1
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Makihara T, Lee N, Guo Y, Guan W, Safavi-Naeini A. A parametrically programmable delay line for microwave photons. Nat Commun 2024; 15:4640. [PMID: 38821933 PMCID: PMC11143279 DOI: 10.1038/s41467-024-48975-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/25/2024] [Accepted: 05/15/2024] [Indexed: 06/02/2024] Open
Abstract
Delay lines that store quantum information are crucial for advancing quantum repeaters and hardware efficient quantum computers. Traditionally, they are realized as extended systems that support wave propagation but provide limited control over the propagating fields. Here, we introduce a parametrically addressed delay line for microwave photons that provides a high level of control over the stored pulses. By parametrically driving a three-wave mixing circuit element that is weakly hybridized with an ensemble of resonators, we engineer a spectral response that simulates that of a physical delay line, while providing fast control over the delay line's properties. We demonstrate this novel degree of control by choosing which photon echo to emit, translating pulses in time, and even swapping two pulses, all with pulse energies on the order of a single photon. We also measure the noise added from our parametric interactions and find it is much less than one photon.
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Affiliation(s)
- Takuma Makihara
- Department of Applied Physics, Stanford University, Stanford, California, USA.
| | - Nathan Lee
- Department of Applied Physics, Stanford University, Stanford, California, USA
| | - Yudan Guo
- Department of Applied Physics, Stanford University, Stanford, California, USA
| | - Wenyan Guan
- Department of Applied Physics, Stanford University, Stanford, California, USA
| | - Amir Safavi-Naeini
- Department of Applied Physics, Stanford University, Stanford, California, USA.
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2
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Filippov S, Termanova A. Superior Resilience of Non-Gaussian Entanglement against Local Gaussian Noises. ENTROPY (BASEL, SWITZERLAND) 2022; 25:75. [PMID: 36673216 PMCID: PMC9857693 DOI: 10.3390/e25010075] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/30/2022] [Revised: 12/27/2022] [Accepted: 12/29/2022] [Indexed: 06/17/2023]
Abstract
Entanglement distribution task encounters a problem of how the initial entangled state should be prepared in order to remain entangled the longest possible time when subjected to local noises. In the realm of continuous-variable states and local Gaussian channels it is tempting to assume that the optimal initial state with the most robust entanglement is Gaussian too; however, this is not the case. Here we prove that specific non-Gaussian two-mode states remain entangled under the effect of deterministic local attenuation or amplification (Gaussian channels with the attenuation factor/power gain κi and the noise parameter μi for modes i=1,2) whenever κ1μ22+κ2μ12<14(κ1+κ2)(1+κ1κ2), which is a strictly larger area of parameters as compared to where Gaussian entanglement is able to tolerate noise. These results shift the “Gaussian world” paradigm in quantum information science (within which solutions to optimization problems involving Gaussian channels are supposed to be attained at Gaussian states).
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Affiliation(s)
| | - Alena Termanova
- Terra Quantum AG, Kornhausstrasse 25, 9000 St. Gallen, Switzerland
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3
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An ultra-high gain single-photon transistor in the microwave regime. Nat Commun 2022; 13:6104. [PMID: 36243719 PMCID: PMC9569345 DOI: 10.1038/s41467-022-33921-6] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/20/2022] [Accepted: 10/07/2022] [Indexed: 11/08/2022] Open
Abstract
A photonic transistor that can switch or amplify an optical signal with a single gate photon requires strong non-linear interaction at the single-photon level. Circuit quantum electrodynamics provides great flexibility to generate such an interaction, and thus could serve as an effective platform to realize a high-performance single-photon transistor. Here we demonstrate such a photonic transistor in the microwave regime. Our device consists of two microwave cavities dispersively coupled to a superconducting qubit. A single gate photon imprints a phase shift on the qubit state through one cavity, and further shifts the resonance frequency of the other cavity. In this way, we realize a gain of the transistor up to 53.4 dB, with an extinction ratio better than 20 dB. Our device outperforms previous devices in the optical regime by several orders in terms of optical gain, which indicates a great potential for application in the field of microwave quantum photonics and quantum information processing. Successfully controlling an optical signal by a single gate photon would have great applicability for quantum networks and all-optical computing. Here, the authors realise a single-photon transistor in the microwave regime based on superconducting quantum circuits.
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4
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Aamir MA, Moreno CC, Sundelin S, Biznárová J, Scigliuzzo M, Patel KE, Osman A, Lozano DP, Strandberg I, Gasparinetti S. Engineering Symmetry-Selective Couplings of a Superconducting Artificial Molecule to Microwave Waveguides. PHYSICAL REVIEW LETTERS 2022; 129:123604. [PMID: 36179204 DOI: 10.1103/physrevlett.129.123604] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/24/2022] [Accepted: 08/08/2022] [Indexed: 06/16/2023]
Abstract
Tailoring the decay rate of structured quantum emitters into their environment opens new avenues for nonlinear quantum optics, collective phenomena, and quantum communications. Here, we demonstrate a novel coupling scheme between an artificial molecule comprising two identical, strongly coupled transmon qubits and two microwave waveguides. In our scheme, the coupling is engineered so that transitions between states of the same (opposite) symmetry, with respect to the permutation operator, are predominantly coupled to one (the other) waveguide. The symmetry-based coupling selectivity, as quantified by the ratio of the coupling strengths, exceeds a factor of 30 for both waveguides in our device. In addition, we implement a Raman process activated by simultaneously driving both waveguides, and show that it can be used to coherently couple states of different symmetry in the single-excitation manifold of the molecule. Using that process, we implement frequency conversion across the waveguides, mediated by the molecule, with efficiency of about 95%. Finally, we show that this coupling arrangement makes it possible to straightforwardly generate spatially separated Bell states propagating across the waveguides. We envisage further applications to quantum thermodynamics, microwave photodetection, and photon-photon gates.
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Affiliation(s)
- Mohammed Ali Aamir
- Department of Microtechnology and Nanoscience, Chalmers University of Technology, 412 96 Gothenburg, Sweden
| | - Claudia Castillo Moreno
- Department of Microtechnology and Nanoscience, Chalmers University of Technology, 412 96 Gothenburg, Sweden
| | - Simon Sundelin
- Department of Microtechnology and Nanoscience, Chalmers University of Technology, 412 96 Gothenburg, Sweden
| | - Janka Biznárová
- Department of Microtechnology and Nanoscience, Chalmers University of Technology, 412 96 Gothenburg, Sweden
| | - Marco Scigliuzzo
- Department of Microtechnology and Nanoscience, Chalmers University of Technology, 412 96 Gothenburg, Sweden
| | - Kowshik Erappaji Patel
- Department of Microtechnology and Nanoscience, Chalmers University of Technology, 412 96 Gothenburg, Sweden
| | - Amr Osman
- Department of Microtechnology and Nanoscience, Chalmers University of Technology, 412 96 Gothenburg, Sweden
| | - D P Lozano
- Department of Microtechnology and Nanoscience, Chalmers University of Technology, 412 96 Gothenburg, Sweden
| | - Ingrid Strandberg
- Department of Microtechnology and Nanoscience, Chalmers University of Technology, 412 96 Gothenburg, Sweden
| | - Simone Gasparinetti
- Department of Microtechnology and Nanoscience, Chalmers University of Technology, 412 96 Gothenburg, Sweden
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5
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Wang Z, Bao Z, Wu Y, Li Y, Cai W, Wang W, Ma Y, Cai T, Han X, Wang J, Song Y, Sun L, Zhang H, Duan L. A flying Schrödinger's cat in multipartite entangled states. SCIENCE ADVANCES 2022; 8:eabn1778. [PMID: 35275710 PMCID: PMC8916730 DOI: 10.1126/sciadv.abn1778] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/09/2021] [Accepted: 01/19/2022] [Indexed: 06/14/2023]
Abstract
Schrödinger's cat originates from the famous thought experiment querying the counterintuitive quantum superposition of macroscopic objects. As a natural extension, several "cats" (quasi-classical objects) can be prepared into coherent quantum superposition states, which is known as multipartite cat states demonstrating quantum entanglement among macroscopically distinct objects. Here, we present a highly scalable approach to deterministically create flying multipartite Schrödinger's cat states by reflecting coherent-state photons from a microwave cavity containing a superconducting qubit. We perform full quantum state tomography on the cat states with up to four photonic modes and confirm the existence of quantum entanglement among them. We also witness the hybrid entanglement between discrete-variable states (the qubit) and continuous-variable states (the flying multipartite cat) through a joint quantum state tomography. Our work provides an enabling step for implementing a series of quantum metrology and quantum information processing protocols based on cat states.
