1
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Daviet R, Zelle CP, Rosch A, Diehl S. Nonequilibrium Criticality at the Onset of Time-Crystalline Order. PHYSICAL REVIEW LETTERS 2024; 132:167102. [PMID: 38701486 DOI: 10.1103/physrevlett.132.167102] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/09/2024] [Accepted: 03/25/2024] [Indexed: 05/05/2024]
Abstract
We explore the phase transitions at the onset of time-crystalline order in O(N) models driven out of equilibrium. The spontaneous breaking of time translation symmetry and its Goldstone mode are captured by an effective description with O(N)×SO(2) symmetry, where the emergent external SO(2) results from a transmutation of the internal symmetry of time translations. Using the renormalization group and the ε=4-d expansion in a leading two-loop analysis, we identify a new nonequilibrium universality class. Strikingly, it controls the long-distance physics no matter how small the microscopic breaking of equilibrium conditions is. The O(N=2)×SO(2) symmetry group is realized for magnon condensation in pumped yttrium iron garnet films and in exciton-polariton systems with a polarization degree of freedom.
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Affiliation(s)
- Romain Daviet
- Institut für Theoretische Physik, Universität zu Köln, 50937 Cologne, Germany
| | - Carl Philipp Zelle
- Institut für Theoretische Physik, Universität zu Köln, 50937 Cologne, Germany
| | - Achim Rosch
- Institut für Theoretische Physik, Universität zu Köln, 50937 Cologne, Germany
| | - Sebastian Diehl
- Institut für Theoretische Physik, Universität zu Köln, 50937 Cologne, Germany
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2
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Chen YH, Zhang X. Realization of an inherent time crystal in a dissipative many-body system. Nat Commun 2023; 14:6161. [PMID: 37789006 PMCID: PMC10547780 DOI: 10.1038/s41467-023-41905-3] [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: 10/30/2022] [Accepted: 09/21/2023] [Indexed: 10/05/2023] Open
Abstract
Time crystals are many-body states that spontaneously break translation symmetry in time the way that ordinary crystals do in space. While experimental observations have confirmed the existence of discrete or continuous time crystals, these realizations have relied on the utilization of periodic forces or effective modulation through cavity feedback. The original proposal for time crystals is that they would represent self-sustained motions without any external periodicity, but realizing such purely self-generated behavior has not yet been achieved. Here, we provide theoretical and experimental evidence that many-body interactions can give rise to an inherent time crystalline phase. Following a calculation that shows an ensemble of pumped four-level atoms can spontaneously break continuous time translation symmetry, we observe periodic motions in an erbium-doped solid. The inherent time crystal produced by our experiment is self-protected by many-body interactions and has a measured coherence time beyond that of individual erbium ions.
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Affiliation(s)
- Yu-Hui Chen
- Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurements of Ministry of Education, School of Physics, Beijing Institute of Technology, 100081, Beijing, China
- Beijing Key Laboratory of Nanophotonics & Ultrafine Optoelectronic Systems, School of Physics, Beijing Institute of Technology, 100081, Beijing, China
| | - Xiangdong Zhang
- Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurements of Ministry of Education, School of Physics, Beijing Institute of Technology, 100081, Beijing, China.
- Beijing Key Laboratory of Nanophotonics & Ultrafine Optoelectronic Systems, School of Physics, Beijing Institute of Technology, 100081, Beijing, China.
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3
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Limit cycles and chaos in the hybrid atom-optomechanics system. Sci Rep 2022; 12:15288. [PMID: 36088462 PMCID: PMC9464193 DOI: 10.1038/s41598-022-15249-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/15/2022] [Accepted: 06/21/2022] [Indexed: 11/17/2022] Open
Abstract
We consider atoms in two different periodic potentials induced by different lasers, one of which is coupled to a mechanical membrane via radiation pressure force. The atoms are intrinsically two-level systems that can absorb or emit photons, but the dynamics of their position and momentum are treated classically. On the other hand, the membrane, the cavity field, and the intrinsic two-level atoms are treated quantum mechanically. We show that the mean excitation of the three systems can be stable, periodically oscillating, or in a chaotic state depending on the strength of the coupling between them. We define regular, limit cycle, and chaotic phases, and present a phase diagram where the three phases can be achieved by manipulating the field-membrane and field-atom coupling strengths. We also computed other observable quantities that can reflect the system’s phase such as position, momentum, and correlation functions. Our proposal offers a new way to generate and tune the limit cycle and chaotic phases in a well-established atom-optomechanics system.
