1
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Setoyama W, Hasegawa Y. Lie Algebraic Quantum Phase Reduction. PHYSICAL REVIEW LETTERS 2024; 132:093602. [PMID: 38489612 DOI: 10.1103/physrevlett.132.093602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/01/2022] [Revised: 08/10/2023] [Accepted: 01/22/2024] [Indexed: 03/17/2024]
Abstract
We introduce a general framework of phase reduction theory for quantum nonlinear oscillators. By employing the quantum trajectory theory, we define the limit-cycle trajectory and the phase according to a stochastic Schrödinger equation. Because a perturbation is represented by unitary transformation in quantum dynamics, we calculate phase response curves with respect to generators of a Lie algebra. Our method shows that the continuous measurement yields phase clusters and alters the phase response curves. The observable clusters capture the phase dynamics of individual quantum oscillators, unlike indirect indicators obtained from density operators. Furthermore, our method can be applied to finite-level systems that lack classical counterparts.
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Affiliation(s)
- Wataru Setoyama
- Department of Information and Communication Engineering, Graduate School of Information Science and Technology, The University of Tokyo, Tokyo 113-8656, Japan
| | - Yoshihiko Hasegawa
- Department of Information and Communication Engineering, Graduate School of Information Science and Technology, The University of Tokyo, Tokyo 113-8656, Japan
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2
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Berritta F, Rasmussen T, Krzywda JA, van der Heijden J, Fedele F, Fallahi S, Gardner GC, Manfra MJ, van Nieuwenburg E, Danon J, Chatterjee A, Kuemmeth F. Real-time two-axis control of a spin qubit. Nat Commun 2024; 15:1676. [PMID: 38395978 PMCID: PMC10891052 DOI: 10.1038/s41467-024-45857-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/22/2023] [Accepted: 02/05/2024] [Indexed: 02/25/2024] Open
Abstract
Optimal control of qubits requires the ability to adapt continuously to their ever-changing environment. We demonstrate a real-time control protocol for a two-electron singlet-triplet qubit with two fluctuating Hamiltonian parameters. Our approach leverages single-shot readout classification and dynamic waveform generation, allowing full Hamiltonian estimation to dynamically stabilize and optimize the qubit performance. Powered by a field-programmable gate array (FPGA), the quantum control electronics estimates the Overhauser field gradient between the two electrons in real time, enabling controlled Overhauser-driven spin rotations and thus bypassing the need for micromagnets or nuclear polarization protocols. It also estimates the exchange interaction between the two electrons and adjusts their detuning, resulting in extended coherence of Hadamard rotations when correcting for fluctuations of both qubit axes. Our study highlights the role of feedback in enhancing the performance and stability of quantum devices affected by quasistatic noise.
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Affiliation(s)
- Fabrizio Berritta
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100, Copenhagen, Denmark.
| | - Torbjørn Rasmussen
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100, Copenhagen, Denmark
| | - Jan A Krzywda
- Lorentz Institute and Leiden Institute of Advanced Computer Science, Leiden University, P.O. Box 9506, 2300 RA, Leiden, The Netherlands
| | | | - Federico Fedele
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100, Copenhagen, Denmark
| | - Saeed Fallahi
- Department of Physics and Astronomy, Purdue University, West Lafayette, IN, 47907, USA
- Birck Nanotechnology Center, Purdue University, West Lafayette, IN, 47907, USA
| | - Geoffrey C Gardner
- Birck Nanotechnology Center, Purdue University, West Lafayette, IN, 47907, USA
| | - Michael J Manfra
- Department of Physics and Astronomy, Purdue University, West Lafayette, IN, 47907, USA
- Birck Nanotechnology Center, Purdue University, West Lafayette, IN, 47907, USA
- Elmore Family School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN, 47907, USA
- School of Materials Engineering, Purdue University, West Lafayette, IN, 47907, USA
| | - Evert van Nieuwenburg
- Lorentz Institute and Leiden Institute of Advanced Computer Science, Leiden University, P.O. Box 9506, 2300 RA, Leiden, The Netherlands
| | - Jeroen Danon
- Department of Physics, Norwegian University of Science and Technology, NO-7491, Trondheim, Norway
| | - Anasua Chatterjee
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100, Copenhagen, Denmark.
| | - Ferdinand Kuemmeth
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100, Copenhagen, Denmark.
- QDevil, Quantum Machines, 2750, Ballerup, Denmark.
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3
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Liu ZQ, Liu L, Meng ZZ, Tan L, Liu WM. Simultaneously enhanced magnomechanical cooling and entanglement assisted by an auxiliary microwave cavity. OPTICS EXPRESS 2024; 32:722-741. [PMID: 38175094 DOI: 10.1364/oe.504580] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/22/2023] [Accepted: 11/17/2023] [Indexed: 01/05/2024]
Abstract
We propose a mechanism to simultaneously enhance quantum cooling and entanglement via coupling an auxiliary microwave cavity to a magnomechanical cavity. The auxiliary cavity acts as a dissipative cold reservoir that can efficiently cool multiple localized modes in the primary system via beam-splitter interactions, which enables us to obtain strong quantum cooling and entanglement. We analyze the stability of the system and determine the optimal parameter regime for cooling and entanglement under the auxiliary-microwave-cavity-assisted (AMCA) scheme. The maximum cooling enhancement rate of the magnon mode can reach 98.53%, which clearly reveals that the magnomechanical cooling is significantly improved in the presence of the AMCA. More importantly, the dual-mode entanglement of the system can also be significantly enhanced by AMCA in the full parameter region, where the initial magnon-phonon entanglement can be maximally enhanced by a factor of about 11. Another important result of the AMCA is that it also increases the robustness of the entanglement against temperature. Our approach provides a promising platform for the experimental realization of entanglement and quantum information processing based on cavity magnomechanics.
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4
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Vijayan J, Zhang Z, Piotrowski J, Windey D, van der Laan F, Frimmer M, Novotny L. Scalable all-optical cold damping of levitated nanoparticles. NATURE NANOTECHNOLOGY 2023; 18:49-54. [PMID: 36411375 DOI: 10.1038/s41565-022-01254-6] [Citation(s) in RCA: 8] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/11/2022] [Accepted: 09/28/2022] [Indexed: 06/16/2023]
Abstract
Motional control of levitated nanoparticles relies on either autonomous feedback via a cavity or measurement-based feedback via external forces. Recent demonstrations of the measurement-based ground-state cooling of a single nanoparticle employ linear velocity feedback, also called cold damping, and require the use of electrostatic forces on charged particles via external electrodes. Here we introduce an all-optical cold damping scheme based on the spatial modulation of trap position, which has the advantage of being scalable to multiple particles. The scheme relies on programmable optical tweezers to provide full independent control over the trap frequency and position of each tweezer. We show that the technique cools the centre-of-mass motion of particles along one axis down to 17 mK at a pressure of 2 × 10-6 mbar and demonstrate its scalability by simultaneously cooling the motion of two particles. Our work paves the way towards studying quantum interactions between particles; achieving three-dimensional quantum control of particle motion without cavity-based cooling, electrodes or charged particles; and probing multipartite entanglement in levitated optomechanical systems.