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6
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Wang Q, Pérez-Bernal F. Signatures of excited-state quantum phase transitions in quantum many-body systems: Phase space analysis. Phys Rev E 2021; 104:034119. [PMID: 34654165 DOI: 10.1103/physreve.104.034119] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/08/2021] [Accepted: 08/31/2021] [Indexed: 11/07/2022]
Abstract
Using the Husimi quasiprobability distribution, we investigate the phase space signatures of excited-state quantum phase transitions (ESQPTs) in the Lipkin-Meshkov-Glick and coupled top models. We show that the ESQPT is evinced by the dynamics of the Husimi function, that exhibits a distinct time dependence in the different ESQPT phases. We also discuss how to identify the ESQPT signatures from the long-time averaged Husimi function and its associated marginal distributions. Moreover, from the calculated second moment and Wherl entropy of the long-time averaged Husimi function, we estimate the critical points of the ESQPT in both models, obtaining a good agreement with analytical (mean field) results. We provide a firm evidence that phase space methods are both a new probe for the detection and a valuable tool for the study of ESQPTs.
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Affiliation(s)
- Qian Wang
- Department of Physics, Zhejiang Normal University, Jinhua 321004, China and CAMTP-Center for Applied Mathematics and Theoretical Physics, University of Maribor, Mladinska 3, SI-2000 Maribor, Slovenia
| | - Francisco Pérez-Bernal
- Departamento de Ciencias Integradas y Centro de Estudios Avanzados en Física, Matemáticas y Computación, Universidad de Huelva, Huelva 21071, Spain and Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, Granada 18071, Spain
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7
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Patel RN, McKenna TP, Wang Z, Witmer JD, Jiang W, Van Laer R, Sarabalis CJ, Safavi-Naeini AH. Room-Temperature Mechanical Resonator with a Single Added or Subtracted Phonon. PHYSICAL REVIEW LETTERS 2021; 127:133602. [PMID: 34623823 DOI: 10.1103/physrevlett.127.133602] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/24/2021] [Accepted: 07/19/2021] [Indexed: 06/13/2023]
Abstract
A room-temperature mechanical oscillator undergoes thermal Brownian motion with an amplitude much larger than the amplitude associated with a single phonon of excitation. This motion can be read out and manipulated using laser light using a cavity-optomechanical approach. By performing a strong quantum measurement (i.e., counting single photons in the sidebands imparted on a laser), we herald the addition and subtraction of single phonons on the 300 K thermal motional state of a 4 GHz mechanical oscillator. To understand the resulting mechanical state, we implement a tomography scheme and observe highly non-Gaussian phase-space distributions. Using a maximum likelihood method, we infer the density matrix of the oscillator, and we confirm the counterintuitive doubling of the mean phonon number resulting from phonon addition and subtraction.
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Affiliation(s)
- Rishi N Patel
- Department of Applied Physics, Ginzton Laboratory, Stanford University, Stanford, California 94305, USA
| | - Timothy P McKenna
- Department of Applied Physics, Ginzton Laboratory, Stanford University, Stanford, California 94305, USA
| | - Zhaoyou Wang
- Department of Applied Physics, Ginzton Laboratory, Stanford University, Stanford, California 94305, USA
| | - Jeremy D Witmer
- Department of Applied Physics, Ginzton Laboratory, Stanford University, Stanford, California 94305, USA
| | - Wentao Jiang
- Department of Applied Physics, Ginzton Laboratory, Stanford University, Stanford, California 94305, USA
| | - Raphaël Van Laer
- Department of Applied Physics, Ginzton Laboratory, Stanford University, Stanford, California 94305, USA
| | - Christopher J Sarabalis
- Department of Applied Physics, Ginzton Laboratory, Stanford University, Stanford, California 94305, USA
| | - Amir H Safavi-Naeini
- Department of Applied Physics, Ginzton Laboratory, Stanford University, Stanford, California 94305, USA
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8
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Lu Y, Strandberg I, Quijandría F, Johansson G, Gasparinetti S, Delsing P. Propagating Wigner-Negative States Generated from the Steady-State Emission of a Superconducting Qubit. PHYSICAL REVIEW LETTERS 2021; 126:253602. [PMID: 34241509 DOI: 10.1103/physrevlett.126.253602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/05/2021] [Accepted: 06/01/2021] [Indexed: 06/13/2023]
Abstract
We experimentally demonstrate the steady-state generation of propagating Wigner-negative states from a continuously driven superconducting qubit. We reconstruct the Wigner function of the radiation emitted into propagating modes defined by their temporal envelopes, using digital filtering. For an optimized temporal filter, we observe a large Wigner logarithmic negativity, in excess of 0.08, in agreement with theory. The fidelity between the theoretical predictions and the states generated experimentally is up to 99%, reaching state-of-the-art realizations in the microwave frequency domain. Our results provide a new way to generate and control nonclassical states, and may enable promising applications such as quantum networks and quantum computation based on waveguide quantum electrodynamics.
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Affiliation(s)
- Yong Lu
- Department of Microtechnology and Nanoscience MC2, Chalmers University of Technology, SE-412 96 Göteborg, Sweden
| | - Ingrid Strandberg
- Department of Microtechnology and Nanoscience MC2, Chalmers University of Technology, SE-412 96 Göteborg, Sweden
| | - Fernando Quijandría
- Department of Microtechnology and Nanoscience MC2, Chalmers University of Technology, SE-412 96 Göteborg, Sweden
| | - Göran Johansson
- Department of Microtechnology and Nanoscience MC2, Chalmers University of Technology, SE-412 96 Göteborg, Sweden
| | - Simone Gasparinetti
- Department of Microtechnology and Nanoscience MC2, Chalmers University of Technology, SE-412 96 Göteborg, Sweden
| | - Per Delsing
- Department of Microtechnology and Nanoscience MC2, Chalmers University of Technology, SE-412 96 Göteborg, Sweden
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9
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Kannan B, Campbell DL, Vasconcelos F, Winik R, Kim DK, Kjaergaard M, Krantz P, Melville A, Niedzielski BM, Yoder JL, Orlando TP, Gustavsson S, Oliver WD. Generating spatially entangled itinerant photons with waveguide quantum electrodynamics. SCIENCE ADVANCES 2020; 6:6/41/eabb8780. [PMID: 33028523 PMCID: PMC7541065 DOI: 10.1126/sciadv.abb8780] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/24/2020] [Accepted: 08/21/2020] [Indexed: 05/31/2023]
Abstract
Realizing a fully connected network of quantum processors requires the ability to distribute quantum entanglement. For distant processing nodes, this can be achieved by generating, routing, and capturing spatially entangled itinerant photons. In this work, we demonstrate the deterministic generation of such photons using superconducting transmon qubits that are directly coupled to a waveguide. In particular, we generate two-photon N00N states and show that the state and spatial entanglement of the emitted photons are tunable via the qubit frequencies. Using quadrature amplitude detection, we reconstruct the moments and correlations of the photonic modes and demonstrate state preparation fidelities of 84%. Our results provide a path toward realizing quantum communication and teleportation protocols using itinerant photons generated by quantum interference within a waveguide quantum electrodynamics architecture.
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Affiliation(s)
- B Kannan
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA.
- Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - D L Campbell
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - F Vasconcelos
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
- Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - R Winik
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - D K Kim
- MIT Lincoln Laboratory, 244 Wood Street, Lexington, MA 02420, USA
| | - M Kjaergaard
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - P Krantz
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - A Melville
- MIT Lincoln Laboratory, 244 Wood Street, Lexington, MA 02420, USA
| | - B M Niedzielski
- MIT Lincoln Laboratory, 244 Wood Street, Lexington, MA 02420, USA
| | - J L Yoder
- MIT Lincoln Laboratory, 244 Wood Street, Lexington, MA 02420, USA
| | - T P Orlando
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
- Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - S Gustavsson
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - W D Oliver
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
- Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
- MIT Lincoln Laboratory, 244 Wood Street, Lexington, MA 02420, USA
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
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10
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Sánchez-Burillo E, Martín-Moreno L, García-Ripoll JJ, Zueco D. Single Photons by Quenching the Vacuum. PHYSICAL REVIEW LETTERS 2019; 123:013601. [PMID: 31386390 DOI: 10.1103/physrevlett.123.013601] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/09/2018] [Indexed: 06/10/2023]
Abstract
Heisenberg's uncertainty principle implies that the quantum vacuum is not empty but fluctuates. These fluctuations can be converted into radiation through nonadiabatic changes in the Hamiltonian. Here, we discuss how to control this vacuum radiation, engineering a single-photon emitter out of a two-level system (2LS) ultrastrongly coupled to a finite-band waveguide in a vacuum state. More precisely, we show the 2LS nonlinearity shapes the vacuum radiation into a non-Gaussian superposition of even and odd cat states. When the 2LS bare frequency lays within the band gaps, this emission can be well approximated by individual photons. This picture is confirmed by a characterization of the ground and bound states, and a study of the dynamics with matrix-product states and polaron Hamiltonian methods.