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4
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LeBlanc LJ. Unleashing spontaneity in a time crystal. Science 2022; 377:576-577. [PMID: 35926056 DOI: 10.1126/science.add2015] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
Ordered patterns reoccur over time in an ultracold atomic gas trapped in light.
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5
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Kongkhambut P, Skulte J, Mathey L, Cosme JG, Hemmerich A, Keßler H. Observation of a continuous time crystal. Science 2022; 377:670-673. [PMID: 35679353 DOI: 10.1126/science.abo3382] [Citation(s) in RCA: 11] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
Time crystals are classified as discrete or continuous depending on whether they spontaneously break discrete or continuous time translation symmetry. While discrete time crystals have been extensively studied in periodically driven systems, the experimental realization of a continuous time crystal is still pending. We report the observation of a limit cycle phase in a continuously pumped dissipative atom-cavity system, that is characterized by emergent oscillations in the intracavity photon number. The phase of the oscillation found to be random for different realizations, and hence this dynamical many-body state breaks continuous time translation symmetry spontaneously. Furthermore, the observed limit cycles are robust against temporal perturbations and therefore demonstrate the realization of a continuous time crystal.
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Affiliation(s)
- Phatthamon Kongkhambut
- Zentrum für Optische Quantentechnologien and Institut für Laser-Physik, Universität Hamburg, 22761 Hamburg, Germany
| | - Jim Skulte
- Zentrum für Optische Quantentechnologien and Institut für Laser-Physik, Universität Hamburg, 22761 Hamburg, Germany.,The Hamburg Center for Ultrafast Imaging, 22761 Hamburg, Germany
| | - Ludwig Mathey
- Zentrum für Optische Quantentechnologien and Institut für Laser-Physik, Universität Hamburg, 22761 Hamburg, Germany.,The Hamburg Center for Ultrafast Imaging, 22761 Hamburg, Germany
| | - Jayson G Cosme
- National Institute of Physics, University of the Philippines, Diliman, Quezon City 1101, Philippines
| | - Andreas Hemmerich
- Zentrum für Optische Quantentechnologien and Institut für Laser-Physik, Universität Hamburg, 22761 Hamburg, Germany.,The Hamburg Center for Ultrafast Imaging, 22761 Hamburg, Germany
| | - Hans Keßler
- Zentrum für Optische Quantentechnologien and Institut für Laser-Physik, Universität Hamburg, 22761 Hamburg, Germany
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6
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Lin R, Rosa-Medina R, Ferri F, Finger F, Kroeger K, Donner T, Esslinger T, Chitra R. Dissipation-Engineered Family of Nearly Dark States in Many-Body Cavity-Atom Systems. PHYSICAL REVIEW LETTERS 2022; 128:153601. [PMID: 35499900 DOI: 10.1103/physrevlett.128.153601] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/21/2021] [Accepted: 02/24/2022] [Indexed: 06/14/2023]
Abstract
Three-level atomic systems coupled to light have the capacity to host dark states. We study a system of V-shaped three-level atoms coherently coupled to the two quadratures of a dissipative cavity. The interplay between the atomic level structure and dissipation makes the phase diagram of the open system drastically different from the closed one. In particular, it leads to the stabilization of a continuous family of dark and nearly dark excited many-body states with inverted atomic populations as the steady states. The multistability of these states can be probed via their distinct fluctuations and excitation spectra, as well as the system's Liouvillian dynamics which are highly sensitive to ramp protocols. Our model can be implemented experimentally by encoding the two higher-energy modes in orthogonal density-modulated states in a bosonic quantum gas. This implementation offers prospects for potential applications like the realization of quantum optical random walks and microscopy with subwavelength spatial resolution.
