L, Stoklasa B, Sánchez-Soto LL. Local Sampling of the Wigner Function at Telecom Wavelength with Loss-Tolerant Detection of Photon Statistics. PHYSICAL REVIEW LETTERS 2016; 116:133601. [PMID: 27081977 DOI: 10.1103/physrevlett.116.133601] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/11/2016] [Indexed: 06/05/2023]
Abstract
We report the experimental point-by-point sampling of the Wigner function for nonclassical states created in an ultrafast pulsed type-II parametric down-conversion source. We use a loss-tolerant time-multiplexed detector based on a fiber-optical setup and a pair of photon-number-resolving avalanche photodiodes. By capitalizing on an expedient data-pattern tomography, we assess the properties of the light states with outstanding accuracy. The method allows us to reliably infer the squeezing of genuine two-mode states without any phase reference.
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Affiliation(s)
- G Harder
- Department of Physics, University of Paderborn, Warburger Straße 100, 33098 Paderborn, Germany
| | - Ch Silberhorn
- Department of Physics, University of Paderborn, Warburger Straße 100, 33098 Paderborn, Germany
- Max-Planck-Institut für die Physik des Lichts, Günther-Scharowsky-Straße 1, Bau 24, 91058 Erlangen, Germany
| | - J Rehacek
- Department of Optics, Palacký University, 17. listopadu 12, 77146 Olomouc, Czech Republic
| | - Z Hradil
- Department of Optics, Palacký University, 17. listopadu 12, 77146 Olomouc, Czech Republic
| | - L Motka
- Department of Optics, Palacký University, 17. listopadu 12, 77146 Olomouc, Czech Republic
| | - B Stoklasa
- Department of Optics, Palacký University, 17. listopadu 12, 77146 Olomouc, Czech Republic
| | - L L Sánchez-Soto
- Max-Planck-Institut für die Physik des Lichts, Günther-Scharowsky-Straße 1, Bau 24, 91058 Erlangen, Germany
- Departamento de Óptica, Facultad de Física, Universidad Complutense, 28040 Madrid, Spain
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34
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Xia K, Johnsson M, Knight PL, Twamley J. Cavity-Free Scheme for Nondestructive Detection of a Single Optical Photon. PHYSICAL REVIEW LETTERS 2016; 116:023601. [PMID: 26824538 DOI: 10.1103/physrevlett.116.023601] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/15/2015] [Indexed: 06/05/2023]
Abstract
Detecting a single photon without absorbing it is a long-standing challenge in quantum optics. All experiments demonstrating the nondestructive detection of a photon make use of a high quality cavity. We present a cavity-free scheme for nondestructive single-photon detection. By pumping a nonlinear medium we implement an interfield Rabi oscillation which leads to a ∼π phase shift on a weak probe coherent laser field in the presence of a single signal photon without destroying the signal photon. Our cavity-free scheme operates with a fast intrinsic time scale in comparison with similar cavity-based schemes. We implement a full real-space multimode numerical analysis of the interacting photonic modes and confirm the validity of our nondestructive scheme in the multimode case.
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Affiliation(s)
- Keyu Xia
- Centre for Engineered Quantum Systems, Department of Physics and Astronomy, Macquarie University, NSW 2109, Australia
| | - Mattias Johnsson
- Centre for Engineered Quantum Systems, Department of Physics and Astronomy, Macquarie University, NSW 2109, Australia
| | - Peter L Knight
- Department of Physics, Blackett Laboratory, Imperial College, London SW72AZ, United Kingdom
| | - Jason Twamley
- Centre for Engineered Quantum Systems, Department of Physics and Astronomy, Macquarie University, NSW 2109, Australia
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35
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Holland ET, Vlastakis B, Heeres RW, Reagor MJ, Vool U, Leghtas Z, Frunzio L, Kirchmair G, Devoret MH, Mirrahimi M, Schoelkopf RJ. Single-Photon-Resolved Cross-Kerr Interaction for Autonomous Stabilization of Photon-Number States. PHYSICAL REVIEW LETTERS 2015; 115:180501. [PMID: 26565448 DOI: 10.1103/physrevlett.115.180501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/13/2015] [Indexed: 06/05/2023]
Abstract
Quantum states can be stabilized in the presence of intrinsic and environmental losses by either applying an active feedback condition on an ancillary system or through reservoir engineering. Reservoir engineering maintains a desired quantum state through a combination of drives and designed entropy evacuation. We propose and implement a quantum-reservoir engineering protocol that stabilizes Fock states in a microwave cavity. This protocol is realized with a circuit quantum electrodynamics platform where a Josephson junction provides direct, nonlinear coupling between two superconducting waveguide cavities. The nonlinear coupling results in a single-photon-resolved cross-Kerr effect between the two cavities enabling a photon-number-dependent coupling to a lossy environment. The quantum state of the microwave cavity is discussed in terms of a net polarization and is analyzed by a measurement of its steady state Wigner function.