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Affiliation(s)
| | - Zhao Zhang
- Photonics Laboratory, ETH Zürich, Zürich, Switzerland
| | | | | | | | | | - Lukas Novotny
- Photonics Laboratory, ETH Zürich, Zürich, Switzerland
- Quantum Center, ETH Zürich, Zürich, Switzerland
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5
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Annby-Andersson B, Bakhshinezhad F, Bhattacharyya D, De Sousa G, Jarzynski C, Samuelsson P, Potts PP. Quantum Fokker-Planck Master Equation for Continuous Feedback Control. PHYSICAL REVIEW LETTERS 2022; 129:050401. [PMID: 35960579 DOI: 10.1103/physrevlett.129.050401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/08/2021] [Accepted: 06/24/2022] [Indexed: 06/15/2023]
Abstract
Measurement and feedback control are essential features of quantum science, with applications ranging from quantum technology protocols to information-to-work conversion in quantum thermodynamics. Theoretical descriptions of feedback control are typically given in terms of stochastic equations requiring numerical solutions, or are limited to linear feedback protocols. Here we present a formalism for continuous quantum measurement and feedback, both linear and nonlinear. Our main result is a quantum Fokker-Planck master equation describing the joint dynamics of a quantum system and a detector with finite bandwidth. For fast measurements, we derive a Markovian master equation for the system alone, amenable to analytical treatment. We illustrate our formalism by investigating two basic information engines, one quantum and one classical.
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Affiliation(s)
| | - Faraj Bakhshinezhad
- Physics Department and NanoLund, Lund University, Box 118, 22100 Lund, Sweden
| | - Debankur Bhattacharyya
- Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA
| | - Guilherme De Sousa
- Department of Physics, University of Maryland, College Park, Maryland 20742, USA
| | - Christopher Jarzynski
- Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA
| | - Peter Samuelsson
- Physics Department and NanoLund, Lund University, Box 118, 22100 Lund, Sweden
| | - Patrick P Potts
- Physics Department and NanoLund, Lund University, Box 118, 22100 Lund, Sweden
- Department of Physics, University of Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland
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6
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Yao Y, Shao XQ. Optimal charging of open spin-chain quantum batteries via homodyne-based feedback control. Phys Rev E 2022; 106:014138. [PMID: 35974574 DOI: 10.1103/physreve.106.014138] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/05/2022] [Accepted: 07/08/2022] [Indexed: 06/15/2023]
Abstract
We study the problem of charging a dissipative one-dimensional XXX spin-chain quantum battery using local magnetic fields in the presence of spin decay. The introduction of quantum feedback control based on homodyne measurement contributes to improving various performances of the quantum battery, such as energy storage, ergotropy, and effective space utilization rate. For the zero-temperature environment, there is a set of optimal parameters to ensure that the spin-chain quantum battery can be fully charged and the energy stored in the battery can be fully extracted under the perfect measurement condition, which is found through the analytical calculation of a simple two-site spin-chain quantum battery and further verified by numerical simulation of a four-site spin-chain counterpart. For completeness, the adverse effects of imperfect measurement, anisotropic parameter, and finite temperature on the charging process of the quantum battery are also considered.
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Affiliation(s)
- Y Yao
- Center for Quantum Sciences and School of Physics, Northeast Normal University, Changchun 130024, China and Center for Advanced Optoelectronic Functional Materials Research, and Key Laboratory for UV Light-Emitting Materials and Technology of Ministry of Education, Northeast Normal University, Changchun 130024, China
| | - X Q Shao
- Center for Quantum Sciences and School of Physics, Northeast Normal University, Changchun 130024, China and Center for Advanced Optoelectronic Functional Materials Research, and Key Laboratory for UV Light-Emitting Materials and Technology of Ministry of Education, Northeast Normal University, Changchun 130024, China
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7
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Kolokoltsov VN. Quantum mean-field games. ANN APPL PROBAB 2022. [DOI: 10.1214/21-aap1733] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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8
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Manikandan SK, Elouard C, Murch KW, Auffèves A, Jordan AN. Efficiently fueling a quantum engine with incompatible measurements. Phys Rev E 2022; 105:044137. [PMID: 35590558 DOI: 10.1103/physreve.105.044137] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/29/2021] [Accepted: 03/25/2022] [Indexed: 06/15/2023]
Abstract
We propose a quantum harmonic oscillator measurement engine fueled by simultaneous quantum measurements of the noncommuting position and momentum quadratures of the quantum oscillator. The engine extracts work by moving the harmonic trap suddenly, conditioned on the measurement outcomes. We present two protocols for work extraction, respectively based on single-shot and time-continuous quantum measurements. In the single-shot limit, the oscillator is measured in a coherent state basis; the measurement adds an average of one quantum of energy to the oscillator, which is then extracted in the feedback step. In the time-continuous limit, continuous weak quantum measurements of both position and momentum of the quantum oscillator result in a coherent state, whose coordinates diffuse in time. We relate the extractable work to the noise added by quadrature measurements, and present exact results for the work distribution at arbitrary finite time. Both protocols can achieve unit work conversion efficiency in principle.
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Affiliation(s)
- Sreenath K Manikandan
- Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627, USA
- Center for Coherence and Quantum Optics, University of Rochester, Rochester, New York 14627, USA
- Nordita, KTH Royal Institute of Technology and Stockholm University, Hannes Alfvéns väg 12, SE-106 91 Stockholm, Sweden
| | - Cyril Elouard
- Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627, USA
- QUANTIC laboratory, INRIA Paris, 2 Rue Simone Iff, 75012 Paris, France
| | - Kater W Murch
- Department of Physics, Washington University, St. Louis, Missouri 63130, USA
| | - Alexia Auffèves
- Université Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, 38000 Grenoble, France
| | - Andrew N Jordan
- Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627, USA
- Center for Coherence and Quantum Optics, University of Rochester, Rochester, New York 14627, USA
- Institute for Quantum Studies, Chapman University, Orange, California, 92866, USA
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9
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Kiesewetter S, Drummond PD. Phase-space simulations of feedback coherent Ising machines. OPTICS LETTERS 2022; 47:649-652. [PMID: 35103702 DOI: 10.1364/ol.434114] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/14/2021] [Accepted: 12/12/2021] [Indexed: 06/14/2023]
Abstract
A new, to the best of our knowledge, technique is demonstrated for carrying out exact positive-P phase-space simulations of the coherent Ising machine quantum computer. By suitable design of the coupling matrix, general hard optimization problems can be solved. Here, computational quantum simulations of a feedback type of photonic parametric network are carried out, which is the implementation of the coherent Ising machine. Results for success rates are obtained using this scalable phase-space algorithm for quantum simulations of quantum feedback devices.
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10
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Anka MF, de Oliveira TR, Jonathan D. Measurement-based quantum heat engine in a multilevel system. Phys Rev E 2021; 104:054128. [PMID: 34942804 DOI: 10.1103/physreve.104.054128] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/06/2021] [Accepted: 10/25/2021] [Indexed: 11/07/2022]
Abstract
We compare quantum Otto engines based on two different cycle models: a two-bath model, with a standard heat source and sink, and a measurement-based protocol, where the role of heat source is played by a quantum measurement. We furthermore study these cycles using two different "working substances": a single qutrit (spin-1 particle) or a pair of qubits (spin-1/2 particles) interacting via the XXZ Heisenberg interaction. Although both cycle models have the same efficiency when applied on a single-qubit working substance, we find that both can reach higher efficiencies using these more complex working substances by exploiting the existence of "idle" levels, i.e., levels that do not shift while the spins are subjected to a variable magnetic field. Furthermore, with an appropriate choice of measurement, the measurement-based protocol becomes more efficient than the two-bath model.