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Affiliation(s)
| | - L Martín-Moreno
- Instituto de Ciencia de Materiales de Aragón and Departamento de Física de la Materia Condensada, CSIC-Universidad de Zaragoza, E-50009 Zaragoza, Spain
| | - J J García-Ripoll
- Instituto de Física Fundamental, IFF-CSIC, Calle Serrano 113b, Madrid E-28006
| | - D Zueco
- Instituto de Ciencia de Materiales de Aragón and Departamento de Física de la Materia Condensada, CSIC-Universidad de Zaragoza, E-50009 Zaragoza, Spain
- Fundación ARAID, Paseo María Agustín 36, E-50004 Zaragoza, Spain
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11
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Potts PP. Certifying Nonclassical Behavior for Negative Keldysh Quasiprobabilities. PHYSICAL REVIEW LETTERS 2019; 122:110401. [PMID: 30951341 DOI: 10.1103/physrevlett.122.110401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/12/2018] [Indexed: 06/09/2023]
Abstract
We introduce an experimental test for ruling out classical explanations for the statistics obtained when measuring arbitrary observables at arbitrary times using individual detectors. This test requires some trust in the measurements, represented by a few natural assumptions on the detectors. In quantum theory, the considered scenarios are well captured by von Neumann measurements. These can be described naturally in terms of the Keldysh quasiprobability distribution (KQPD), and the imprecision and backaction exerted by the measurement apparatus. We find that classical descriptions can be ruled out from measured data if and only if the KQPD exhibits negative values. We provide examples based on simulated data, considering the influence of a finite amount of statistics. In addition to providing an experimental tool for certifying nonclassicality, our results bestow an operational meaning upon the nonclassical nature of negative quasiprobability distributions such as the Wigner function and the full counting statistics.
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Affiliation(s)
- Patrick P Potts
- Physics Department and NanoLund, Lund University, Box 118, 22100 Lund, Sweden
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12
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Sundaresan NM, Lundgren R, Zhu G, Gorshkov AV, Houck AA. Interacting Qubit-Photon Bound States with Superconducting Circuits. PHYSICAL REVIEW. X 2019; 9:10.1103/physrevx.9.011021. [PMID: 32117578 PMCID: PMC7047877 DOI: 10.1103/physrevx.9.011021] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
Qubits strongly coupled to a photonic crystal give rise to qubit-photon dressed bound states. These bound states, comprising the qubits and spatially localized photonic modes induced around the qubits, are the basis for many exotic physical scenarios. The localization of these states changes with qubit detuning from the photonic crystal band edge, offering an avenue of in situ control of bound-state interaction. Here, we present experimental results from a device with two transmon qubits coupled to a superconducting microwave photonic crystal and realize tunable on-site and interbound state interactions. We observe a fourth-order two-photon virtual process between bound states indicating strong coupling between the photonic crystal and transmon qubits. Because of their localization-dependent interaction, these states offer the ability to realize one-dimensional chains of bound states with tunable and potentially long-range interactions that preserve the qubits' spatial organization. The widely tunable, strong, and robust interactions demonstrated with this system are promising benchmarks towards realizing larger, more complex systems that use bound states to build and study quantum spin models.
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Affiliation(s)
- Neereja M Sundaresan
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Rex Lundgren
- Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA
| | - Guanyu Zhu
- Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA
| | - Alexey V Gorshkov
- Joint Quantum Institute and Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA
| | - Andrew A Houck
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
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13
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Di Stefano O, Kockum AF, Ridolfo A, Savasta S, Nori F. Photodetection probability in quantum systems with arbitrarily strong light-matter interaction. Sci Rep 2018; 8:17825. [PMID: 30546126 PMCID: PMC6292927 DOI: 10.1038/s41598-018-36056-1] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/26/2018] [Accepted: 11/14/2018] [Indexed: 12/02/2022] Open
Abstract
Cavity-QED systems have recently reached a regime where the light-matter interaction strength amounts to a non-negligible fraction of the resonance frequencies of the bare subsystems. In this regime, it is known that the usual normal-order correlation functions for the cavity-photon operators fail to describe both the rate and the statistics of emitted photons. Following Glauber’s original approach, we derive a simple and general quantum theory of photodetection, valid for arbitrary light-matter interaction strengths. Our derivation uses Fermi’s golden rule, together with an expansion of system operators in the eigenbasis of the interacting light-matter system, to arrive at the correct photodetection probabilities. We consider both narrow- and wide-band photodetectors. Our description is also valid for point-like detectors placed inside the optical cavity. As an application, we propose a gedanken experiment confirming the virtual nature of the bare excitations that enrich the ground state of the quantum Rabi model.
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Affiliation(s)
- Omar Di Stefano
- Theoretical Quantum Physics Laboratory, RIKEN Cluster for Pioneering Research, Wako-shi, Saitama, 351-0198, Japan
| | - Anton Frisk Kockum
- Theoretical Quantum Physics Laboratory, RIKEN Cluster for Pioneering Research, Wako-shi, Saitama, 351-0198, Japan.,Wallenberg Centre for Quantum Technology, Department of Microtechnology and Nanoscience, Chalmers University of Technology, 412 96, Gothenburg, Sweden
| | - Alessandro Ridolfo
- Theoretical Quantum Physics Laboratory, RIKEN Cluster for Pioneering Research, Wako-shi, Saitama, 351-0198, Japan
| | - Salvatore Savasta
- Theoretical Quantum Physics Laboratory, RIKEN Cluster for Pioneering Research, Wako-shi, Saitama, 351-0198, Japan. .,MIFT - Dipartimento di Scienze Matematiche e Informatiche Scienze Fisiche e Scienze della Terra, Università di Messina, I-98166, Messina, Italy.
| | - Franco Nori
- Theoretical Quantum Physics Laboratory, RIKEN Cluster for Pioneering Research, Wako-shi, Saitama, 351-0198, Japan.,Physics Department, The University of Michigan, Ann Arbor, Michigan, 48109-1040, USA
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14
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Marković D, Jezouin S, Ficheux Q, Fedortchenko S, Felicetti S, Coudreau T, Milman P, Leghtas Z, Huard B. Demonstration of an Effective Ultrastrong Coupling between Two Oscillators. PHYSICAL REVIEW LETTERS 2018; 121:040505. [PMID: 30095939 DOI: 10.1103/physrevlett.121.040505] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/23/2018] [Indexed: 06/08/2023]
Abstract
When the coupling rate between two quantum systems becomes as large as their characteristic frequencies, it induces dramatic effects on their dynamics and even on the nature of their ground state. The case of a qubit coupled to a harmonic oscillator in this ultrastrong coupling regime has been investigated theoretically and experimentally. Here, we explore the case of two harmonic oscillators in the ultrastrong coupling regime. Probing the properties of their ground state remains out of reach in natural implementations. Therefore, we have realized an analog quantum simulation of this coupled system by dual frequency pumping a nonlinear superconducting circuit. The pump amplitudes directly tune the effective coupling rate. We observe spectroscopic signature of a mode hybridization that is characteristic of the ultrastrong coupling. We experimentally demonstrate a key property of the ground state of this simulated ultrastrong coupling between modes by observing simultaneous single- and two-mode squeezing of the radiated field below vacuum fluctuations.