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Affiliation(s)
- Rui Lin
- Institute for Theoretical Physics, ETH Zürich, 8093 Zurich, Switzerland
| | | | - Francesco Ferri
- Institute for Quantum Electronics, ETH Zürich, 8093 Zurich, Switzerland
| | - Fabian Finger
- Institute for Quantum Electronics, ETH Zürich, 8093 Zurich, Switzerland
| | - Katrin Kroeger
- Institute for Quantum Electronics, ETH Zürich, 8093 Zurich, Switzerland
| | - Tobias Donner
- Institute for Quantum Electronics, ETH Zürich, 8093 Zurich, Switzerland
| | - Tilman Esslinger
- Institute for Quantum Electronics, ETH Zürich, 8093 Zurich, Switzerland
| | - R Chitra
- Institute for Theoretical Physics, ETH Zürich, 8093 Zurich, Switzerland
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7
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Colella E, Kosior A, Mivehvar F, Ritsch H. Open Quantum System Simulation of Faraday's Induction Law via Dynamical Instabilities. PHYSICAL REVIEW LETTERS 2022; 128:070603. [PMID: 35244413 DOI: 10.1103/physrevlett.128.070603] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/09/2021] [Revised: 12/13/2021] [Accepted: 02/01/2022] [Indexed: 06/14/2023]
Abstract
We propose a novel type of a Bose-Hubbard ladder model based on an open quantum-gas-cavity-QED setup to study the physics of dynamical gauge potentials. Atomic tunneling along opposite directions in the two legs of the ladder is mediated by photon scattering from transverse pump lasers to two distinct cavity modes. The resulting interplay between cavity photon dissipation and the optomechanical atomic backaction then induces an average-density-dependent dynamical gauge field. The dissipation-stabilized steady-state atomic motion along the legs of the ladder leads either to a pure chiral current, screening the induced dynamical magnetic field as in the Meissner effect, or generates simultaneously chiral and particle currents. For a sufficiently strong pump the system enters into a dynamically unstable regime exhibiting limit-cycle and period-doubled oscillations. Intriguingly, an electromotive force is induced in this dynamical regime as expected from an interpretation based on Faraday's law of induction for the time-dependent synthetic magnetic flux.
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Affiliation(s)
- Elvia Colella
- Institut für Theoretische Physik, Universität Innsbruck, A-6020 Innsbruck, Austria
| | - Arkadiusz Kosior
- Institut für Theoretische Physik, Universität Innsbruck, A-6020 Innsbruck, Austria
| | - Farokh Mivehvar
- Institut für Theoretische Physik, Universität Innsbruck, A-6020 Innsbruck, Austria
| | - Helmut Ritsch
- Institut für Theoretische Physik, Universität Innsbruck, A-6020 Innsbruck, Austria
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8
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Kongkhambut P, Keßler H, Skulte J, Mathey L, Cosme JG, Hemmerich A. Realization of a Periodically Driven Open Three-Level Dicke Model. PHYSICAL REVIEW LETTERS 2021; 127:253601. [PMID: 35029416 DOI: 10.1103/physrevlett.127.253601] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/26/2021] [Accepted: 11/02/2021] [Indexed: 06/14/2023]
Abstract
A periodically driven open three-level Dicke model is realized by resonantly shaking the pump field in an atom-cavity system. As an unambiguous signature, we demonstrate the emergence of a dynamical phase, in which the atoms periodically localize between the antinodes of the pump lattice, associated with an oscillating net momentum along the pump axis. We observe this dynamical phase through the periodic switching of the relative phase between the pump and cavity fields at a small fraction of the driving frequency, suggesting that it exhibits a time crystalline character.