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Affiliation(s)
- Maron F Anka
- Instituto de Física Universidade Federal Fluminense - Av. Gal. Milton Tavares de Souza s/n, 24210-346 Niterói, Rio de Janeiro, Brazil
| | - Thiago R de Oliveira
- Instituto de Física Universidade Federal Fluminense - Av. Gal. Milton Tavares de Souza s/n, 24210-346 Niterói, Rio de Janeiro, Brazil
| | - Daniel Jonathan
- Instituto de Física Universidade Federal Fluminense - Av. Gal. Milton Tavares de Souza s/n, 24210-346 Niterói, Rio de Janeiro, Brazil
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11
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Holubec V, Geiss D, Loos SAM, Kroy K, Cichos F. Finite-Size Scaling at the Edge of Disorder in a Time-Delay Vicsek Model. PHYSICAL REVIEW LETTERS 2021; 127:258001. [PMID: 35029446 DOI: 10.1103/physrevlett.127.258001] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/13/2021] [Revised: 09/29/2021] [Accepted: 11/16/2021] [Indexed: 06/14/2023]
Abstract
Living many-body systems often exhibit scale-free collective behavior reminiscent of thermal critical phenomena. But their mutual interactions are inevitably retarded due to information processing and delayed actuation. We numerically investigate the consequences for the finite-size scaling in the Vicsek model of motile active matter. A growing delay time initially facilitates but ultimately impedes collective ordering and turns the dynamical scaling from diffusive to ballistic. It provides an alternative explanation of swarm traits previously attributed to inertia.
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Affiliation(s)
- Viktor Holubec
- Institut für Theoretische Physik, Universität Leipzig, Postfach 100 920, D-04009 Leipzig, Germany
- Charles University, Faculty of Mathematics and Physics, Department of Macromolecular Physics, V Holešovičkách 2, CZ-180 00 Praha, Czech Republic
| | - Daniel Geiss
- Institut für Theoretische Physik, Universität Leipzig, Postfach 100 920, D-04009 Leipzig, Germany
- Max Planck Institute for Mathematics in the Sciences, D-04103 Leipzig, Germany
| | - Sarah A M Loos
- Institut für Theoretische Physik, Universität Leipzig, Postfach 100 920, D-04009 Leipzig, Germany
- ICTP - International Centre for Theoretical Physics, Strada Costiera 11, 34151, Trieste, Italy
| | - Klaus Kroy
- Institut für Theoretische Physik, Universität Leipzig, Postfach 100 920, D-04009 Leipzig, Germany
| | - Frank Cichos
- Peter Debye Institute for Soft Matter Physics, Universität Leipzig, 04103 Leipzig, Germany
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12
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Cerchiari G, Araneda G, Podhora L, Slodička L, Colombe Y, Blatt R. Measuring Ion Oscillations at the Quantum Level with Fluorescence Light. PHYSICAL REVIEW LETTERS 2021; 127:063603. [PMID: 34420343 DOI: 10.1103/physrevlett.127.063603] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/07/2020] [Accepted: 05/17/2021] [Indexed: 06/13/2023]
Abstract
We demonstrate an optical method for detecting the mechanical oscillations of an atom with single-phonon sensitivity. The measurement signal results from the interference between the light scattered by a trapped atomic ion and that of its mirror image. We detect the oscillations of the atom in the Doppler cooling limit and reconstruct average trajectories in phase space. We demonstrate single-phonon sensitivity near the ground state of motion after electronically induced transparency cooling. These results could be applied for motion detection of other light scatterers of fundamental interest, such as trapped nanoparticles.
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Affiliation(s)
- G Cerchiari
- Institut für Experimentalphysik, Universität Innsbruck, Technikerstrasse 25, 6020 Innsbruck, Austria
| | - G Araneda
- Institut für Experimentalphysik, Universität Innsbruck, Technikerstrasse 25, 6020 Innsbruck, Austria
- Department of Physics, University of Oxford, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, United Kingdom
| | - L Podhora
- Department of Optics, Palacký University, 17. Listopadu 12, 77146 Olomouc, Czech Republic
| | - L Slodička
- Department of Optics, Palacký University, 17. Listopadu 12, 77146 Olomouc, Czech Republic
| | - Y Colombe
- Institut für Experimentalphysik, Universität Innsbruck, Technikerstrasse 25, 6020 Innsbruck, Austria
| | - R 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
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13
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Abstract
Quantum games and mean-field games (MFG) represent two important new branches of game theory. In a recent paper the author developed quantum MFGs merging these two branches. These quantum MFGs were based on the theory of continuous quantum observations and filtering of diffusive type. In the present paper we develop the analogous quantum MFG theory based on continuous quantum observations and filtering of counting type. However, proving existence and uniqueness of the solutions for resulting limiting forward-backward system based on jump-type processes on manifolds seems to be more complicated than for diffusions. In this paper we only prove that if a solution exists, then it gives an ϵ-Nash equilibrium for the corresponding N-player quantum game. The existence of solutions is suggested as an interesting open problem.
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14
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Pluchar CM, Agrawal AR, Schenk E, Wilson DJ. Towards cavity-free ground-state cooling of an acoustic-frequency silicon nitride membrane. APPLIED OPTICS 2020; 59:G107-G111. [PMID: 32749322 DOI: 10.1364/ao.394388] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/03/2020] [Accepted: 05/10/2020] [Indexed: 06/11/2023]
Abstract
We demonstrate feedback cooling of a millimeter-scale, 40 kHz SiN membrane from room temperature to 5 mK (3000 phonons) using a Michelson interferometer, and discuss the challenges to ground-state cooling without an optical cavity. This advance appears within reach of current membrane technology, positioning it as a compelling alternative to levitated systems for quantum sensing and fundamental weak force measurements.
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15
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Ivanov DA, Ivanova TY, Caballero-Benitez SF, Mekhov IB. Cavityless self-organization of ultracold atoms due to the feedback-induced phase transition. Sci Rep 2020; 10:10550. [PMID: 32601416 PMCID: PMC7324615 DOI: 10.1038/s41598-020-67280-3] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/27/2020] [Accepted: 06/04/2020] [Indexed: 11/08/2022] Open
Abstract
Feedback is a general idea of modifying system behavior depending on the measurement outcomes. It spreads from natural sciences, engineering, and artificial intelligence to contemporary classical and rock music. Recently, feedback has been suggested as a tool to induce phase transitions beyond the dissipative ones and tune their universality class. Here, we propose and theoretically investigate a system possessing such a feedback-induced phase transition. The system contains a Bose-Einstein condensate placed in an optical potential with the depth that is feedback-controlled according to the intensity of the Bragg-reflected probe light. We show that there is a critical value of the feedback gain where the uniform gas distribution loses its stability and the ordered periodic density distribution emerges. Due to the external feedback, the presence of a cavity is not necessary for this type of atomic self-organization. We analyze the dynamics after a sudden change of the feedback control parameter. The feedback time constant is shown to determine the relaxation above the critical point. We show as well that the control algorithm with the derivative of the measured signal dramatically decreases the transient time.