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Affiliation(s)
- D Marković
- Département de physique de l'ENS, Laboratoire Pierre Aigrain, École normale supérieure, PSL Research University, Université Paris Diderot, Sorbonne Paris Cité, Sorbonne Universités, UPMC University Paris 06, CNRS, 75005 Paris, France
| | - S Jezouin
- Département de physique de l'ENS, Laboratoire Pierre Aigrain, École normale supérieure, PSL Research University, Université Paris Diderot, Sorbonne Paris Cité, Sorbonne Universités, UPMC University Paris 06, CNRS, 75005 Paris, France
| | - Q Ficheux
- Département de physique de l'ENS, Laboratoire Pierre Aigrain, École normale supérieure, PSL Research University, Université Paris Diderot, Sorbonne Paris Cité, Sorbonne Universités, UPMC University Paris 06, CNRS, 75005 Paris, France
- Université Lyon, ENS de Lyon, Université Claude Bernard Lyon 1, CNRS, Laboratoire de Physique, F-69342 Lyon, France
| | - S Fedortchenko
- Laboratoire Matériaux et Phénomènes Quantiques, Sorbonne Paris Cité, Université Paris Diderot, CNRS UMR 7162, 75013 Paris, France
| | - S Felicetti
- Laboratoire Matériaux et Phénomènes Quantiques, Sorbonne Paris Cité, Université Paris Diderot, CNRS UMR 7162, 75013 Paris, France
| | - T Coudreau
- Laboratoire Matériaux et Phénomènes Quantiques, Sorbonne Paris Cité, Université Paris Diderot, CNRS UMR 7162, 75013 Paris, France
| | - P Milman
- Laboratoire Matériaux et Phénomènes Quantiques, Sorbonne Paris Cité, Université Paris Diderot, CNRS UMR 7162, 75013 Paris, France
| | - Z Leghtas
- Département de physique de l'ENS, Laboratoire Pierre Aigrain, École normale supérieure, PSL Research University, Université Paris Diderot, Sorbonne Paris Cité, Sorbonne Universités, UPMC University Paris 06, CNRS, 75005 Paris, France
- Centre Automatique et Systèmes, Mines ParisTech, PSL Research University, 60 Boulevard Saint-Michel, 75272 Paris Cedex 6, France
- QUANTIC Team, INRIA de Paris, 2 Rue Simone Iff, 75012 Paris, France
| | - B Huard
- Département de physique de l'ENS, Laboratoire Pierre Aigrain, École normale supérieure, PSL Research University, Université Paris Diderot, Sorbonne Paris Cité, Sorbonne Universités, UPMC University Paris 06, CNRS, 75005 Paris, France
- Université Lyon, ENS de Lyon, Université Claude Bernard Lyon 1, CNRS, Laboratoire de Physique, F-69342 Lyon, France
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15
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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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16
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Gasparinetti S, Pechal M, Besse JC, Mondal M, Eichler C, Wallraff A. Correlations and Entanglement of Microwave Photons Emitted in a Cascade Decay. PHYSICAL REVIEW LETTERS 2017; 119:140504. [PMID: 29053288 DOI: 10.1103/physrevlett.119.140504] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/02/2017] [Indexed: 06/07/2023]
Abstract
We use a three-level artificial atom in the ladder configuration as a source of correlated, single microwave photons of different frequency. The artificial atom, a transmon-type superconducting circuit, is driven at the two-photon transition between ground and second-excited state, and embedded into an on-chip switch that selectively routes different-frequency photons into different spatial modes. Under continuous driving, we measure power cross-correlations between the two modes and observe a crossover between strong antibunching and superbunching, typical of cascade decay, and an oscillatory pattern as the drive strength becomes comparable to the radiative decay rate. By preparing the source in a superposition state using an excitation pulse, we achieve deterministic generation of entangled photon pairs, as demonstrated by nonvanishing phase correlations and more generally by joint quantum state tomography of the two itinerant photonic modes.
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Affiliation(s)
| | - Marek Pechal
- Department of Physics, ETH Zurich, CH-8093 Zurich, Switzerland
| | | | - Mintu Mondal
- Department of Physics, ETH Zurich, CH-8093 Zurich, Switzerland
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17
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Kurpiers P, Walter T, Magnard P, Salathe Y, Wallraff A. Characterizing the attenuation of coaxial and rectangular microwave-frequency waveguides at cryogenic temperatures. EPJ QUANTUM TECHNOLOGY 2017; 4:8. [PMID: 31179200 PMCID: PMC6529057 DOI: 10.1140/epjqt/s40507-017-0059-7] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/02/2017] [Accepted: 04/04/2017] [Indexed: 05/07/2023]
Abstract
Low-loss waveguides are required for quantum communication at distances beyond the chip-scale for any low-temperature solid-state implementation of quantum information processors. We measure and analyze the attenuation constant of commercially available microwave-frequency waveguides down to millikelvin temperatures and single photon levels. More specifically, we characterize the frequency-dependent loss of a range of coaxial and rectangular microwave waveguides down to 0.005 dB / m using a resonant-cavity technique. We study the loss tangent and relative permittivity of commonly used dielectric waveguide materials by measurements of the internal quality factors and their comparison with established loss models. The results of our characterization are relevant for accurately predicting the signal levels at the input of cryogenic devices, for reducing the loss in any detection chain, and for estimating the heat load induced by signal dissipation in cryogenic systems.
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Affiliation(s)
| | - Theodore Walter
- Department of Physics, ETH Zürich, Zürich, CH-8093 Switzerland
| | - Paul Magnard
- Department of Physics, ETH Zürich, Zürich, CH-8093 Switzerland
| | - Yves Salathe
- Department of Physics, ETH Zürich, Zürich, CH-8093 Switzerland
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18
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Goetz J, Pogorzalek S, Deppe F, Fedorov KG, Eder P, Fischer M, Wulschner F, Xie E, Marx A, Gross R. Photon Statistics of Propagating Thermal Microwaves. PHYSICAL REVIEW LETTERS 2017; 118:103602. [PMID: 28339239 DOI: 10.1103/physrevlett.118.103602] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/29/2016] [Indexed: 06/06/2023]
Abstract
In experiments with superconducting quantum circuits, characterizing the photon statistics of propagating microwave fields is a fundamental task. We quantify the n^{2}+n photon number variance of thermal microwave photons emitted from a blackbody radiator for mean photon numbers, 0.05≲n≲1.5. We probe the fields using either correlation measurements or a transmon qubit coupled to a microwave resonator. Our experiments provide a precise quantitative characterization of weak microwave states and information on the noise emitted by a Josephson parametric amplifier.
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Affiliation(s)
- J Goetz
- Walther-Meißner-Institut, Bayerische Akademie der Wissenschaften, 85748 Garching, Germany
- Physik-Department, Technische Universität München, 85748 Garching, Germany
| | - S Pogorzalek
- Walther-Meißner-Institut, Bayerische Akademie der Wissenschaften, 85748 Garching, Germany
- Physik-Department, Technische Universität München, 85748 Garching, Germany
| | - F Deppe
- Walther-Meißner-Institut, Bayerische Akademie der Wissenschaften, 85748 Garching, Germany
- Physik-Department, Technische Universität München, 85748 Garching, Germany
- Nanosystems Initiative Munich (NIM), Schellingstraße 4, 80799 München, Germany
| | - K G Fedorov
- Walther-Meißner-Institut, Bayerische Akademie der Wissenschaften, 85748 Garching, Germany
- Physik-Department, Technische Universität München, 85748 Garching, Germany
| | - P Eder
- Walther-Meißner-Institut, Bayerische Akademie der Wissenschaften, 85748 Garching, Germany
- Physik-Department, Technische Universität München, 85748 Garching, Germany
- Nanosystems Initiative Munich (NIM), Schellingstraße 4, 80799 München, Germany
| | - M Fischer
- Walther-Meißner-Institut, Bayerische Akademie der Wissenschaften, 85748 Garching, Germany
- Physik-Department, Technische Universität München, 85748 Garching, Germany
- Nanosystems Initiative Munich (NIM), Schellingstraße 4, 80799 München, Germany
| | - F Wulschner
- Walther-Meißner-Institut, Bayerische Akademie der Wissenschaften, 85748 Garching, Germany
- Physik-Department, Technische Universität München, 85748 Garching, Germany
| | - E Xie
- Walther-Meißner-Institut, Bayerische Akademie der Wissenschaften, 85748 Garching, Germany
- Physik-Department, Technische Universität München, 85748 Garching, Germany
- Nanosystems Initiative Munich (NIM), Schellingstraße 4, 80799 München, Germany
| | - A Marx
- Walther-Meißner-Institut, Bayerische Akademie der Wissenschaften, 85748 Garching, Germany
| | - R Gross
- Walther-Meißner-Institut, Bayerische Akademie der Wissenschaften, 85748 Garching, Germany
- Physik-Department, Technische Universität München, 85748 Garching, Germany
- Nanosystems Initiative Munich (NIM), Schellingstraße 4, 80799 München, Germany
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19
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Revealing nonclassicality beyond Gaussian states via a single marginal distribution. Proc Natl Acad Sci U S A 2017; 114:891-896. [PMID: 28077456 DOI: 10.1073/pnas.1617621114] [Citation(s) in RCA: 29] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
A standard method to obtain information on a quantum state is to measure marginal distributions along many different axes in phase space, which forms a basis of quantum-state tomography. We theoretically propose and experimentally demonstrate a general framework to manifest nonclassicality by observing a single marginal distribution only, which provides a unique insight into nonclassicality and a practical applicability to various quantum systems. Our approach maps the 1D marginal distribution into a factorized 2D distribution by multiplying the measured distribution or the vacuum-state distribution along an orthogonal axis. The resulting fictitious Wigner function becomes unphysical only for a nonclassical state; thus the negativity of the corresponding density operator provides evidence of nonclassicality. Furthermore, the negativity measured this way yields a lower bound for entanglement potential-a measure of entanglement generated using a nonclassical state with a beam-splitter setting that is a prototypical model to produce continuous-variable (CV) entangled states. Our approach detects both Gaussian and non-Gaussian nonclassical states in a reliable and efficient manner. Remarkably, it works regardless of measurement axis for all non-Gaussian states in finite-dimensional Fock space of any size, also extending to infinite-dimensional states of experimental relevance for CV quantum informatics. We experimentally illustrate the power of our criterion for motional states of a trapped ion, confirming their nonclassicality in a measurement-axis-independent manner. We also address an extension of our approach combined with phase-shift operations, which leads to a stronger test of nonclassicality, that is, detection of genuine non-Gaussianity under a CV measurement.