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Affiliation(s)
- Phatthamon Kongkhambut
- Zentrum für Optische Quantentechnologien and Institut für Laser-Physik, Universität Hamburg, 22761 Hamburg, Germany
| | - Hans Keßler
- Zentrum für Optische Quantentechnologien and Institut für Laser-Physik, Universität Hamburg, 22761 Hamburg, Germany
| | - Jim Skulte
- Zentrum für Optische Quantentechnologien and Institut für Laser-Physik, Universität Hamburg, 22761 Hamburg, Germany
- The Hamburg Center for Ultrafast Imaging, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Ludwig Mathey
- Zentrum für Optische Quantentechnologien and Institut für Laser-Physik, Universität Hamburg, 22761 Hamburg, Germany
- The Hamburg Center for Ultrafast Imaging, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Jayson G Cosme
- National Institute of Physics, University of the Philippines, Diliman, Quezon City 1101, Philippines
| | - Andreas Hemmerich
- Zentrum für Optische Quantentechnologien and Institut für Laser-Physik, Universität Hamburg, 22761 Hamburg, Germany
- The Hamburg Center for Ultrafast Imaging, Luruper Chaussee 149, 22761 Hamburg, Germany
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9
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Fazzini S, Chudzinski P, Dauer C, Schneider I, Eggert S. Nonequilibrium Floquet Steady States of Time-Periodic Driven Luttinger Liquids. PHYSICAL REVIEW LETTERS 2021; 126:243401. [PMID: 34213948 DOI: 10.1103/physrevlett.126.243401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/16/2020] [Revised: 03/08/2021] [Accepted: 05/20/2021] [Indexed: 06/13/2023]
Abstract
Time-periodic driving facilitates a wealth of novel quantum states and quantum engineering. The interplay of Floquet states and strong interactions is particularly intriguing, which we study using time-periodic fields in a one-dimensional quantum gas, modeled by a Luttinger liquid with periodically changing interactions. By developing a time-periodic operator algebra, we are able to solve and analyze the complete set of nonequilibrium steady states in terms of a Floquet-Bogoliubov ansatz and known analytic functions. Complex valued Floquet eigenenergies occur when integer multiples of the driving frequency approximately match twice the dispersion energy, which correspond to resonant states. In experimental systems of Lieb-Liniger bosons we predict a change from power-law correlations to dominant collective density wave excitations at the corresponding wave numbers as the frequency is lowered below a characteristic cutoff.
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Affiliation(s)
- Serena Fazzini
- Physics Department and Research Center OPTIMAS, Technische Universität Kaiserslautern, 67663 Kaiserslautern, Germany
| | - Piotr Chudzinski
- School of Mathematics and Physics, Queen's University of Belfast, BT7 1NN Belfast, United Kingdom
- Institute of Fundamental Technological Research, Polish Academy of Science, 02-106 Warszawa, Poland
| | - Christoph Dauer
- Physics Department and Research Center OPTIMAS, Technische Universität Kaiserslautern, 67663 Kaiserslautern, Germany
| | - Imke Schneider
- Physics Department and Research Center OPTIMAS, Technische Universität Kaiserslautern, 67663 Kaiserslautern, Germany
- Institute of Physics, Universität Augsburg, 86135 Augsburg, Germany
| | - Sebastian Eggert
- Physics Department and Research Center OPTIMAS, Technische Universität Kaiserslautern, 67663 Kaiserslautern, Germany
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10
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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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11
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Ivanov DA, Ivanova TY, Caballero-Benitez SF, Mekhov IB. Feedback-Induced Quantum Phase Transitions Using Weak Measurements. PHYSICAL REVIEW LETTERS 2020; 124:010603. [PMID: 31976715 DOI: 10.1103/physrevlett.124.010603] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/01/2019] [Revised: 09/15/2019] [Indexed: 06/10/2023]
Abstract
We show that applying feedback and weak measurements to a quantum system induces phase transitions beyond the dissipative ones. Feedback enables controlling essentially quantum properties of the transition, i.e., its critical exponent, as it is driven by the fundamental quantum fluctuations due to measurement. Feedback provides the non-Markovianity and nonlinearity to the hybrid quantum-classical system, and enables simulating effects similar to spin-bath problems and Floquet time crystals with tunable long-range (long-memory) interactions.