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Affiliation(s)
- Denis A Ivanov
- St. Petersburg State University, Ulianovskaya 3, Petrodvorets, St. Petersburg, 198504, Russia.
| | - Tatiana Yu Ivanova
- St. Petersburg State University, Ulianovskaya 3, Petrodvorets, St. Petersburg, 198504, Russia
| | | | - Igor B Mekhov
- St. Petersburg State University, Ulianovskaya 3, Petrodvorets, St. Petersburg, 198504, Russia
- University of Oxford, Department of Physics, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, Oxford, UK
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16
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Sommer C, Asjad M, Genes C. Prospects of reinforcement learning for the simultaneous damping of many mechanical modes. Sci Rep 2020; 10:2623. [PMID: 32060483 PMCID: PMC7021687 DOI: 10.1038/s41598-020-59435-z] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/25/2019] [Accepted: 01/28/2020] [Indexed: 11/08/2022] Open
Abstract
We apply adaptive feedback for the partial refrigeration of a mechanical resonator, i.e. with the aim to simultaneously cool the classical thermal motion of more than one vibrational degree of freedom. The feedback is obtained from a neural network parametrized policy trained via a reinforcement learning strategy to choose the correct sequence of actions from a finite set in order to simultaneously reduce the energy of many modes of vibration. The actions are realized either as optical modulations of the spring constants in the so-called quadratic optomechanical coupling regime or as radiation pressure induced momentum kicks in the linear coupling regime. As a proof of principle we numerically illustrate efficient simultaneous cooling of four independent modes with an overall strong reduction of the total system temperature.
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Affiliation(s)
- Christian Sommer
- Max Planck Institute for the Science of Light, Staudtstraße 2, D-91058, Erlangen, Germany.
| | - Muhammad Asjad
- Max Planck Institute for the Science of Light, Staudtstraße 2, D-91058, Erlangen, Germany
| | - Claudiu Genes
- Max Planck Institute for the Science of Light, Staudtstraße 2, D-91058, Erlangen, Germany
- Department of Physics, University of Erlangen-Nuremberg, Staudtstraße 2, D-91058, Erlangen, Germany
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17
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Sommer C, Genes C. Partial Optomechanical Refrigeration via Multimode Cold-Damping Feedback. PHYSICAL REVIEW LETTERS 2019; 123:203605. [PMID: 31809091 DOI: 10.1103/physrevlett.123.203605] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/21/2019] [Indexed: 06/10/2023]
Abstract
We provide a fully analytical treatment for the partial refrigeration of the thermal motion of a quantum mechanical resonator under the action of feedback. As opposed to standard cavity optomechanics where the aim is to isolate and cool a single mechanical mode, the aim here is to extract the thermal energy from many vibrational modes within a large frequency bandwidth. We consider a standard cold-damping technique, where homodyne readout of the cavity output field is fed into a feedback loop that provides a cooling action directly applied on the mechanical resonator. Analytical and numerical results predict that low final occupancies are achievable independent of the number of modes addressed by the feedback, as long as the cooling rate is smaller than the intermode frequency separation. For resonators exhibiting a few nearly degenerate pairs of modes, cooling is less efficient and a weak dependence on the number of modes is obtained. These scalings hint toward the design of frequency-resolved mechanical resonators, where efficient refrigeration is possible via simultaneous cold-damping feedback.
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Affiliation(s)
- Christian Sommer
- Max Planck Institute for the Science of Light, Staudtstraße 2, D-91058 Erlangen, Germany
| | - Claudiu Genes
- Max Planck Institute for the Science of Light, Staudtstraße 2, D-91058 Erlangen, Germany
- Department of Physics, University of Erlangen-Nuremberg, Staudtstraße 2, D-91058 Erlangen, Germany
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18
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Conangla GP, Ricci F, Cuairan MT, Schell AW, Meyer N, Quidant R. Optimal Feedback Cooling of a Charged Levitated Nanoparticle with Adaptive Control. PHYSICAL REVIEW LETTERS 2019; 122:223602. [PMID: 31283263 DOI: 10.1103/physrevlett.122.223602] [Citation(s) in RCA: 20] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/31/2018] [Indexed: 06/09/2023]
Abstract
We use an optimal control protocol to cool one mode of the center-of-mass motion of an optically levitated nanoparticle. The feedback technique relies on exerting a Coulomb force on a charged particle with a pair of electrodes and follows the control law of a linear quadratic regulator, whose gains are optimized by a machine learning algorithm in under 5 s. With a simpler and more robust setup than optical feedback schemes, we achieve a minimum center-of-mass temperature of 5 mK at 3×10^{-7} mbar and transients 10-600 times faster than cold damping. This cooling technique can be easily extended to 3D cooling and is particularly relevant for studies demanding high repetition rates and force sensing experiments with levitated objects.
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Affiliation(s)
- Gerard P Conangla
- ICFO Institut de Ciencies Fotoniques, Mediterranean Technology Park, 08860 Castelldefels (Barcelona), Spain
| | - Francesco Ricci
- ICFO Institut de Ciencies Fotoniques, Mediterranean Technology Park, 08860 Castelldefels (Barcelona), Spain
| | - Marc T Cuairan
- ICFO Institut de Ciencies Fotoniques, Mediterranean Technology Park, 08860 Castelldefels (Barcelona), Spain
| | - Andreas W Schell
- ICFO Institut de Ciencies Fotoniques, Mediterranean Technology Park, 08860 Castelldefels (Barcelona), Spain
- Quantum Optical Technology Group, Central European Institute of Technology, Brno University of Technology, 612 00 Brno, Czech Republic
| | - Nadine Meyer
- ICFO Institut de Ciencies Fotoniques, Mediterranean Technology Park, 08860 Castelldefels (Barcelona), Spain
| | - Romain Quidant
- ICFO Institut de Ciencies Fotoniques, Mediterranean Technology Park, 08860 Castelldefels (Barcelona), Spain
- ICREA-Institució Catalana de Recerca i Estudis Avançats, 08010 Barcelona, Spain
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19
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Tebbenjohanns F, Frimmer M, Militaru A, Jain V, Novotny L. Cold Damping of an Optically Levitated Nanoparticle to Microkelvin Temperatures. PHYSICAL REVIEW LETTERS 2019; 122:223601. [PMID: 31283294 DOI: 10.1103/physrevlett.122.223601] [Citation(s) in RCA: 34] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/24/2018] [Indexed: 06/09/2023]
Abstract
We implement a cold-damping scheme to cool one mode of the center-of-mass motion of an optically levitated nanoparticle in ultrahigh vacuum (10^{-8} mbar) from room temperature to a record-low temperature of 100 μK. The measured temperature dependence on the feedback gain and thermal decoherence rate is in excellent agreement with a parameter-free model. For the first time, we determine the imprecision-backaction product for a levitated optomechanical system and discuss the resulting implications for ground-state cooling of an optically levitated nanoparticle.