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20
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Chang Y, González-Tudela A, Sánchez Muñoz C, Navarrete-Benlloch C, Shi T. Deterministic Down-Converter and Continuous Photon-Pair Source within the Bad-Cavity Limit. PHYSICAL REVIEW LETTERS 2016; 117:203602. [PMID: 27886465 DOI: 10.1103/physrevlett.117.203602] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/02/2015] [Indexed: 06/06/2023]
Abstract
The development, characterization, and control of N-photon sources are instrumental for quantum technological applications. This work constitutes a step forward in this direction, where we propose a cavity quantum electrodynamics setup designed for the generation of photon pairs. We identify both the regime where our system works as a deterministic down-converter of a single input photon and as an optimal two-photon source under weak continuous driving. We use both the scattering and master equation formalisms to characterize the system, and from their connection naturally arises a physical criterion characterizing when weakly driven systems behave as continuous antibunched two-photon sources. We also show that the outgoing photons share nontrivial quantum correlations in general. We provide a specific implementation based on state-of-the-art superconducting circuits, showing how our proposal is within the reach of current technologies. As an outlook, we show the proposal can be extended to achieve deterministic conversion of a single photon into N photons.
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Affiliation(s)
- Yue Chang
- Max-Planck Institut für Quantenoptik, Hans-Kopfermann-Strasse 1, D-85748 Garching, Germany
| | | | - Carlos Sánchez Muñoz
- Max-Planck Institut für Quantenoptik, Hans-Kopfermann-Strasse 1, D-85748 Garching, Germany
- Física Teórica de la Materia Condensada, Universidad Autónoma de Madrid, 28049 Madrid, Spain
| | - Carlos Navarrete-Benlloch
- Max-Planck Institut für Quantenoptik, Hans-Kopfermann-Strasse 1, D-85748 Garching, Germany
- Institute for Theoretical Physics II, Universität Erlangen-Nürnberg, Staudtstrasse 7, 91058 Erlangen, Germany
| | - Tao Shi
- Max-Planck Institut für Quantenoptik, Hans-Kopfermann-Strasse 1, D-85748 Garching, Germany
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21
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Fedorov KG, Zhong L, Pogorzalek S, Eder P, Fischer M, Goetz J, Xie E, Wulschner F, Inomata K, Yamamoto T, Nakamura Y, Di Candia R, Las Heras U, Sanz M, Solano E, Menzel EP, Deppe F, Marx A, Gross R. Displacement of Propagating Squeezed Microwave States. PHYSICAL REVIEW LETTERS 2016; 117:020502. [PMID: 27447495 DOI: 10.1103/physrevlett.117.020502] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/15/2016] [Indexed: 06/06/2023]
Abstract
Displacement of propagating quantum states of light is a fundamental operation for quantum communication. It enables fundamental studies on macroscopic quantum coherence and plays an important role in quantum teleportation protocols with continuous variables. In our experiments, we have successfully implemented this operation for propagating squeezed microwave states. We demonstrate that, even for strong displacement amplitudes, there is no degradation of the squeezing level in the reconstructed quantum states. Furthermore, we confirm that path entanglement generated by using displaced squeezed states remains constant over a wide range of the displacement power.
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Affiliation(s)
- Kirill G Fedorov
- Walther-Meißner-Institut, Bayerische Akademie der Wissenschaften, D-85748 Garching, Germany
| | - L Zhong
- Walther-Meißner-Institut, Bayerische Akademie der Wissenschaften, D-85748 Garching, Germany
- Physik-Department, Technische Universität München, D-85748 Garching, Germany
- Nanosystems Initiative Munich (NIM), Schellingstraße 4, 80799 München, Germany
| | - S Pogorzalek
- Walther-Meißner-Institut, Bayerische Akademie der Wissenschaften, D-85748 Garching, Germany
- Physik-Department, Technische Universität München, D-85748 Garching, Germany
| | - P Eder
- Walther-Meißner-Institut, Bayerische Akademie der Wissenschaften, D-85748 Garching, Germany
- Physik-Department, Technische Universität München, D-85748 Garching, Germany
- Nanosystems Initiative Munich (NIM), Schellingstraße 4, 80799 München, Germany
| | - M Fischer
- Walther-Meißner-Institut, Bayerische Akademie der Wissenschaften, D-85748 Garching, Germany
- Physik-Department, Technische Universität München, D-85748 Garching, Germany
| | - J Goetz
- Walther-Meißner-Institut, Bayerische Akademie der Wissenschaften, D-85748 Garching, Germany
- Physik-Department, Technische Universität München, D-85748 Garching, Germany
| | - E Xie
- Walther-Meißner-Institut, Bayerische Akademie der Wissenschaften, D-85748 Garching, Germany
- Physik-Department, Technische Universität München, D-85748 Garching, Germany
- Nanosystems Initiative Munich (NIM), Schellingstraße 4, 80799 München, Germany
| | - F Wulschner
- Walther-Meißner-Institut, Bayerische Akademie der Wissenschaften, D-85748 Garching, Germany
- Physik-Department, Technische Universität München, D-85748 Garching, Germany
| | - K Inomata
- RIKEN Center for Emergent Matter Science (CEMS), Wako, Saitama 351-0198, Japan
| | - T Yamamoto
- NEC IoT Device Research Laboratories, Tsukuba, Ibaraki 305-8501, Japan
| | - Y Nakamura
- RIKEN Center for Emergent Matter Science (CEMS), Wako, Saitama 351-0198, Japan
- Research Center for Advanced Science and Technology (RCAST), The University of Tokyo, Meguro-ku, Tokyo 153-8904, Japan
| | - R Di Candia
- Department of Physical Chemistry, University of the Basque Country UPV/EHU, Apartado 644, E-48080 Bilbao, Spain
| | - U Las Heras
- Department of Physical Chemistry, University of the Basque Country UPV/EHU, Apartado 644, E-48080 Bilbao, Spain
| | - M Sanz
- Department of Physical Chemistry, University of the Basque Country UPV/EHU, Apartado 644, E-48080 Bilbao, Spain
| | - E Solano
- Physik-Department, Technische Universität München, D-85748 Garching, Germany
- Department of Physical Chemistry, University of the Basque Country UPV/EHU, Apartado 644, E-48080 Bilbao, Spain
- IKERBASQUE, Basque Foundation for Science, Maria Diaz de Haro 3, 48013 Bilbao, Spain
| | - E P Menzel
- Walther-Meißner-Institut, Bayerische Akademie der Wissenschaften, D-85748 Garching, Germany
| | - F Deppe
- Walther-Meißner-Institut, Bayerische Akademie der Wissenschaften, D-85748 Garching, Germany
- Physik-Department, Technische Universität München, D-85748 Garching, Germany
- Nanosystems Initiative Munich (NIM), Schellingstraße 4, 80799 München, Germany
| | - A Marx
- Walther-Meißner-Institut, Bayerische Akademie der Wissenschaften, D-85748 Garching, Germany
| | - R Gross
- Walther-Meißner-Institut, Bayerische Akademie der Wissenschaften, D-85748 Garching, Germany
- Physik-Department, Technische Universität München, D-85748 Garching, Germany
- Nanosystems Initiative Munich (NIM), Schellingstraße 4, 80799 München, Germany
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22
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Slodička L, Marek P, Filip R. Deterministic nonclassicality from thermal states. OPTICS EXPRESS 2016; 24:7858-7870. [PMID: 27137228 DOI: 10.1364/oe.24.007858] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
Coupling an oscillator to a single two-level system is one of the most fundamental interactions in quantum physics. We report on a dynamical effect during which a thermal state of an oscillator is unconditionally transformed to a highly nonclassical state with negative Wigner function values by mere absorbtion by a single uncontrolled two-level system. This complements the traditional test of Rabi oscillations and it serves as a simply measurable witness that the process in question is highly nonclassical. The process is experimentally feasible with possible experimental implementation in a number of experimental platforms with intrinsic Jaynes-Cummings interaction and it has the potential of enabling deterministic generation of nonclassical quantum states.