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Affiliation(s)
- E T Holland
- Departments of Physics and Applied Physics, Yale University, New Haven, Connecticut 06520, USA
| | - B Vlastakis
- Departments of Physics and Applied Physics, Yale University, New Haven, Connecticut 06520, USA
| | - R W Heeres
- Departments of Physics and Applied Physics, Yale University, New Haven, Connecticut 06520, USA
| | - M J Reagor
- Departments of Physics and Applied Physics, Yale University, New Haven, Connecticut 06520, USA
| | - U Vool
- Departments of Physics and Applied Physics, Yale University, New Haven, Connecticut 06520, USA
| | - Z Leghtas
- Departments of Physics and Applied Physics, Yale University, New Haven, Connecticut 06520, USA
| | - L Frunzio
- Departments of Physics and Applied Physics, Yale University, New Haven, Connecticut 06520, USA
| | - G Kirchmair
- Departments of Physics and Applied Physics, Yale University, New Haven, Connecticut 06520, USA
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, A-6020 Innsbruck, Austria
- Institute for Experimental Physics, University of Innsbruck, A-6020 Innsbruck, Austria
| | - M H Devoret
- Departments of Physics and Applied Physics, Yale University, New Haven, Connecticut 06520, USA
| | - M Mirrahimi
- Departments of Physics and Applied Physics, Yale University, New Haven, Connecticut 06520, USA
- INRIA Paris-Rocquencourt, Domaine de Voluceau, B.P. 105, 78153 Le Chesnay Cedex, France
| | - R J Schoelkopf
- Departments of Physics and Applied Physics, Yale University, New Haven, Connecticut 06520, USA
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36
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Parity-dependent State Engineering and Tomography in the ultrastrong coupling regime. Sci Rep 2015; 5:11818. [PMID: 26152809 PMCID: PMC5155612 DOI: 10.1038/srep11818] [Citation(s) in RCA: 33] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/19/2015] [Accepted: 06/08/2015] [Indexed: 11/28/2022] Open
Abstract
Reaching the strong coupling regime of light-matter interaction has led to an impressive development in fundamental quantum physics and applications to quantum information processing. Latests advances in different quantum technologies, like superconducting circuits or semiconductor quantum wells, show that the ultrastrong coupling regime (USC) can also be achieved, where novel physical phenomena and potential computational benefits have been predicted. Nevertheless, the lack of effective decoupling mechanism in this regime has so far hindered control and measurement processes. Here, we propose a method based on parity symmetry conservation that allows for the generation and reconstruction of arbitrary states in the ultrastrong coupling regime of light-matter interactions. Our protocol requires minimal external resources by making use of the coupling between the USC system and an ancillary two-level quantum system.
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37
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Bretheau L, Campagne-Ibarcq P, Flurin E, Mallet F, Huard B. Quantum dynamics of an electromagnetic mode that cannot contain N photons. Science 2015; 348:776-9. [DOI: 10.1126/science.1259345] [Citation(s) in RCA: 54] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
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38
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Jullien T, Roulleau P, Roche B, Cavanna A, Jin Y, Glattli DC. Quantum tomography of an electron. Nature 2014; 514:603-7. [PMID: 25355360 DOI: 10.1038/nature13821] [Citation(s) in RCA: 132] [Impact Index Per Article: 13.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/02/2014] [Accepted: 08/29/2014] [Indexed: 11/09/2022]
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39
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Sun L, Petrenko A, Leghtas Z, Vlastakis B, Kirchmair G, Sliwa KM, Narla A, Hatridge M, Shankar S, Blumoff J, Frunzio L, Mirrahimi M, Devoret MH, Schoelkopf RJ. Tracking photon jumps with repeated quantum non-demolition parity measurements. Nature 2014; 511:444-8. [DOI: 10.1038/nature13436] [Citation(s) in RCA: 169] [Impact Index Per Article: 16.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/12/2013] [Accepted: 05/06/2014] [Indexed: 12/26/2022]
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40
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Wang HF, Zhu AD, Zhang S. One-step implementation of a multiqubit phase gate with one control qubit and multiple target qubits in coupled cavities. OPTICS LETTERS 2014; 39:1489-1492. [PMID: 24690820 DOI: 10.1364/ol.39.001489] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
We propose a one-step scheme to implement a multiqubit controlled phase gate with one qubit simultaneously controlling multiple qubits with three-level atoms at distant nodes in coupled cavity arrays. Selective qubit-qubit couplings are achieved by adiabatically eliminating the atomic excited states and photonic states, and the required phase shifts between the control qubit and any target qubit can be realized through suitable choices of the parameters of the external fields. Moreover, the effective model is robust against decoherence because neither the atoms nor the field modes are excited during the gate operation, leading to a useful step toward scalable quantum computing networks.