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Affiliation(s)
| | - Martin Frimmer
- Photonics Laboratory, ETH Zürich, CH-8093 Zürich, Switzerland
| | - Andrei Militaru
- Photonics Laboratory, ETH Zürich, CH-8093 Zürich, Switzerland
| | - Vijay Jain
- Photonics Laboratory, ETH Zürich, CH-8093 Zürich, Switzerland
| | - Lukas Novotny
- Photonics Laboratory, ETH Zürich, CH-8093 Zürich, Switzerland
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20
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Measurement-based quantum control of mechanical motion. Nature 2018; 563:53-58. [DOI: 10.1038/s41586-018-0643-8] [Citation(s) in RCA: 187] [Impact Index Per Article: 31.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/31/2018] [Accepted: 09/13/2018] [Indexed: 11/08/2022]
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21
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Pichler H, Zoller P. Photonic Circuits with Time Delays and Quantum Feedback. PHYSICAL REVIEW LETTERS 2016; 116:093601. [PMID: 26991174 DOI: 10.1103/physrevlett.116.093601] [Citation(s) in RCA: 29] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/15/2015] [Indexed: 06/05/2023]
Abstract
We study the dynamics of photonic quantum circuits consisting of nodes coupled by quantum channels. We are interested in the regime where the time delay in communication between the nodes is significant. This includes the problem of quantum feedback, where a quantum signal is fed back on a system with a time delay. We develop a matrix product state approach to solve the quantum stochastic Schrödinger equation with time delays, which accounts in an efficient way for the entanglement of nodes with the stream of emitted photons in the waveguide, and thus the non-Markovian character of the dynamics. We illustrate this approach with two paradigmatic quantum optical examples: two coherently driven distant atoms coupled to a photonic waveguide with a time delay, and a driven atom coupled to its own output field with a time delay as an instance of a quantum feedback problem.
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Affiliation(s)
- Hannes Pichler
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, A-6020 Innsbruck, Austria and Institute for Theoretical Physics, University of Innsbruck, A-6020 Innsbruck, Austria
| | - Peter Zoller
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, A-6020 Innsbruck, Austria and Institute for Theoretical Physics, University of Innsbruck, A-6020 Innsbruck, Austria
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22
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23
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Guevara I, Wiseman H. Quantum State Smoothing. PHYSICAL REVIEW LETTERS 2015; 115:180407. [PMID: 26565446 DOI: 10.1103/physrevlett.115.180407] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/13/2015] [Indexed: 06/05/2023]
Abstract
Smoothing is an estimation method whereby a classical state (probability distribution for classical variables) at a given time is conditioned on all-time (both earlier and later) observations. Here we define a smoothed quantum state for a partially monitored open quantum system, conditioned on an all-time monitoring-derived record. We calculate the smoothed distribution for a hypothetical unobserved record which, when added to the real record, would complete the monitoring, yielding a pure-state "quantum trajectory." Averaging the pure state over this smoothed distribution yields the (mixed) smoothed quantum state. We study how the choice of actual unraveling affects the purity increase over that of the conventional (filtered) state conditioned only on the past record.
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Affiliation(s)
- Ivonne Guevara
- Centre for Quantum Computation and Communication Technology (Australian Research Council), Centre for Quantum Dynamics, Griffith University, Brisbane, Queensland 4111, Australia
| | - Howard Wiseman
- Centre for Quantum Computation and Communication Technology (Australian Research Council), Centre for Quantum Dynamics, Griffith University, Brisbane, Queensland 4111, Australia
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24
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Measurement-based control of a mechanical oscillator at its thermal decoherence rate. Nature 2015; 524:325-9. [DOI: 10.1038/nature14672] [Citation(s) in RCA: 204] [Impact Index Per Article: 22.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/17/2014] [Accepted: 06/03/2015] [Indexed: 11/09/2022]
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25
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Abstract
Quantum thermodynamics supplies a consistent description of quantum heat engines and refrigerators up to a single few-level system coupled to the environment. Once the environment is split into three (a hot, cold, and work reservoir), a heat engine can operate. The device converts the positive gain into power, with the gain obtained from population inversion between the components of the device. Reversing the operation transforms the device into a quantum refrigerator. The quantum tricycle, a device connected by three external leads to three heat reservoirs, is used as a template for engines and refrigerators. The equation of motion for the heat currents and power can be derived from first principles. Only a global description of the coupling of the device to the reservoirs is consistent with the first and second laws of thermodynamics. Optimization of the devices leads to a balanced set of parameters in which the couplings to the three reservoirs are of the same order and the external driving field is in resonance. When analyzing refrigerators, one needs to devote special attention to a dynamical version of the third law of thermodynamics. Bounds on the rate of cooling when Tc→0 are obtained by optimizing the cooling current. All refrigerators as Tc→0 show universal behavior. The dynamical version of the third law imposes restrictions on the scaling as Tc→0 of the relaxation rate γc and heat capacity cV of the cold bath.
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Affiliation(s)
- Ronnie Kosloff
- Institute of Chemistry, The Hebrew University, Jerusalem 91904, Israel;
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26
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Su SL, Shao XQ, Wang HF, Zhang S. Preparation of three-dimensional entanglement for distant atoms in coupled cavities via atomic spontaneous emission and cavity decay. Sci Rep 2014; 4:7566. [PMID: 25523944 PMCID: PMC4271254 DOI: 10.1038/srep07566] [Citation(s) in RCA: 30] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/24/2014] [Accepted: 12/01/2014] [Indexed: 11/15/2022] Open
Abstract
We propose a dissipative scheme to prepare a three-dimensional entangled state for two atoms trapped in separate coupled cavities. Our work shows that both atomic spontaneous emission and cavity decay, which are two typical obstacles in unitary-dynamics-based schemes, are no longer detrimental, but necessary for three-dimensional entangled state preparation without specifying initial state and controlling the evolution time precisely. Final numerical simulation with one group of experimental parameters indicates that the performance of our scheme could be better than the unitary-dynamics-based scheme.
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Affiliation(s)
- Shi-Lei Su
- Department of Physics, Harbin Institute of Technology, Harbin 150001, China
- Department of Physics, College of Science, YanBian University, Yanji, Jilin 133002, China
| | - Xiao-Qiang Shao
- Centre for Quantum Sciences and School of Physics, Northeast Normal University, Changchun 130024, China
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore, 117543
| | - Hong-Fu Wang
- Department of Physics, College of Science, YanBian University, Yanji, Jilin 133002, China
| | - Shou Zhang
- Department of Physics, Harbin Institute of Technology, Harbin 150001, China
- Department of Physics, College of Science, YanBian University, Yanji, Jilin 133002, China
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27
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Szigeti SS, Carvalho ARR, Morley JG, Hush MR. Ignorance is bliss: general and robust cancellation of decoherence via no-knowledge quantum feedback. PHYSICAL REVIEW LETTERS 2014; 113:020407. [PMID: 25062148 DOI: 10.1103/physrevlett.113.020407] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/04/2014] [Indexed: 06/03/2023]
Abstract
A "no-knowledge" measurement of an open quantum system yields no information about any system observable; it only returns noise input from the environment. Surprisingly, performing such a no-knowledge measurement can be advantageous. We prove that a system undergoing no-knowledge monitoring has reversible noise, which can be canceled by directly feeding back the measurement signal. We show how no-knowledge feedback control can be used to cancel decoherence in an arbitrary quantum system coupled to a Markovian reservoir that is being monitored. Since no-knowledge feedback does not depend on the system state or Hamiltonian, such decoherence cancellation is guaranteed to be general and robust, and can operate in conjunction with any other quantum control protocol. As an application, we show that no-knowledge feedback could be used to improve the performance of dissipative quantum computers subjected to local loss.