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Affiliation(s)
- D A Ivanov
- Department of Physics, St. Petersburg State University, 198504 St. Petersburg, Russia
| | - T Yu Ivanova
- Department of Physics, St. Petersburg State University, 198504 St. Petersburg, Russia
| | - S F Caballero-Benitez
- Instituto de Física, Universidad Nacional Autónoma de México, Ciudad de Mexico 04510, Mexico
| | - I B Mekhov
- Department of Physics, St. Petersburg State University, 198504 St. Petersburg, Russia
- Department of Physics, University of Oxford, Oxford OX1 3PU, United Kingdom
- SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay, 91191 Gif-sur-Yvette, France
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12
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Dogra N, Landini M, Kroeger K, Hruby L, Donner T, Esslinger T. Dissipation-induced structural instability and chiral dynamics in a quantum gas. Science 2019; 366:1496-1499. [DOI: 10.1126/science.aaw4465] [Citation(s) in RCA: 53] [Impact Index Per Article: 10.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/20/2018] [Accepted: 11/06/2019] [Indexed: 01/17/2023]
Affiliation(s)
- Nishant Dogra
- Institute for Quantum Electronics, ETH Zurich, CH-8093 Zurich, Switzerland
| | - Manuele Landini
- Institute for Quantum Electronics, ETH Zurich, CH-8093 Zurich, Switzerland
| | - Katrin Kroeger
- Institute for Quantum Electronics, ETH Zurich, CH-8093 Zurich, Switzerland
| | - Lorenz Hruby
- Institute for Quantum Electronics, ETH Zurich, CH-8093 Zurich, Switzerland
| | - Tobias Donner
- Institute for Quantum Electronics, ETH Zurich, CH-8093 Zurich, Switzerland
| | - Tilman Esslinger
- Institute for Quantum Electronics, ETH Zurich, CH-8093 Zurich, Switzerland
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13
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Zupancic P, Dreon D, Li X, Baumgärtner A, Morales A, Zheng W, Cooper NR, Esslinger T, Donner T. P-Band Induced Self-Organization and Dynamics with Repulsively Driven Ultracold Atoms in an Optical Cavity. PHYSICAL REVIEW LETTERS 2019; 123:233601. [PMID: 31868492 DOI: 10.1103/physrevlett.123.233601] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/27/2019] [Indexed: 06/10/2023]
Abstract
We investigate a Bose-Einstein condensate strongly coupled to an optical cavity via a repulsive optical lattice. We detect a stable self-ordered phase in this regime, and show that the atoms order through an antisymmetric coupling to the P band of the lattice, limiting the extent of the phase and changing the geometry of the emergent density modulation. Furthermore, we find a nonequilibrium phase with repeated intense bursts of the intracavity photon number, indicating nontrivial driven-dissipative dynamics.
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Affiliation(s)
- P Zupancic
- Institute for Quantum Electronics, Eidgenössische Technische Hochschule Zürich, Otto-Stern-Weg 1, 8093 Zurich, Switzerland
| | - D Dreon
- Institute for Quantum Electronics, Eidgenössische Technische Hochschule Zürich, Otto-Stern-Weg 1, 8093 Zurich, Switzerland
| | - X Li
- Institute for Quantum Electronics, Eidgenössische Technische Hochschule Zürich, Otto-Stern-Weg 1, 8093 Zurich, Switzerland
| | - A Baumgärtner
- Institute for Quantum Electronics, Eidgenössische Technische Hochschule Zürich, Otto-Stern-Weg 1, 8093 Zurich, Switzerland
| | - A Morales
- Institute for Quantum Electronics, Eidgenössische Technische Hochschule Zürich, Otto-Stern-Weg 1, 8093 Zurich, Switzerland
| | - W Zheng
- T.C.M. Group, Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - N R Cooper
- T.C.M. Group, Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - T Esslinger
- Institute for Quantum Electronics, Eidgenössische Technische Hochschule Zürich, Otto-Stern-Weg 1, 8093 Zurich, Switzerland
| | - T Donner
- Institute for Quantum Electronics, Eidgenössische Technische Hochschule Zürich, Otto-Stern-Weg 1, 8093 Zurich, Switzerland
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14
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Kroeze RM, Guo Y, Vaidya VD, Keeling J, Lev BL. Spinor Self-Ordering of a Quantum Gas in a Cavity. PHYSICAL REVIEW LETTERS 2018; 121:163601. [PMID: 30387632 DOI: 10.1103/physrevlett.121.163601] [Citation(s) in RCA: 39] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/13/2018] [Indexed: 06/08/2023]
Abstract
We observe the joint spin-spatial (spinor) self-organization of a two-component Bose-Einstein condensate (BEC) strongly coupled to an optical cavity. This unusual nonequilibrium Hepp-Lieb-Dicke phase transition is driven by an off-resonant Raman transition formed from a classical pump field and the emergent quantum dynamical cavity field. This mediates a spinor-spinor interaction that, above a critical strength, simultaneously organizes opposite spinor states of the BEC on opposite checkerboard configurations of an emergent 2D lattice. The resulting spinor density-wave polariton condensate is observed by directly detecting the atomic spin and momentum state and by holographically reconstructing the phase of the emitted cavity field. The latter provides a direct measure of the spin state, and a spin-spatial domain wall is observed. The photon-mediated spin interactions demonstrated here may be engineered to create dynamical gauge fields and quantum spin glasses.