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23
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Bruschi DE, Sabín C, Kok P, Johansson G, Delsing P, Fuentes I. Towards universal quantum computation through relativistic motion. Sci Rep 2016; 6:18349. [PMID: 26860584 PMCID: PMC4748225 DOI: 10.1038/srep18349] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/14/2015] [Accepted: 11/16/2015] [Indexed: 11/25/2022] Open
Abstract
We show how to use relativistic motion to generate continuous variable Gaussian cluster states within cavity modes. Our results can be demonstrated experimentally using superconducting circuits where tuneable boundary conditions correspond to mirrors moving with velocities close to the speed of light. In particular, we propose the generation of a quadripartite square cluster state as a first example that can be readily implemented in the laboratory. Since cluster states are universal resources for universal one-way quantum computation, our results pave the way for relativistic quantum computation schemes.
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Affiliation(s)
- David Edward Bruschi
- School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom.,School of Electronic and Electrical Engineering, University of Leeds, Woodhouse Lane, Leeds, LS2 9JT, United Kingdom
| | - Carlos Sabín
- Instituto de Física Fundamental, CSIC, Serrano 113-bis, 28006 Madrid, Spain
| | - Pieter Kok
- Department of Physics &Astronomy, University of Sheffield, Sheffield S3 7RH, United Kingdom
| | - Göran Johansson
- Microtechnology and Nanoscience, MC2, Chalmers University of Technology, S-41296 Göteborg, Sweden
| | - Per Delsing
- Microtechnology and Nanoscience, MC2, Chalmers University of Technology, S-41296 Göteborg, Sweden
| | - Ivette Fuentes
- School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
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24
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Friis N, Melnikov AA, Kirchmair G, Briegel HJ. Coherent controlization using superconducting qubits. Sci Rep 2015; 5:18036. [PMID: 26667893 PMCID: PMC4678369 DOI: 10.1038/srep18036] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/17/2015] [Accepted: 11/10/2015] [Indexed: 11/08/2022] Open
Abstract
Coherent controlization, i.e., coherent conditioning of arbitrary single- or multi-qubit operations on the state of one or more control qubits, is an important ingredient for the flexible implementation of many algorithms in quantum computation. This is of particular significance when certain subroutines are changing over time or when they are frequently modified, such as in decision-making algorithms for learning agents. We propose a scheme to realize coherent controlization for any number of superconducting qubits coupled to a microwave resonator. For two and three qubits, we present an explicit construction that is of high relevance for quantum learning agents. We demonstrate the feasibility of our proposal, taking into account loss, dephasing, and the cavity self-Kerr effect.
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Affiliation(s)
- Nicolai Friis
- Institute for Theoretical Physics, University of Innsbruck, Technikerstraße 21a, A-6020 Innsbruck, Austria
| | - Alexey A. Melnikov
- Institute for Theoretical Physics, University of Innsbruck, Technikerstraße 21a, A-6020 Innsbruck, Austria
- Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Technikerstraße 21a, A-6020 Innsbruck, Austria
| | - Gerhard Kirchmair
- Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Technikerstraße 21a, A-6020 Innsbruck, Austria
- Institute for Experimental Physics, University of Innsbruck, Technikerstraße 25, A-6020 Innsbruck, Austria
| | - Hans J. Briegel
- Institute for Theoretical Physics, University of Innsbruck, Technikerstraße 21a, A-6020 Innsbruck, Austria
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25
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Biondi M, van Nieuwenburg EPL, Blatter G, Huber SD, Schmidt S. Incompressible Polaritons in a Flat Band. PHYSICAL REVIEW LETTERS 2015; 115:143601. [PMID: 26551811 DOI: 10.1103/physrevlett.115.143601] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/09/2015] [Indexed: 06/05/2023]
Abstract
We study the interplay of geometric frustration and interactions in a nonequilibrium photonic lattice system exhibiting a polariton flat band as described by a variant of the Jaynes-Cummings-Hubbard model. We show how to engineer strong photonic correlations in such a driven, dissipative system by quenching the kinetic energy through frustration. This produces an incompressible state of photons characterized by short-ranged crystalline order with period doubling. The latter manifests itself in strong spatial correlations, i.e., on-site and nearest-neighbor antibunching combined with extended density-wave oscillations at larger distances. We propose a state-of-the-art circuit QED realization of our system, which is tunable in situ.
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Affiliation(s)
- Matteo Biondi
- Institute for Theoretical Physics, ETH Zurich, 8093 Zürich, Switzerland
| | | | - Gianni Blatter
- Institute for Theoretical Physics, ETH Zurich, 8093 Zürich, Switzerland
| | - Sebastian D Huber
- Institute for Theoretical Physics, ETH Zurich, 8093 Zürich, Switzerland
| | - Sebastian Schmidt
- Institute for Theoretical Physics, ETH Zurich, 8093 Zürich, Switzerland
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26
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Lecocq F, Clark JB, Simmonds R, Aumentado J, Teufel JD. Quantum Nondemolition Measurement of a Nonclassical State of a Massive Object. PHYSICAL REVIEW. X 2015; 5:041037. [PMID: 27057422 PMCID: PMC4821547 DOI: 10.1103/physrevx.5.041037] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/05/2023]
Abstract
By coupling a macroscopic mechanical oscillator to two microwave cavities, we simultaneously prepare and monitor a nonclassical steady state of mechanical motion. In each cavity, correlated radiation pressure forces induced by two coherent drives engineer the coupling between the quadratures of light and motion. We, first, demonstrate the ability to perform a continuous quantum nondemolition measurement of a single mechanical quadrature at a rate that exceeds the mechanical decoherence rate, while avoiding measurement backaction by more than 13 dB. Second, we apply this measurement technique to independently verify the preparation of a squeezed state in the mechanical oscillator, resolving quadrature fluctuations 20% below the quantum noise.
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27
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Forgues JC, Lupien C, Reulet B. Experimental violation of bell-like inequalities by electronic shot noise. PHYSICAL REVIEW LETTERS 2015; 114:130403. [PMID: 25884119 DOI: 10.1103/physrevlett.114.130403] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/23/2014] [Indexed: 06/04/2023]
Abstract
We report measurements of the correlations between electromagnetic field quadratures at two frequencies f1=7 GHz and f1=7.5 GHz of the radiation emitted by a tunnel junction placed at very low temperature and excited at frequency f1+f2. We demonstrate the existence of two-mode squeezing and violation of a Bell-like inequality, thereby proving the existence of entanglement in the quantum shot noise radiated by the tunnel junction.
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Affiliation(s)
- Jean-Charles Forgues
- Département de Physique, Université de Sherbrooke, Sherbrooke, Québec J1K 2R1, Canada
| | - Christian Lupien
- Département de Physique, Université de Sherbrooke, Sherbrooke, Québec J1K 2R1, Canada
| | - Bertrand Reulet
- Département de Physique, Université de Sherbrooke, Sherbrooke, Québec J1K 2R1, Canada
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28
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Liu YY, Stehlik J, Eichler C, Gullans MJ, Taylor JM, Petta JR. Semiconductor double quantum dot micromaser. Science 2015; 347:285-7. [DOI: 10.1126/science.aaa2501] [Citation(s) in RCA: 99] [Impact Index Per Article: 11.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Affiliation(s)
- Y.-Y. Liu
- Department of Physics, Princeton University, Princeton, NJ 08544, USA
| | - J. Stehlik
- Department of Physics, Princeton University, Princeton, NJ 08544, USA
| | - C. Eichler
- Department of Physics, Princeton University, Princeton, NJ 08544, USA
| | - M. J. Gullans
- Joint Quantum Institute, University of Maryland–National Institute of Standards and Technology, College Park, MD 20742, USA
| | - J. M. Taylor
- Joint Quantum Institute, University of Maryland–National Institute of Standards and Technology, College Park, MD 20742, USA
- Joint Center for Quantum Information and Computer Science, University of Maryland and NIST, College Park, MD 20742, USA
| | - J. R. Petta
- Department of Physics, Princeton University, Princeton, NJ 08544, USA
- Department of Physics, University of California, Santa Barbara, CA 93106, USA
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29
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Filip R, Klapka P. Purely lossy and robust quantum interfaces between light and matter. OPTICS EXPRESS 2014; 22:30697-30706. [PMID: 25607017 DOI: 10.1364/oe.22.030697] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
The commonly used teleportation-based interfaces between light and matter are very sensitive to noise of matter systems and also to the optical in-coupling and out-coupling losses. These imperfections produce classical noise in the teleportation interface, which significantly limits the transmission of quantum states. We propose robust quantum interfaces between weakly coupled continuous variables of light and matter. The state transfer introduces only pure loss, without any additional classical noise, despite a presence of in-coupling and out-coupling optical losses. These interfaces qualitatively overcome commonly used interfaces based on quantum teleportation.