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Affiliation(s)
| | - Andre R R Carvalho
- Department of Quantum Science, Research School of Physics and Engineering, The Australian National University, Canberra, Australian Capital Territory 0200, Australia and ARC Centre for Quantum Computation and Communication Technology, The Australian National University, Canberra, Australian Capital Territory 0200, Australia
| | - James G Morley
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - Michael R Hush
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
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28
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Hofer SG, Vasilyev DV, Aspelmeyer M, Hammerer K. Time-continuous Bell measurements. PHYSICAL REVIEW LETTERS 2013; 111:170404. [PMID: 24206465 DOI: 10.1103/physrevlett.111.170404] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/28/2013] [Indexed: 06/02/2023]
Abstract
We combine the concept of Bell measurements, in which two systems are projected into a maximally entangled state, with the concept of continuous measurements, which concerns the evolution of a continuously monitored quantum system. For such time-continuous Bell measurements we derive the corresponding stochastic Schrödinger equations, as well as the unconditional feedback master equations. Our results apply to a wide range of physical systems, and are easily adapted to describe an arbitrary number of systems and measurements. Time-continuous Bell measurements therefore provide a versatile tool for the control of complex quantum systems and networks. As examples we show that (i) two two-level systems can be deterministically entangled via homodyne detection, tolerating photon loss up to 50%, and (ii) a quantum state of light can be continuously teleported to a mechanical oscillator, which works under the same conditions as are required for optomechanical ground-state cooling.
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Affiliation(s)
- Sebastian G Hofer
- Vienna Center for Quantum Science and Technology (VCQ), Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria and Institute for Theoretical Physics, Institute for Gravitational Physics (Albert Einstein Institute), Leibniz University Hannover, Callinstraße 38, 30167 Hannover, Germany
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29
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Behbood N, Colangelo G, Ciurana FM, Napolitano M, Sewell RJ, Mitchell MW. Feedback cooling of an atomic spin ensemble. PHYSICAL REVIEW LETTERS 2013; 111:103601. [PMID: 25166664 DOI: 10.1103/physrevlett.111.103601] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/24/2013] [Indexed: 06/03/2023]
Abstract
We apply entropy removal by measurement and feedback to a cold atomic spin ensemble. Using quantum nondemolition probing by Faraday rotation measurement, and feedback by weak optical pumping, we drive the initially random collective spin variable F toward the origin F=0. We use input-output relations and ensemble quantum noise models to describe this quantum control process and identify an optimal two-round control procedure. We observe 12 dB of spin noise reduction, or a factor-of-63 reduction in phase-space volume. The method offers a nonthermal route to generation of exotic entangled states in ultracold gases, including macroscopic singlet states and strongly correlated states of quantum lattice gases.
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Affiliation(s)
- N Behbood
- ICFO-Institut de Ciencies Fotoniques, Mediterranean Technology Park, 08860 Castelldefels (Barcelona), Spain
| | - G Colangelo
- ICFO-Institut de Ciencies Fotoniques, Mediterranean Technology Park, 08860 Castelldefels (Barcelona), Spain
| | - F Martin Ciurana
- ICFO-Institut de Ciencies Fotoniques, Mediterranean Technology Park, 08860 Castelldefels (Barcelona), Spain
| | - M Napolitano
- ICFO-Institut de Ciencies Fotoniques, Mediterranean Technology Park, 08860 Castelldefels (Barcelona), Spain
| | - R J Sewell
- ICFO-Institut de Ciencies Fotoniques, Mediterranean Technology Park, 08860 Castelldefels (Barcelona), Spain
| | - M W Mitchell
- ICFO-Institut de Ciencies Fotoniques, Mediterranean Technology Park, 08860 Castelldefels (Barcelona), Spain and ICREA-Institució Catalana de Recerca i Estudis Avançats, 08015 Barcelona, Spain
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30
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31
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Bushev P, Hétet G, Slodička L, Rotter D, Wilson MA, Schmidt-Kaler F, Eschner J, Blatt R. Shot-noise-limited monitoring and phase locking of the motion of a single trapped ion. PHYSICAL REVIEW LETTERS 2013; 110:133602. [PMID: 23581319 DOI: 10.1103/physrevlett.110.133602] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/10/2012] [Revised: 12/05/2012] [Indexed: 06/02/2023]
Abstract
We perform a high-resolution real-time readout of the motion of a single trapped and laser-cooled Ba+ ion. By using an interferometric setup, we demonstrate a shot-noise-limited measurement of thermal oscillations with a resolution of 4 times the standard quantum limit. We apply the real-time monitoring for phase control of the ion motion through a feedback loop, suppressing the photon recoil-induced phase diffusion. Because of the spectral narrowing in the phase-locked mode, the coherent ion oscillation is measured with a resolution of about 0.3 times the standard quantum limit.
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Affiliation(s)
- P Bushev
- Physikalisches Institut, Karlsruher Institut für Technologie, D-76128 Karlsruhe, Germany
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32
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Ristè D, Bultink CC, Lehnert KW, DiCarlo L. Feedback control of a solid-state qubit using high-fidelity projective measurement. PHYSICAL REVIEW LETTERS 2012; 109:240502. [PMID: 23368293 DOI: 10.1103/physrevlett.109.240502] [Citation(s) in RCA: 42] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/12/2012] [Indexed: 06/01/2023]
Abstract
We demonstrate feedback control of a superconducting transmon qubit using discrete, projective measurement and conditional coherent driving. Feedback realizes a fast and deterministic qubit reset to a target state with 2.4% error averaged over input superposition states, and allows concatenating experiments more than 10 times faster than by passive initialization. This closed-loop qubit control is necessary for measurement-based protocols such as quantum error correction and teleportation.
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Affiliation(s)
- D Ristè
- Kavli Institute of Nanoscience, Delft University of Technology, PO Box 5046, 2600 GA Delft, The Netherlands
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33
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Hamerly R, Mabuchi H. Advantages of coherent feedback for cooling quantum oscillators. PHYSICAL REVIEW LETTERS 2012; 109:173602. [PMID: 23215186 DOI: 10.1103/physrevlett.109.173602] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/31/2012] [Revised: 07/03/2012] [Indexed: 06/01/2023]
Abstract
We model the cooling of open optical and optomechanical resonators via optical feedback in the linear quadratic Gaussian setting of stochastic control theory. We show that coherent feedback control schemes, in which the resonator is embedded in an interferometer to achieve all-optical feedback, can outperform the best possible linear quadratic Gaussian measurement-based schemes in the quantum regime of low steady-state excitation number. Such performance gains are attributed to the coherent controller's ability to process noncommuting output field quadratures simultaneously without loss of fidelity, and may provide important clues for the design of coherent feedback schemes for more general problems of nonlinear and robust control.
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Affiliation(s)
- Ryan Hamerly
- Edward L. Ginzton Laboratory, Stanford University, Stanford, California 94305, USA.
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34
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Cormick C, Morigi G. Structural transitions of ion strings in quantum potentials. PHYSICAL REVIEW LETTERS 2012; 109:053003. [PMID: 23006169 DOI: 10.1103/physrevlett.109.053003] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/02/2012] [Indexed: 06/01/2023]
Abstract
We analyze the stability and dynamics of an ion chain confined inside a high-finesse optical resonator. When the dipolar transition of the ions strongly couples to one cavity mode, the mechanical effects of light modify the chain properties close to a structural transition. We focus on the linear chain close to the zigzag instability and show that linear and zigzag arrays are bistable for certain strengths of the laser pumping the cavity. For these regimes the chain is cooled into one of the configurations by cavity-enhanced photon scattering. The excitations of these structures mix photonic and vibrational fluctuations, which can be entangled at steady state. These features are signaled by Fano-like resonances in the spectrum of light at the cavity output.