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Affiliation(s)
- Ronen M Kroeze
- Department of Physics, Stanford University, Stanford, California 94305, USA
- E. L. Ginzton Laboratory, Stanford University, Stanford, California 94305, USA
| | - Yudan Guo
- Department of Physics, Stanford University, Stanford, California 94305, USA
- E. L. Ginzton Laboratory, Stanford University, Stanford, California 94305, USA
| | - Varun D Vaidya
- Department of Physics, Stanford University, Stanford, California 94305, USA
- E. L. Ginzton Laboratory, Stanford University, Stanford, California 94305, USA
- Department of Applied Physics, Stanford University, Stanford, California 94305, USA
| | - Jonathan Keeling
- SUPA, School of Physics and Astronomy, University of St. Andrews, St. Andrews KY16 9SS United Kingdom
| | - Benjamin L Lev
- Department of Physics, Stanford University, Stanford, California 94305, USA
- E. L. Ginzton Laboratory, Stanford University, Stanford, California 94305, USA
- Department of Applied Physics, Stanford University, Stanford, California 94305, USA
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15
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Zhang YC, Walther V, Pohl T. Long-Range Interactions and Symmetry Breaking in Quantum Gases through Optical Feedback. PHYSICAL REVIEW LETTERS 2018; 121:073604. [PMID: 30169082 DOI: 10.1103/physrevlett.121.073604] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/11/2018] [Indexed: 06/08/2023]
Abstract
We consider a quasi-two-dimensional atomic Bose-Einstein condensate interacting with a near-resonant laser field that is backreflected onto the condensate by a planar mirror. We show that this single-mirror optical feedback leads to an unusual type of effective interaction between the ultracold atoms giving rise to a rich spectrum of ground states. In particular, we find that it can cause the spontaneous contraction of the quasi-two-dimensional condensate to form a self-bound one-dimensional chain of mesoscopic quantum droplets, and demonstrate that the observation of this exotic effect is within reach of current experiments.
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Affiliation(s)
- Yong-Chang Zhang
- Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120, 8000 Aarhus C, Denmark
| | - Valentin Walther
- Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120, 8000 Aarhus C, Denmark
| | - Thomas Pohl
- Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120, 8000 Aarhus C, Denmark
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16
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Luo XW, Zhang C. Self-Adapted Floquet Dynamics of Ultracold Bosons in a Cavity. PHYSICAL REVIEW LETTERS 2018; 120:263202. [PMID: 30004716 DOI: 10.1103/physrevlett.120.263202] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/19/2017] [Revised: 05/04/2018] [Indexed: 06/08/2023]
Abstract
Floquet dynamics of a quantum system subject to periodic modulations of system parameters provides a powerful tool for engineering new quantum matter with exotic properties. While system dynamics is significantly altered, the periodic modulation itself is usually induced externally and independent of Floquet dynamics. Here we propose a new type of Floquet physics for a Bose-Einstein condensate (BEC) subject to a shaken lattice generated inside a cavity, where the shaken lattice and atomic Floquet bands are mutually dependent, resulting in self-adapted Floquet dynamics. In particular, the shaken lattice induces Floquet quasienergy bands for the BEC, whose backaction leads to a self-adapted dynamical normal-superradiant phase transition for the shaken lattice. Such self-adapted Floquet dynamics shows two surprising and unique features: (i) The normal-superradiant phase transition possesses a hysteresis even without atom interactions. (ii) The dynamical atom-cavity steady state could exist at free energy maxima. The atom interactions strongly affect the phase transition of the BEC from zero to finite momenta. Our results provide a powerful platform for exploring self-adapted Floquet physics, which may open an avenue for engineering novel quantum materials.
