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Tang Y, Liang C, Wen X, Li W, Xu AN, Liu YC. PT-Symmetric Feedback Induced Linewidth Narrowing. Phys Rev Lett 2023; 130:193602. [PMID: 37243661 DOI: 10.1103/physrevlett.130.193602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/05/2022] [Accepted: 04/14/2023] [Indexed: 05/29/2023]
Abstract
Narrow linewidth is a long-pursued goal in precision measurement and sensing. We propose a parity-time symmetric (PT-symmetric) feedback method to narrow the linewidths of resonance systems. By using a quadrature measurement-feedback loop, we transform a dissipative resonance system into a PT-symmetric system. Unlike the conventional PT-symmetric systems that typically require two or more modes, here the PT-symmetric feedback system contains only a single resonance mode, which greatly extends the scope of applications. The method enables remarkable linewidth narrowing and enhancement of measurement sensitivity. We illustrate the concept in a thermal ensemble of atoms, achieving a 48-fold narrowing of the magnetic resonance linewidth. By applying the method in magnetometry, we realize a 22-times improvement of the measurement sensitivity. This work opens the avenue for studying non-Hermitian physics and high-precision measurements in resonance systems with feedback.
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Affiliation(s)
- Yuanjiang Tang
- State Key Laboratory of Low-Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
| | - Chao Liang
- State Key Laboratory of Low-Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
| | - Xin Wen
- State Key Laboratory of Low-Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
| | - Weipeng Li
- State Key Laboratory of Low-Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
| | - An-Ning Xu
- State Key Laboratory of Low-Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
| | - Yong-Chun Liu
- State Key Laboratory of Low-Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
- Frontier Science Center for Quantum Information, Beijing 100084, China
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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] [What about the content of this article? (0)] [Affiliation(s)] [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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Gajdacz M, Hilliard AJ, Kristensen MA, Pedersen PL, Klempt C, Arlt JJ, Sherson JF. Preparation of Ultracold Atom Clouds at the Shot Noise Level. Phys Rev Lett 2016; 117:073604. [PMID: 27563964 DOI: 10.1103/physrevlett.117.073604] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/15/2016] [Indexed: 06/06/2023]
Abstract
We prepare number stabilized ultracold atom clouds through the real-time analysis of nondestructive images and the application of feedback. In our experiments, the atom number N∼10^{6} is determined by high precision Faraday imaging with uncertainty ΔN below the shot noise level, i.e., ΔN<sqrt[N]. Based on this measurement, feedback is applied to reduce the atom number to a user-defined target, whereupon a second imaging series probes the number stabilized cloud. By this method, we show that the atom number in ultracold clouds can be prepared below the shot noise level.
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Affiliation(s)
- M Gajdacz
- Institut for Fysik og Astronomi, Aarhus Universitet, Ny Munkegade 120, 8000 Aarhus C, Denmark
| | - A J Hilliard
- Institut for Fysik og Astronomi, Aarhus Universitet, Ny Munkegade 120, 8000 Aarhus C, Denmark
| | - M A Kristensen
- Institut for Fysik og Astronomi, Aarhus Universitet, Ny Munkegade 120, 8000 Aarhus C, Denmark
| | - P L Pedersen
- Institut for Fysik og Astronomi, Aarhus Universitet, Ny Munkegade 120, 8000 Aarhus C, Denmark
| | - C Klempt
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
| | - J J Arlt
- Institut for Fysik og Astronomi, Aarhus Universitet, Ny Munkegade 120, 8000 Aarhus C, Denmark
| | - J F Sherson
- Institut for Fysik og Astronomi, Aarhus Universitet, Ny Munkegade 120, 8000 Aarhus C, Denmark
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Sadgrove M, Nakagawa K. Fast, externally triggered, digital phase controller for an optical lattice. Rev Sci Instrum 2011; 82:113104. [PMID: 22128963 DOI: 10.1063/1.3655447] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
We present a method to control the phase of an optical lattice according to an external trigger signal. The method has a latency of less than 30 μs. Two phase locked digital synthesizers provide the driving signal for two acousto-optic modulators which control the frequency and phase of the counter-propagating beams which form a standing wave (optical lattice). A micro-controller with an external interrupt function is connected to the desired external signal, and updates the phase register of one of the synthesizers when the external signal changes. The standing wave (period λ/2 = 390 nm) can be moved by units of 49 nm with a mean jitter of 28 nm. The phase change is well known due to the digital nature of the synthesizer, and does not need calibration. The uses of the scheme include coherent control of atomic matter-wave dynamics.
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Affiliation(s)
- Mark Sadgrove
- Institute for Laser Science, The University of Electro-Communication, 1-5-1 Chofugaoka, Chofu, Japan.
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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] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/17/2009] [Accepted: 10/07/2009] [Indexed: 11/09/2022]
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Balint-kurti GG, Zou S, Brown A. Optimal Control Theory for Manipulating Molecular Processes. In: Rice SA, editor. Advances in Chemical Physics. Hoboken: John Wiley & Sons, Inc.; 2008. pp. 43-94. [DOI: 10.1002/9780470259474.ch2] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register]
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Bushev P, Rotter D, Wilson A, Dubin F, Becher C, Eschner J, Blatt R, Steixner V, Rabl P, Zoller P. Feedback cooling of a single trapped ion. Phys Rev Lett 2006; 96:043003. [PMID: 16486818 DOI: 10.1103/physrevlett.96.043003] [Citation(s) in RCA: 44] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/16/2005] [Indexed: 05/06/2023]
Abstract
Based on a real-time measurement of the motion of a single ion in a Paul trap, we demonstrate its electromechanical cooling below the Doppler limit by homodyne feedback control (cold damping). The feedback cooling results are well described by a model based on a quantum mechanical master equation.
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Affiliation(s)
- Pavel Bushev
- Institute for Experimental Physics, University of Innsbruck, Technikerstrasse 25, A-6020 Innsbruck, Austria
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Abstract
We propose a novel generic approach to laser cooling based on the nonresonant interactions of atoms and molecules with optical standing waves experiencing sudden phase jumps. The technique, termed "optical shaking," combines the elements of stochastic cooling and Sisyphus cooling. An optical signal that measures the instantaneous force applied by the standing wave on the ensemble of particles is used as feedback to determine the phase jumps. This guarantees a drift towards lower energies and higher phase-space density without the loss of particles typical of evaporative cooling.
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Affiliation(s)
- I Sh Averbukh
- Department of Chemical Physics, The Weizmann Institute of Science, Rehovot 76100, Israel
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Ivanov D, Wallentowitz S. Non-Markovian particle dynamics in continuously controlled quantum gases. Phys Rev Lett 2004; 93:260603. [PMID: 15697963 DOI: 10.1103/physrevlett.93.260603] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/21/2004] [Indexed: 05/24/2023]
Abstract
For a quantum gas, being subject to continuous feedback of a macroscopic observable, the single-particle dynamics is studied. Despite feedback-induced particle correlations, it is shown that analytic solutions are obtained by formally extending the single-particle Hilbert space by an auxiliary degree of freedom. The particle's motion is then fed by colored noise, which effectively maps quantum-statistical correlations onto the single particle. Thus, the single particle in the continuously controlled gas follows a non-Markovian trajectory in phase space.
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Affiliation(s)
- D Ivanov
- Fachbereich Physik, Universität Rostock, Universitätsplatz 3, D-18051 Rostock, Germany
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