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Affiliation(s)
- Cecilia Cormick
- Theoretische Physik, Universität des Saarlandes, Saarbrücken, Germany
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35
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Levy A, Alicki R, Kosloff R. Quantum refrigerators and the third law of thermodynamics. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:061126. [PMID: 23005070 DOI: 10.1103/physreve.85.061126] [Citation(s) in RCA: 30] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/30/2012] [Indexed: 06/01/2023]
Abstract
The rate of temperature decrease of a cooled quantum bath is studied as its temperature is reduced to absolute zero. The third law of thermodynamics is then quantified dynamically by evaluating the characteristic exponent ζ of the cooling process dT(t)/dt∼-T^{ζ} when approaching absolute zero, T→0. A continuous model of a quantum refrigerator is employed consisting of a working medium composed either by two coupled harmonic oscillators or two coupled two-level systems. The refrigerator is a nonlinear device merging three currents from three heat baths: a cold bath to be cooled, a hot bath as an entropy sink, and a driving bath which is the source of cooling power. A heat-driven refrigerator (absorption refrigerator) is compared to a power-driven refrigerator. When optimized, both cases lead to the same exponent ζ, showing a lack of dependence on the form of the working medium and the characteristics of the drivers. The characteristic exponent is therefore determined by the properties of the cold reservoir and its interaction with the system. Two generic heat bath models are considered: a bath composed of harmonic oscillators and a bath composed of ideal Bose/Fermi gas. The restrictions on the interaction Hamiltonian imposed by the third law are discussed. In the Appendices, the theory of periodically driven open systems and its implication for thermodynamics are outlined.
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Affiliation(s)
- Amikam Levy
- Institute of Chemistry, The Hebrew University, Jerusalem 91904, Israel
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36
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Levy A, Kosloff R. Quantum absorption refrigerator. PHYSICAL REVIEW LETTERS 2012; 108:070604. [PMID: 22401189 DOI: 10.1103/physrevlett.108.070604] [Citation(s) in RCA: 33] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/30/2011] [Indexed: 05/31/2023]
Abstract
A quantum absorption refrigerator driven by noise is studied with the purpose of determining the limitations of cooling to absolute zero. The model consists of a working medium coupled simultaneously to hot, cold, and noise baths. Explicit expressions for the cooling power are obtained for Gaussian and Poisson white noise. The quantum model is consistent with the first and second laws of thermodynamics. The third law is quantified; the cooling power J(c) vanishes as J(c) ∝ T(c)(α), when T(c)→0, where α=d+1 for dissipation by emission and absorption of quanta described by a linear coupling to a thermal bosonic field, where d is the dimension of the bath.
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Affiliation(s)
- Amikam Levy
- Institute of Chemistry, The Hebrew University, Jerusalem 91904, Israel
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37
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Sayrin C, Dotsenko I, Zhou X, Peaudecerf B, Rybarczyk T, Gleyzes S, Rouchon P, Mirrahimi M, Amini H, Brune M, Raimond JM, Haroche S. Real-time quantum feedback prepares and stabilizes photon number states. Nature 2011; 477:73-7. [PMID: 21886159 DOI: 10.1038/nature10376] [Citation(s) in RCA: 406] [Impact Index Per Article: 31.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/02/2011] [Accepted: 07/19/2011] [Indexed: 11/09/2022]
Abstract
Feedback loops are central to most classical control procedures. A controller compares the signal measured by a sensor (system output) with the target value or set-point. It then adjusts an actuator (system input) to stabilize the signal around the target value. Generalizing this scheme to stabilize a micro-system's quantum state relies on quantum feedback, which must overcome a fundamental difficulty: the sensor measurements cause a random back-action on the system. An optimal compromise uses weak measurements, providing partial information with minimal perturbation. The controller should include the effect of this perturbation in the computation of the actuator's operation, which brings the incrementally perturbed state closer to the target. Although some aspects of this scenario have been experimentally demonstrated for the control of quantum or classical micro-system variables, continuous feedback loop operations that permanently stabilize quantum systems around a target state have not yet been realized. Here we have implemented such a real-time stabilizing quantum feedback scheme following a method inspired by ref. 13. It prepares on demand photon number states (Fock states) of a microwave field in a superconducting cavity, and subsequently reverses the effects of decoherence-induced field quantum jumps. The sensor is a beam of atoms crossing the cavity, which repeatedly performs weak quantum non-demolition measurements of the photon number. The controller is implemented in a real-time computer commanding the actuator, which injects adjusted small classical fields into the cavity between measurements. The microwave field is a quantum oscillator usable as a quantum memory or as a quantum bus swapping information between atoms. Our experiment demonstrates that active control can generate non-classical states of this oscillator and combat their decoherence, and is a significant step towards the implementation of complex quantum information operations.
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Affiliation(s)
- Clément Sayrin
- Laboratoire Kastler Brossel, ENS, UPMC-Paris 6, CNRS, 24 rue Lhomond, 75005 Paris, France
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38
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Koch M, Sames C, Kubanek A, Apel M, Balbach M, Ourjoumtsev A, Pinkse PWH, Rempe G. Feedback cooling of a single neutral atom. PHYSICAL REVIEW LETTERS 2010; 105:173003. [PMID: 21231041 DOI: 10.1103/physrevlett.105.173003] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/09/2010] [Indexed: 05/30/2023]
Abstract
We demonstrate feedback cooling of the motion of a single rubidium atom trapped in a high-finesse optical resonator to a temperature of about 160 μK. Time-dependent transmission and intensity-correlation measurements prove the reduction of the atomic position uncertainty. The feedback increases the 1/e storage time into the 1 s regime, 30 times longer than without feedback. Feedback cooling therefore rivals state-of-the-art laser cooling, but with the advantages that it requires less optical access and exhibits less optical pumping.
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Affiliation(s)
- Markus Koch
- Max-Planck-Institut für Quantenoptik, Garching, Germany.
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39
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Kosloff R, Feldmann T. Optimal performance of reciprocating demagnetization quantum refrigerators. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:011134. [PMID: 20866592 DOI: 10.1103/physreve.82.011134] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/01/2010] [Indexed: 05/29/2023]
Abstract
A reciprocating quantum refrigerator is studied with the purpose of determining the limitations of cooling to absolute zero. The cycle is based on demagnetization and magnetization of a working medium. We find that if the energy spectrum of the working medium possesses an uncontrollable gap, and in addition there is noise on the controls, then there is a minimum achievable temperature above zero. The reason is that even a negligible amount of noise prevents adiabatic following during the demagnetization stage. This results with a minimum temperature, Tc(min)>0, which scales with the energy gap. The refrigerator is based on an Otto cycle where the working medium is an interacting spin system with an energy gap. For this system the external control Hamiltonian does not commute with the internal interaction. As a result during the demagnetization and magnetization segments of the operating cycle the system cannot follow adiabatically the temporal change in the energy levels. We connect the nonadiabatic dynamics to quantum friction. An adiabatic measure is defined characterizing the rate of change of the Hamiltonian. Closed-form solutions are found for a constant adiabatic measure for all the cycle segments. We have identified a family of quantized frictionless cycles with increasing cycle times. These cycles minimize the entropy production. Such frictionless cycles are able to cool to Tc=0. External noise on the controls eliminates these frictionless cycles. The influence of phase and amplitude noise on the demagnetization and magnetization segments is explicitly derived. An extensive numerical study of optimal cooling cycles was carried out which showed that at sufficiently low temperature the noise always dominated restricting the minimum temperature.