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41
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Bamber C, Lundeen JS. Observing Dirac's classical phase space analog to the quantum state. PHYSICAL REVIEW LETTERS 2014; 112:070405. [PMID: 24579574 DOI: 10.1103/physrevlett.112.070405] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/05/2013] [Indexed: 06/03/2023]
Abstract
In 1945, Dirac attempted to develop a “formal probability” distribution to describe quantum operators in terms of two noncommuting variables, such as position x and momentum p [Rev. Mod. Phys. 17, 195 (1945)]. The resulting quasiprobability distribution is a complete representation of the quantum state and can be observed directly in experiments. We measure Dirac’s distribution for the quantum state of the transverse degree of freedom of a photon by weakly measuring transverse x so as to not randomize the subsequent p measurement. Furthermore, we show that the distribution has the classical-like feature that it transforms (e.g., propagates) according to Bayes’ law.
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Affiliation(s)
- Charles Bamber
- Measurement Science and Standards, National Research Council, Ottawa, Canada K1A 0R6
| | - Jeff S Lundeen
- Physics Department, University of Ottawa, 150 Louis Pasteur, Ottawa, Canada K1N 6N5
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42
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Vlastakis B, Kirchmair G, Leghtas Z, Nigg SE, Frunzio L, Girvin SM, Mirrahimi M, Devoret MH, Schoelkopf RJ. Deterministically encoding quantum information using 100-photon Schrödinger cat states. Science 2013; 342:607-10. [PMID: 24072821 DOI: 10.1126/science.1243289] [Citation(s) in RCA: 126] [Impact Index Per Article: 11.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
In contrast to a single quantum bit, an oscillator can store multiple excitations and coherences provided one has the ability to generate and manipulate complex multiphoton states. We demonstrate multiphoton control by using a superconducting transmon qubit coupled to a waveguide cavity resonator with a highly ideal off-resonant coupling. This dispersive interaction is much greater than decoherence rates and higher-order nonlinearities to allow simultaneous manipulation of hundreds of photons. With a tool set of conditional qubit-photon logic, we mapped an arbitrary qubit state to a superposition of coherent states, known as a "cat state." We created cat states as large as 111 photons and extended this protocol to create superpositions of up to four coherent states. This control creates a powerful interface between discrete and continuous variable quantum computation and could enable applications in metrology and quantum information processing.
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Affiliation(s)
- Brian Vlastakis
- Department of Physics and Department of Applied Physics, Yale University, New Haven, CT 06511, USA
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43
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Goldschleger IU, van Staveren MN, Ara Apkarian V. Quantum tomography of a molecular bond in ice. J Chem Phys 2013; 139:034201. [DOI: 10.1063/1.4813437] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- I. U. Goldschleger
- Department of Chemistry, University of California, Irvine, California 92697-2025, USA
| | - M. N. van Staveren
- Department of Chemistry, University of California, Irvine, California 92697-2025, USA
| | - V. Ara Apkarian
- Department of Chemistry, University of California, Irvine, California 92697-2025, USA
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44
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Shalibo Y, Resh R, Fogel O, Shwa D, Bialczak R, Martinis JM, Katz N. Direct Wigner tomography of a superconducting anharmonic oscillator. PHYSICAL REVIEW LETTERS 2013; 110:100404. [PMID: 23521235 DOI: 10.1103/physrevlett.110.100404] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/12/2012] [Revised: 01/06/2013] [Indexed: 06/01/2023]
Abstract
The analysis of wave-packet dynamics may be greatly simplified when viewed in phase space. While harmonic oscillators are often used as a convenient platform to study wave packets, arbitrary state preparation in these systems is more challenging. Here, we demonstrate a direct measurement of the Wigner distribution of complex photon states in an anharmonic oscillator--a superconducting phase circuit, biased in the small anharmonicity regime. We apply our method on nondispersive wave packets to explicitly show phase locking in states prepared by a frequency chirp. This method requires a simple calibration, and is easily applicable in our system out to the fifth level.