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Affiliation(s)
- Xi-Wang Luo
- Department of Physics, The University of Texas at Dallas, Richardson, Texas 75080-3021, USA
| | - Chuanwei Zhang
- Department of Physics, The University of Texas at Dallas, Richardson, Texas 75080-3021, USA
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Léonard J, Morales A, Zupancic P, Donner T, Esslinger T. Monitoring and manipulating Higgs and Goldstone modes in a supersolid quantum gas. Science 2017; 358:1415-1418. [DOI: 10.1126/science.aan2608] [Citation(s) in RCA: 90] [Impact Index Per Article: 12.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/19/2017] [Accepted: 11/03/2017] [Indexed: 11/02/2022]
Abstract
Higgs and Goldstone modes are collective excitations of the amplitude and phase of an order parameter that is related to the breaking of a continuous symmetry. We directly studied these modes in a supersolid quantum gas created by coupling a Bose-Einstein condensate to two optical cavities, whose field amplitudes form the real and imaginary parts of a U(1)-symmetric order parameter. Monitoring the cavity fields in real time allowed us to observe the dynamics of the associated Higgs and Goldstone modes and revealed their amplitude and phase nature. We used a spectroscopic method to measure their frequencies, and we gave a tunable mass to the Goldstone mode by exploring the crossover between continuous and discrete symmetry. Our experiments link spectroscopic measurements to the theoretical concept of Higgs and Goldstone modes.
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Mivehvar F, Piazza F, Ritsch H. Disorder-Driven Density and Spin Self-Ordering of a Bose-Einstein Condensate in a Cavity. PHYSICAL REVIEW LETTERS 2017; 119:063602. [PMID: 28949625 DOI: 10.1103/physrevlett.119.063602] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/23/2017] [Indexed: 06/07/2023]
Abstract
We study spatial spin and density self-ordering of a two-component Bose-Einstein condensate via collective Raman scattering into a linear cavity mode. The onset of the Dicke superradiance phase transition is marked by a simultaneous appearance of a crystalline density order and a spin-wave order. The latter spontaneously breaks the discrete Z_{2} symmetry between even and odd sites of the cavity optical potential. Moreover, in the superradiant state the continuous U(1) symmetry of the relative phase of the two condensate wave functions is explicitly broken by the cavity-induced position-dependent Raman coupling with a zero spatial average. Thus, the spatially averaged relative condensate phase is locked at either π/2 or -π/2. This continuous symmetry breaking and relative condensate phase locking by a zero-average Raman field can be considered as a generic order-by-disorder process similar to the random-field-induced order in the two-dimensional classical ferromagnetic XY spin model. However, the seed of the random field in our model stems from quantum fluctuations in the cavity field and is a dynamical entity affected by self-ordering. The spectra of elementary excitations exhibit the typical mode softening at the superradiance threshold.
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Affiliation(s)
- Farokh Mivehvar
- Institut für Theoretische Physik, Universität Innsbruck, A-6020 Innsbruck, Austria
| | - Francesco Piazza
- Max-Planck-Institut für Physik komplexer Systeme, D-01187 Dresden, Germany
| | - Helmut Ritsch
- Institut für Theoretische Physik, Universität Innsbruck, A-6020 Innsbruck, Austria
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Mivehvar F, Ritsch H, Piazza F. Superradiant Topological Peierls Insulator inside an Optical Cavity. PHYSICAL REVIEW LETTERS 2017; 118:073602. [PMID: 28256867 DOI: 10.1103/physrevlett.118.073602] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/17/2016] [Indexed: 06/06/2023]
Abstract
We consider a spinless ultracold Fermi gas tightly trapped along the axis of an optical resonator and transversely illuminated by a laser closely tuned to a resonator mode. At a certain threshold pump intensity, the homogeneous gas density breaks a Z_{2} symmetry towards a spatially periodic order, which collectively scatters pump photons into the cavity. We show that this known self-ordering transition also occurs for low field seeking fermionic particles when the laser light is blue detuned to an atomic transition. The emergent superradiant optical lattice in this case is homopolar and possesses two distinct dimerizations. Depending on the spontaneously chosen dimerization, the resulting Bloch bands can have a nontrivial topological structure characterized by a nonvanishing Zak phase. In the case where the Fermi momentum is close to half of the cavity-mode wave number, a Peierls-like instability here creates a topological insulator with a gap at the Fermi surface, which hosts a pair of edge states. The topological features of the system can be nondestructively observed via the cavity output: the Zak phase of the bulk coincides with the relative phase between laser and cavity field, while the fingerprint of edge states can be observed as additional broadening in a well-defined frequency window of the cavity spectrum.