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Affiliation(s)
- Ronnie Kosloff
- Institute of Chemistry, The Hebrew University, Jerusalem 91904, Israel
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40
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Gillett GG, Dalton RB, Lanyon BP, Almeida MP, Barbieri M, Pryde GJ, O'Brien JL, Resch KJ, Bartlett SD, White AG. Experimental feedback control of quantum systems using weak measurements. PHYSICAL REVIEW LETTERS 2010; 104:080503. [PMID: 20366921 DOI: 10.1103/physrevlett.104.080503] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/24/2009] [Indexed: 05/29/2023]
Abstract
A goal of the emerging field of quantum control is to develop methods for quantum technologies to function robustly in the presence of noise. Central issues are the fundamental limitations on the available information about quantum systems and the disturbance they suffer in the process of measurement. In the context of a simple quantum control scenario-the stabilization of nonorthogonal states of a qubit against dephasing-we experimentally explore the use of weak measurements in feedback control. We find that, despite the intrinsic difficultly of implementing them, weak measurements allow us to control the qubit better in practice than is even theoretically possible without them. Our work shows that these more general quantum measurements can play an important role for feedback control of quantum systems.
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Affiliation(s)
- G G Gillett
- Department of Physics and Centre for Quantum Computer Technology, The University of Queensland, Brisbane 4072, Australia.
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Kubanek A, Koch M, Sames C, Ourjoumtsev A, Pinkse PWH, Murr K, Rempe G. Photon-by-photon feedback control of a single-atom trajectory. Nature 2009; 462:898-901. [DOI: 10.1038/nature08563] [Citation(s) in RCA: 67] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/17/2009] [Accepted: 10/07/2009] [Indexed: 11/09/2022]
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42
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Gerber S, Rotter D, Slodicka L, Eschner J, Carmichael HJ, Blatt R. Intensity-field correlation of single-atom resonance fluorescence. PHYSICAL REVIEW LETTERS 2009; 102:183601. [PMID: 19518869 DOI: 10.1103/physrevlett.102.183601] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/10/2008] [Indexed: 05/27/2023]
Abstract
We report measurements of an intensity-field correlation function of the resonance fluorescence of a single trapped 138Ba+ ion. Detection of a photon prepares the atom in its ground state, and we observe its subsequent evolution under interaction with a laser field of well-defined phase. We record the regression of the resonance fluorescence source field. This provides a direct measurement of the field of the radiating dipole of a single atom and exhibits its strong nonclassical behavior. In the setup, an interference measurement is conditioned on the detection of a fluorescence photon.
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Affiliation(s)
- S Gerber
- Institute of Experimental Physics, University of Innsbruck, Technikerstr. 25, A-6020 Innsbruck, Austria
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43
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Sassin NA, Everhart SC, Dangi BB, Ervin KM, Cline JI. Fluorescence and photodissociation of rhodamine 575 cations in a quadrupole ion trap. JOURNAL OF THE AMERICAN SOCIETY FOR MASS SPECTROMETRY 2009; 20:96-104. [PMID: 18849170 DOI: 10.1016/j.jasms.2008.09.009] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/16/2008] [Revised: 09/05/2008] [Accepted: 09/05/2008] [Indexed: 05/26/2023]
Abstract
The fluorescence and photodissociation of rhodamine 575 cations confined to a quadrupole ion trap are observed during laser irradiation at 488 nm. The kinetics of photodissociation is measured by time-dependent mass spectra and time-dependent fluorescence. The rhodamine ion signal and fluorescence decay are studied as functions of buffer gas pressure, laser fluence, and irradiation time. The decay rates of the ions in the mass spectra agree with decay rates of the fluorescence. Some of the fragment ions also fluoresce and further dissociate. The photodissociation rate is found to depend on the incident laser fluence and buffer gas pressure. The implications of rapid absorption/fluorescence cycling for photodissociation of dye-labeled biomolecular ions under continuous irradiation are discussed.
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Affiliation(s)
- Nicholas A Sassin
- Department of Chemistry and Chemical Physics Program, University of Nevada, Reno, Reno, Nevada, USA
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44
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Vilensky MY, Prior Y, Averbukh IS. Cooling in a bistable optical cavity. PHYSICAL REVIEW LETTERS 2007; 99:103002. [PMID: 17930385 DOI: 10.1103/physrevlett.99.103002] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/03/2006] [Indexed: 05/25/2023]
Abstract
We propose a generic approach to nonresonant laser cooling of atoms and molecules in a bistable optical cavity. The method exemplifies a photonic version of Sisyphus cooling, in which the matter-dressed cavity extracts energy from the particles and discharges it to the external field as a result of sudden transitions between two stable states.
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Affiliation(s)
- Mark Y Vilensky
- Department of Chemical Physics, Weizmann Institute of Science, Rehovot, Israel 76100
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45
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Poggio M, Degen CL, Mamin HJ, Rugar D. Feedback cooling of a cantilever's fundamental mode below 5 mK. PHYSICAL REVIEW LETTERS 2007; 99:017201. [PMID: 17678185 DOI: 10.1103/physrevlett.99.017201] [Citation(s) in RCA: 31] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/07/2007] [Indexed: 05/16/2023]
Abstract
We cool the fundamental mechanical mode of an ultrasoft silicon cantilever from a base temperature of 2.2 K down to 2.9+/-0.3 mK using active optomechanical feedback. The lowest observed mode temperature is consistent with limits determined by the properties of the cantilever and by the measurement noise. For high feedback gain, the driven cantilever motion is found to suppress or "squash" the optical interferometer intensity noise below the shot noise level.
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Affiliation(s)
- M Poggio
- IBM Research Division, Almaden Research Center, 650 Harry Rd., San Jose California 95120, USA
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46
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Gigan S, Böhm HR, Paternostro M, Blaser F, Langer G, Hertzberg JB, Schwab KC, Bäuerle D, Aspelmeyer M, Zeilinger A. Self-cooling of a micromirror by radiation pressure. Nature 2006; 444:67-70. [PMID: 17080084 DOI: 10.1038/nature05273] [Citation(s) in RCA: 187] [Impact Index Per Article: 10.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/27/2006] [Accepted: 09/22/2006] [Indexed: 11/08/2022]
Abstract
Cooling of mechanical resonators is currently a popular topic in many fields of physics including ultra-high precision measurements, detection of gravitational waves and the study of the transition between classical and quantum behaviour of a mechanical system. Here we report the observation of self-cooling of a micromirror by radiation pressure inside a high-finesse optical cavity. In essence, changes in intensity in a detuned cavity, as caused by the thermal vibration of the mirror, provide the mechanism for entropy flow from the mirror's oscillatory motion to the low-entropy cavity field. The crucial coupling between radiation and mechanical motion was made possible by producing free-standing micromirrors of low mass (m approximately 400 ng), high reflectance (more than 99.6%) and high mechanical quality (Q approximately 10,000). We observe cooling of the mechanical oscillator by a factor of more than 30; that is, from room temperature to below 10 K. In addition to purely photothermal effects we identify radiation pressure as a relevant mechanism responsible for the cooling. In contrast with earlier experiments, our technique does not need any active feedback. We expect that improvements of our method will permit cooling ratios beyond 1,000 and will thus possibly enable cooling all the way down to the quantum mechanical ground state of the micromirror.
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Affiliation(s)
- S Gigan
- Physics Faculty, Institute for Experimental Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna, Austria
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