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Affiliation(s)
- Yoni Shalibo
- Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
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45
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da Silva MP, Landon-Cardinal O, Poulin D. Practical characterization of quantum devices without tomography. PHYSICAL REVIEW LETTERS 2011; 107:210404. [PMID: 22181862 DOI: 10.1103/physrevlett.107.210404] [Citation(s) in RCA: 50] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/11/2011] [Indexed: 05/31/2023]
Abstract
Quantum tomography is the main method used to assess the quality of quantum information processing devices. However, the amount of resources needed for quantum tomography is exponential in the device size. Part of the problem is that tomography generates much more information than is usually sought. Taking a more targeted approach, we develop schemes that enable (i) estimating the fidelity of an experiment to a theoretical ideal description, (ii) learning which description within a reduced subset best matches the experimental data. Both these approaches yield a significant reduction in resources compared to tomography. In particular, we demonstrate that fidelity can be estimated from a number of simple experiments that is independent of the system size, removing an important roadblock for the experimental study of larger quantum information processing units.
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Affiliation(s)
- Marcus P da Silva
- Disruptive Information Processing Technologies Group, Raytheon BBN Technologies, Cambridge, Massachusetts 02138, USA
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46
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Valente MB. A Case for an Empirically Demonstrable Notion of the Vacuum in Quantum Electrodynamics Independent of Dynamical Fluctuations. JOURNAL FOR GENERAL PHILOSOPHY OF SCIENCE 2011; 42:241-261. [DOI: 10.1007/s10838-011-9162-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/02/2023]
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47
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Keil R, Perez-Leija A, Dreisow F, Heinrich M, Moya-Cessa H, Nolte S, Christodoulides DN, Szameit A. Classical analogue of displaced Fock states and quantum correlations in Glauber-Fock photonic lattices. PHYSICAL REVIEW LETTERS 2011; 107:103601. [PMID: 21981502 DOI: 10.1103/physrevlett.107.103601] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/09/2011] [Indexed: 05/31/2023]
Abstract
Coherent states and their generalizations, displaced Fock states, are of fundamental importance to quantum optics. Here we present a direct observation of a classical analogue for the emergence of these states from the eigenstates of the harmonic oscillator. To this end, the light propagation in a Glauber-Fock waveguide lattice serves as equivalent for the displacement of Fock states in phase space. Theoretical calculations and analogue classical experiments show that the square-root distribution of the coupling parameter in such lattices supports a new family of intriguing quantum correlations not encountered in uniform arrays. Because of the broken shift invariance of the lattice, these correlations strongly depend on the transverse position. Consequently, quantum random walks with this extra degree of freedom may be realized in Glauber-Fock lattices.
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Affiliation(s)
- Robert Keil
- Institute of Applied Physics, Friedrich-Schiller-Universität Jena, Max-Wien-Platz 1, 07743 Jena, Germany.
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48
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Laiho K, Cassemiro KN, Gross D, Silberhorn C. Probing the negative Wigner function of a pulsed single photon point by point. PHYSICAL REVIEW LETTERS 2010; 105:253603. [PMID: 21231590 DOI: 10.1103/physrevlett.105.253603] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/24/2010] [Indexed: 05/30/2023]
Abstract
We investigate quantum properties of pulsed light fields point by point in phase space. We probe the negative region of the Wigner function of a single photon generated by the means of waveguided parametric down conversion. This capability is achieved by employing loss-tolerant photon-number resolving detection, allowing us to directly observe the oscillations of the photon statistics in dependence of applied displacements in phase space. Our scheme is highly mode sensitive and can reveal the single-mode character of the signal state.
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Affiliation(s)
- Kaisa Laiho
- Max Planck Institute for Science of Light, Günther-Scharowsky-straße 1/Building 24, 91058 Erlangen, Germany.
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49
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Smith RP, Wahlstrand JK, Funk AC, Mirin RP, Cundiff ST, Steiner JT, Schafer M, Kira M, Koch SW. Extraction of many-body configurations from nonlinear absorption in semiconductor quantum wells. PHYSICAL REVIEW LETTERS 2010; 104:247401. [PMID: 20867334 DOI: 10.1103/physrevlett.104.247401] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/15/2009] [Indexed: 05/29/2023]
Abstract
Detailed electronic many-body configurations are extracted from quantitatively measured time-resolved nonlinear absorption spectra of resonantly excited GaAs quantum wells. The microscopic theory assigns the observed spectral changes to a unique mixture of electron-hole plasma, exciton, and polarization effects. Strong transient gain is observed only under cocircular pump-probe conditions and is attributed to the transfer of pump-induced coherences to the probe.
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Affiliation(s)
- R P Smith
- JILA, National Institute of Standards and Technology and University of Colorado, Boulder, Colorado 80309-0440, USA
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50
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Synthesizing arbitrary quantum states in a superconducting resonator. Nature 2009; 459:546-9. [DOI: 10.1038/nature08005] [Citation(s) in RCA: 651] [Impact Index Per Article: 43.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/15/2009] [Accepted: 03/19/2009] [Indexed: 11/09/2022]
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