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Affiliation(s)
- Farokh Mivehvar
- Institut für Theoretische Physik, Universität Innsbruck, A-6020 Innsbruck, Austria
| | - Helmut Ritsch
- Institut für Theoretische Physik, Universität Innsbruck, A-6020 Innsbruck, Austria
| | - Francesco Piazza
- Institut für Theoretische Physik, Universität Innsbruck, A-6020 Innsbruck, Austria
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Schütz S, Jäger SB, Morigi G. Dissipation-Assisted Prethermalization in Long-Range Interacting Atomic Ensembles. PHYSICAL REVIEW LETTERS 2016; 117:083001. [PMID: 27588853 DOI: 10.1103/physrevlett.117.083001] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/16/2015] [Indexed: 06/06/2023]
Abstract
We theoretically characterize the semiclassical dynamics of an ensemble of atoms after a sudden quench across a driven-dissipative second-order phase transition. The atoms are driven by a laser and interact via conservative and dissipative long-range forces mediated by the photons of a single-mode cavity. These forces can cool the motion and, above a threshold value of the laser intensity, induce spatial ordering. We show that the relaxation dynamics following the quench exhibits a long prethermalizing behavior which is first dominated by coherent long-range forces and then by their interplay with dissipation. Remarkably, dissipation-assisted prethermalization is orders of magnitude longer than prethermalization due to the coherent dynamics. We show that it is associated with the creation of momentum-position correlations, which remain nonzero for even longer times than mean-field predicts. This implies that cavity cooling of an atomic ensemble into the self-organized phase can require longer time scales than the typical experimental duration. In general, these results demonstrate that noise and dissipation can substantially slow down the onset of thermalization in long-range interacting many-body systems.
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Affiliation(s)
- Stefan Schütz
- Theoretische Physik, Universität des Saarlandes, D-66123 Saarbrücken, Germany
| | - Simon B Jäger
- Theoretische Physik, Universität des Saarlandes, D-66123 Saarbrücken, Germany
| | - Giovanna Morigi
- Theoretische Physik, Universität des Saarlandes, D-66123 Saarbrücken, Germany
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Quantum measurement-induced antiferromagnetic order and density modulations in ultracold Fermi gases in optical lattices. Sci Rep 2016; 6:31196. [PMID: 27510369 PMCID: PMC4980619 DOI: 10.1038/srep31196] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/20/2016] [Accepted: 07/14/2016] [Indexed: 11/16/2022] Open
Abstract
Ultracold atomic systems offer a unique tool for understanding behavior of matter in the quantum degenerate regime, promising studies of a vast range of phenomena covering many disciplines from condensed matter to quantum information and particle physics. Coupling these systems to quantized light fields opens further possibilities of observing delicate effects typical of quantum optics in the context of strongly correlated systems. Measurement backaction is one of the most funda- mental manifestations of quantum mechanics and it is at the core of many famous quantum optics experiments. Here we show that quantum backaction of weak measurement can be used for tailoring long-range correlations of ultracold fermions, realizing quantum states with spatial modulations of the density and magnetization, thus overcoming usual requirement for a strong interatomic interactions. We propose detection schemes for implementing antiferromagnetic states and density waves. We demonstrate that such long-range correlations cannot be realized with local addressing, and they are a consequence of the competition between global but spatially structured backaction of weak quantum measurement and unitary dynamics of fermions.
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