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30
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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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31
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Gustafsson MV, Aref T, Kockum AF, Ekström MK, Johansson G, Delsing P. Propagating phonons coupled to an artificial atom. Science 2014; 346:207-11. [PMID: 25213379 DOI: 10.1126/science.1257219] [Citation(s) in RCA: 86] [Impact Index Per Article: 8.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022]
Abstract
Quantum information can be stored in micromechanical resonators, encoded as quanta of vibration known as phonons. The vibrational motion is then restricted to the stationary eigenmodes of the resonator, which thus serves as local storage for phonons. In contrast, we couple propagating phonons to an artificial atom in the quantum regime and reproduce findings from quantum optics, with sound taking over the role of light. Our results highlight the similarities between phonons and photons but also point to new opportunities arising from the characteristic features of quantum mechanical sound. The low propagation speed of phonons should enable new dynamic schemes for processing quantum information, and the short wavelength allows regimes of atomic physics to be explored that cannot be reached in photonic systems.
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Affiliation(s)
- Martin V Gustafsson
- Microtechnology and Nanoscience, Chalmers University of Technology, Kemivägen 9, SE-41296 Göteborg, Sweden. Department of Chemistry, Columbia University, NWC Building, 550 West 120th Street, New York, NY 10027, USA.
| | - Thomas Aref
- Microtechnology and Nanoscience, Chalmers University of Technology, Kemivägen 9, SE-41296 Göteborg, Sweden
| | - Anton Frisk Kockum
- Microtechnology and Nanoscience, Chalmers University of Technology, Kemivägen 9, SE-41296 Göteborg, Sweden
| | - Maria K Ekström
- Microtechnology and Nanoscience, Chalmers University of Technology, Kemivägen 9, SE-41296 Göteborg, Sweden
| | - Göran Johansson
- Microtechnology and Nanoscience, Chalmers University of Technology, Kemivägen 9, SE-41296 Göteborg, Sweden
| | - Per Delsing
- Microtechnology and Nanoscience, Chalmers University of Technology, Kemivägen 9, SE-41296 Göteborg, Sweden.
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32
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Liu YY, Petersson KD, Stehlik J, Taylor JM, Petta JR. Photon emission from a cavity-coupled double quantum dot. PHYSICAL REVIEW LETTERS 2014; 113:036801. [PMID: 25083659 DOI: 10.1103/physrevlett.113.036801] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/30/2014] [Indexed: 06/03/2023]
Abstract
We study a voltage biased InAs double quantum dot (DQD) that is coupled to a superconducting transmission line resonator. Inelastic tunneling in the DQD is mediated by electron phonon coupling and coupling to the cavity mode. We show that electronic transport through the DQD leads to photon emission from the cavity at a rate of 10 MHz. With a small cavity drive field, we observe a gain of up to 15 in the cavity transmission. Our results are analyzed in the context of existing theoretical models and suggest that it may be necessary to account for inelastic tunneling processes that proceed via simultaneous emission of a phonon and a photon.
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Affiliation(s)
- Y-Y Liu
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - K D Petersson
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - J Stehlik
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - J M Taylor
- Joint Quantum Institute/NIST, College Park, Maryland 20742, USA
| | - J R Petta
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
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33
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Armour AD, Blencowe MP, Brahimi E, Rimberg AJ. Universal quantum fluctuations of a cavity mode driven by a Josephson junction. PHYSICAL REVIEW LETTERS 2013; 111:247001. [PMID: 24483692 DOI: 10.1103/physrevlett.111.247001] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/10/2013] [Indexed: 06/03/2023]
Abstract
We analyze the quantum dynamics of a superconducting cavity coupled to a voltage-biased Josephson junction. The cavity is strongly excited at resonances where the voltage energy lost by a Cooper pair traversing the circuit is a multiple of the cavity photon energy. We find that the resonances are accompanied by substantial squeezing of the quantum fluctuations of the cavity over a broad range of parameters and are able to identify regimes where the fluctuations in the system take on universal values.
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Affiliation(s)
- A D Armour
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - M P Blencowe
- Department of Physics and Astronomy, Dartmouth College, New Hampshire 03755, USA
| | - E Brahimi
- Department of Physics and Astronomy, Dartmouth College, New Hampshire 03755, USA
| | - A J Rimberg
- Department of Physics and Astronomy, Dartmouth College, New Hampshire 03755, USA
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34
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Zheng H, Gauthier DJ, Baranger HU. Waveguide-QED-based photonic quantum computation. PHYSICAL REVIEW LETTERS 2013; 111:090502. [PMID: 24033010 DOI: 10.1103/physrevlett.111.090502] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/08/2012] [Revised: 06/11/2013] [Indexed: 06/02/2023]
Abstract
We propose a new scheme for quantum computation using flying qubits--propagating photons in a one-dimensional waveguide interacting with matter qubits. Photon-photon interactions are mediated by the coupling to a four-level system, based on which photon-photon π-phase gates (CONTROLLED-NOT) can be implemented for universal quantum computation. We show that high gate fidelity is possible, given recent dramatic experimental progress in superconducting circuits and photonic-crystal waveguides. The proposed system can be an important building block for future on-chip quantum networks.
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Affiliation(s)
- Huaixiu Zheng
- Department of Physics, Duke University, Post Office Box 90305, Durham, North Carolina 27708, USA
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35
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Quijandría F, Porras D, García-Ripoll JJ, Zueco D. Circuit QED bright source for chiral entangled light based on dissipation. PHYSICAL REVIEW LETTERS 2013; 111:073602. [PMID: 23992064 DOI: 10.1103/physrevlett.111.073602] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/29/2012] [Revised: 04/01/2013] [Indexed: 06/02/2023]
Abstract
We present a scalable and tunable framework for the quantum simulation of critical dissipative models based on a circuit QED cavity array interacting with driven superconducting qubits. We will show that the strongly correlated many-body state of the cavities can be mapped into the state of propagating photons in a transmission line. This allows not only for an efficient way of accessing the correlations in the many-body system, but also provides a bright source of chiral entangled light where directionality and entanglement are assisted by collective phenomena and breaking of reflection symmetry.
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Affiliation(s)
- Fernando Quijandría
- Instituto de Ciencia de Materiales de Aragón y Departamento de Física de la Materia Condensada, CSIC-Universidad de Zaragoza, Zaragoza E-50012, Spain
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36
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Neumeier L, Leib M, Hartmann MJ. Single-photon transistor in circuit quantum electrodynamics. PHYSICAL REVIEW LETTERS 2013; 111:063601. [PMID: 23971573 DOI: 10.1103/physrevlett.111.063601] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/04/2012] [Revised: 06/06/2013] [Indexed: 06/02/2023]
Abstract
We introduce a circuit quantum electrodynamical setup for a "single-photon" transistor. In our approach photons propagate in two open transmission lines that are coupled via two interacting transmon qubits. The interaction is such that no photons are exchanged between the two transmission lines but a single photon in one line can completely block or enable the propagation of photons in the other line. High on-off ratios can be achieved for feasible experimental parameters. Our approach is inherently scalable as all photon pulses can have the same pulse shape and carrier frequency such that output signals of one transistor can be input signals for a consecutive transistor.
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Affiliation(s)
- Lukas Neumeier
- Technische Universität München, Physik Department, James Franck Straße, 85748 Garching, Germany.
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37
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Stassi R, Ridolfo A, Di Stefano O, Hartmann MJ, Savasta S. Spontaneous conversion from virtual to real photons in the ultrastrong-coupling regime. PHYSICAL REVIEW LETTERS 2013; 110:243601. [PMID: 25165920 DOI: 10.1103/physrevlett.110.243601] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/26/2013] [Indexed: 06/03/2023]
Abstract
We show that a spontaneous release of virtual photon pairs can occur in a quantum optical system in the ultrastrong coupling regime. In this regime, which is attracting interest both in semiconductor and superconducting systems, the light-matter coupling rate Ω(R) becomes comparable to the bare resonance frequency of photons ω(0). In contrast to the dynamical Casimir effect and other pair creation mechanisms, this phenomenon does not require external forces or time dependent parameters in the Hamiltonian.
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Affiliation(s)
- R Stassi
- Dipartimento di Fisica e Scienze della Terra, Università di Messina, Viale F. Stagno d'Alcontres 31, I-98166 Messina, Italy
| | - A Ridolfo
- Physik Department, Technische Universität München, 85748 Garching, Germany
| | - O Di Stefano
- Dipartimento di Fisica e Scienze della Terra, Università di Messina, Viale F. Stagno d'Alcontres 31, I-98166 Messina, Italy
| | - M J Hartmann
- Physik Department, Technische Universität München, 85748 Garching, Germany
| | - S Savasta
- Dipartimento di Fisica e Scienze della Terra, Università di Messina, Viale F. Stagno d'Alcontres 31, I-98166 Messina, Italy
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38
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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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39
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Devoret MH, Schoelkopf RJ. Superconducting Circuits for Quantum Information: An Outlook. Science 2013; 339:1169-74. [DOI: 10.1126/science.1231930] [Citation(s) in RCA: 1301] [Impact Index Per Article: 118.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
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40
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Adhikari P, Hafezi M, Taylor JM. Nonlinear optics quantum computing with circuit QED. PHYSICAL REVIEW LETTERS 2013; 110:060503. [PMID: 23432228 DOI: 10.1103/physrevlett.110.060503] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/15/2012] [Indexed: 06/01/2023]
Abstract
One approach to quantum information processing is to use photons as quantum bits and rely on linear optical elements for most operations. However, some optical nonlinearity is necessary to enable universal quantum computing. Here, we suggest a circuit-QED approach to nonlinear optics quantum computing in the microwave regime, including a deterministic two-photon phase gate. Our specific example uses a hybrid quantum system comprising a LC resonator coupled to a superconducting flux qubit to implement a nonlinear coupling. Compared to the self-Kerr nonlinearity, we find that our approach has improved tolerance to noise in the qubit while maintaining fast operation.
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Affiliation(s)
- Prabin Adhikari
- Joint Quantum Institute, University of Maryland, College Park, Maryland 20742, USA
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41
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Menzel EP, Di Candia R, Deppe F, Eder P, Zhong L, Ihmig M, Haeberlein M, Baust A, Hoffmann E, Ballester D, Inomata K, Yamamoto T, Nakamura Y, Solano E, Marx A, Gross R. Path entanglement of continuous-variable quantum microwaves. PHYSICAL REVIEW LETTERS 2012; 109:250502. [PMID: 23368439 DOI: 10.1103/physrevlett.109.250502] [Citation(s) in RCA: 30] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/08/2012] [Indexed: 06/01/2023]
Abstract
Path entanglement constitutes an essential resource in quantum information and communication protocols. Here, we demonstrate frequency-degenerate entanglement between continuous-variable quantum microwaves propagating along two spatially separated paths. We combine a squeezed and a vacuum state using a microwave beam splitter. Via correlation measurements, we detect and quantify the path entanglement contained in the beam splitter output state. Our experiments open the avenue to quantum teleportation, quantum communication, or quantum radar with continuous variables at microwave frequencies.
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Affiliation(s)
- E P Menzel
- Walther-Meißner-Institut, Bayerische Akademie der Wissenschaften, D-85748 Garching, Germany.
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42
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Eichler C, Lang C, Fink JM, Govenius J, Filipp S, Wallraff A. Observation of entanglement between itinerant microwave photons and a superconducting qubit. PHYSICAL REVIEW LETTERS 2012; 109:240501. [PMID: 23368292 DOI: 10.1103/physrevlett.109.240501] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/03/2012] [Indexed: 05/23/2023]
Abstract
A localized qubit entangled with a propagating quantum field is well suited to study nonlocal aspects of quantum mechanics and may also provide a channel to communicate between spatially separated nodes in a quantum network. Here, we report the on-demand generation and characterization of Bell-type entangled states between a superconducting qubit and propagating microwave fields composed of zero-, one-, and two-photon Fock states. Using low noise linear amplification and efficient data acquisition we extract all relevant correlations between the qubit and the photon states and demonstrate entanglement with high fidelity.
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Affiliation(s)
- C Eichler
- Department of Physics, ETH Zürich, CH-8093 Zürich, Switzerland.
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43
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Hoi IC, Palomaki T, Lindkvist J, Johansson G, Delsing P, Wilson CM. Generation of nonclassical microwave states using an artificial atom in 1D open space. PHYSICAL REVIEW LETTERS 2012; 108:263601. [PMID: 23004976 DOI: 10.1103/physrevlett.108.263601] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/10/2012] [Indexed: 06/01/2023]
Abstract
We have embedded an artificial atom, a superconducting transmon qubit, in a 1D open space and investigated the scattering properties of an incident microwave coherent state. By studying the statistics of the reflected and transmitted fields, we demonstrate that the scattered states can be nonclassical. In particular, by measuring the second-order correlation function, g((2)), we show photon antibunching in the reflected field and superbunching in the transmitted field. We also compare the elastically and inelastically scattered fields using both phase-sensitive and phase-insensitive measurements.
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Affiliation(s)
- Io-Chun Hoi
- Department of Microtechnology and Nanoscience (MC2), Chalmers University of Technology, SE-41296, Göteborg, Sweden
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44
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Genway S, Garrahan JP, Lesanovsky I, Armour AD. Phase transitions in trajectories of a superconducting single-electron transistor coupled to a resonator. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:051122. [PMID: 23004718 DOI: 10.1103/physreve.85.051122] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/11/2012] [Indexed: 06/01/2023]
Abstract
Recent progress in the study of dynamical phase transitions has been made with a large-deviation approach to study trajectories of stochastic jumps using a thermodynamic formalism. We study this method applied to an open quantum system consisting of a superconducting single-electron transistor, near the Josephson quasiparticle resonance, coupled to a resonator. We find that the dynamical behavior shown in rare trajectories can be rich even when the mean dynamical activity is small, and thus the formalism gives insights into the form of fluctuations. The structure of the dynamical phase diagram found from the quantum-jump trajectories of the resonator is studied, and we see that sharp transitions in the dynamical activity may be related to the appearance and disappearance of bistabilities in the state of the resonator as system parameters are changed. We also demonstrate that for a fast resonator, the trajectories of quasiparticles are similar to the resonator trajectories.
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Affiliation(s)
- Sam Genway
- School of Physics and Astronomy, University of Nottingham, Nottingham, NG7 2RD, United Kingdom
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45
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Chen YF, Hover D, Sendelbach S, Maurer L, Merkel ST, Pritchett EJ, Wilhelm FK, McDermott R. Microwave photon counter based on Josephson junctions. PHYSICAL REVIEW LETTERS 2011; 107:217401. [PMID: 22181922 DOI: 10.1103/physrevlett.107.217401] [Citation(s) in RCA: 32] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/28/2011] [Revised: 07/12/2011] [Indexed: 05/27/2023]
Abstract
We describe a microwave photon counter based on the current-biased Josephson junction. The junction is tuned to absorb single microwave photons from the incident field, after which it tunnels into a classically observable voltage state. Using two such detectors, we have performed a microwave version of the Hanbury Brown-Twiss experiment at 4 GHz and demonstrated a clear signature of photon bunching for a thermal source. The design is readily scalable to tens of parallelized junctions, a configuration that would allow number-resolved counting of microwave photons.
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Affiliation(s)
- Y-F Chen
- Department of Physics, University of Wisconsin, Madison, 53706, USA
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46
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Eichler C, Bozyigit D, Lang C, Baur M, Steffen L, Fink JM, Filipp S, Wallraff A. Observation of two-mode squeezing in the microwave frequency domain. PHYSICAL REVIEW LETTERS 2011; 107:113601. [PMID: 22026665 DOI: 10.1103/physrevlett.107.113601] [Citation(s) in RCA: 51] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/24/2011] [Revised: 06/08/2011] [Indexed: 05/31/2023]
Abstract
Continuous variable entanglement between two modes of a radiation field is usually studied at optical frequencies. Here we demonstrate experiments that show the entanglement between microwave photons of different energy in a broadband squeezed beam. We use a Josephson parametric amplifier to generate the two-mode correlated state and detect all four quadrature components simultaneously in a two-channel heterodyne setup using amplitude detectors. Analyzing two-dimensional phase space histograms for all possible pairs of quadratures allows us to determine the full covariance matrix, which is in good agreement with the one expected for a two-mode squeezed state.
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Affiliation(s)
- C Eichler
- Department of Physics, ETH Zürich, CH-8093, Zürich, Switzerland
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47
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Mallet F, Castellanos-Beltran MA, Ku HS, Glancy S, Knill E, Irwin KD, Hilton GC, Vale LR, Lehnert KW. Quantum state tomography of an itinerant squeezed microwave field. PHYSICAL REVIEW LETTERS 2011; 106:220502. [PMID: 21702586 DOI: 10.1103/physrevlett.106.220502] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/03/2010] [Indexed: 05/31/2023]
Abstract
We perform state tomography of an itinerant squeezed state of the microwave field prepared by a Josephson parametric amplifier (JPA). We use a second JPA as a preamplifier to improve the quantum efficiency of the field quadrature measurement from 2% to 36%±4%. Without correcting for the detection inefficiency we observe a minimum quadrature variance which is 68(-7)(+9)% of the variance of the vacuum. We reconstruct the state's density matrix by a maximum likelihood method and infer that the squeezed state has a minimum variance less than 40% of the vacuum, with uncertainty mostly caused by calibration systematics.
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Affiliation(s)
- F Mallet
- JILA, National Institute of Standards and Technology and the University of Colorado, Boulder, Colorado 80309, USA
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