1
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Li HC, Huang W, Xiong W. Exploring global symmetry-breaking superradiant phase via phase competition. OPTICS LETTERS 2024; 49:2137-2140. [PMID: 38621095 DOI: 10.1364/ol.522886] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/01/2024] [Accepted: 03/21/2024] [Indexed: 04/17/2024]
Abstract
Superradiant phase transitions play a fundamental role in understanding the mechanism of collective light-matter interaction at the quantum level. Here we investigate multiple superradiant phases and phase transitions with different symmetry-breaking patterns in a two-mode V-type Dicke model. Interestingly, we show that there exists a quadruple point where one normal phase, one global symmetry-breaking superradiant phase, and two local symmetry-breaking superradiant phases meet. Such a global phase results from the phase competition between two local superradiant phases and cannot occur in the standard Λ- and Ξ-type three-level configurations in quantum optics. Moreover, we exhibit a sequential first-order quantum phase transition from one local to the global again to the other local superradiant phase. Our study opens up a perspective of exploring multilevel quantum critical phenomena with global symmetry breaking.
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2
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Bastarrachea-Magnani MA, Villaseñor D, Chávez-Carlos J, Lerma-Hernández S, Santos LF, Hirsch JG. Quantum multifractality as a probe of phase space in the Dicke model. Phys Rev E 2024; 109:034202. [PMID: 38632765 DOI: 10.1103/physreve.109.034202] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/12/2023] [Accepted: 01/31/2024] [Indexed: 04/19/2024]
Abstract
We study the multifractal behavior of coherent states projected in the energy eigenbasis of the spin-boson Dicke Hamiltonian, a paradigmatic model describing the collective interaction between a single bosonic mode and a set of two-level systems. By examining the linear approximation and parabolic correction to the mass exponents, we find ergodic and multifractal coherent states and show that they reflect details of the structure of the classical phase space, including chaos, regularity, and features of localization. The analysis of multifractality stands as a sensitive tool to detect changes and structures in phase space, complementary to classical tools to investigate it. We also address the difficulties involved in the multifractal analyses of systems with unbounded Hilbert spaces.
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Affiliation(s)
- M A Bastarrachea-Magnani
- Departamento de Física, Universidad Autónoma Metropolitana-Iztapalapa, Av. Ferrocarril San Rafael Atlixco 186, C.P. 09310 Mexico City, Mexico
| | - D Villaseñor
- Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, C.P. 04510, Mexico City, Mexico
| | - J Chávez-Carlos
- Department of Physics, University of Connecticut, Storrs, Connecticut 06269, USA
| | - S Lerma-Hernández
- Facultad de Física, Universidad Veracruzana, Campus Arco Sur, Paseo 112, C.P. 91097 Xalapa, Mexico
| | - L F Santos
- Department of Physics, University of Connecticut, Storrs, Connecticut 06269, USA
| | - J G Hirsch
- Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Apdo. Postal 70-543, C.P. 04510 Mexico City, Mexico
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3
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Hotter C, Ritsch H, Gietka K. Combining Critical and Quantum Metrology. PHYSICAL REVIEW LETTERS 2024; 132:060801. [PMID: 38394596 DOI: 10.1103/physrevlett.132.060801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/11/2023] [Accepted: 01/16/2024] [Indexed: 02/25/2024]
Abstract
Critical metrology relies on the precise preparation of a system in its ground state near a quantum phase transition point where quantum correlations get very strong. Typically, this increases the quantum Fisher information with respect to changes in system parameters and thus improves the optimally possible measurement precision limited by the Cramér-Rao bound. Hence critical metrology involves encoding information about the unknown parameter in changes of the system's ground state. Conversely, in conventional metrology methods like Ramsey interferometry, the eigenstates of the system remain unchanged, and information about the unknown parameter is encoded in the relative phases that excited system states accumulate during their time evolution. Here we introduce an approach combining these two methodologies into a unified protocol applicable to closed and driven-dissipative systems. We show that the quantum Fisher information in this case exhibits an additional interference term originating from the interplay between eigenstate and relative phase changes. We provide analytical expressions for the quantum and classical Fisher information in such a setup, elucidating as well a straightforward measurement approach that nearly attains the maximum precision permissible under the Cramér-Rao bound. We showcase these results by focusing on the squeezing Hamiltonian, which characterizes the thermodynamic limit of Dicke and Lipkin-Meshkov-Glick Hamiltonians.
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Affiliation(s)
- Christoph Hotter
- Institut für Theoretische Physik, Universität Innsbruck, A-6020 Innsbruck, Austria
| | - Helmut Ritsch
- Institut für Theoretische Physik, Universität Innsbruck, A-6020 Innsbruck, Austria
| | - Karol Gietka
- Institut für Theoretische Physik, Universität Innsbruck, A-6020 Innsbruck, Austria
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4
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Xu HG, Jin J, Neto GDM, de Almeida NG. Universal quantum Otto heat machine based on the Dicke model. Phys Rev E 2024; 109:014122. [PMID: 38366433 DOI: 10.1103/physreve.109.014122] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/13/2023] [Accepted: 12/15/2023] [Indexed: 02/18/2024]
Abstract
In this paper we study a quantum Otto thermal machine where the working substance is composed of N identical qubits coupled to a single mode of a bosonic field, where the atoms and the field interact with a reservoir, as described by the so-called open Dicke model. By controlling the relevant and experimentally accessible parameters of the model we show that it is possible to build a universal quantum heat machine (UQHM) that can function as an engine, refrigerator, heater, or accelerator. The heat and work exchanges are computed taking into account the growth of the number N of atoms as well as the coupling regimes characteristic of the Dicke model for several ratios of temperatures of the two thermal reservoirs. The analysis of quantum features such as entanglement and second-order correlation shows that these quantum resources do not affect either the efficiency or the performance of the UQHM based on the open Dicke model. In addition, we show that the improvement in both efficiency and coefficient of performance of our UQHM occurs for regions around the critical value of the phase transition parameter of the model.
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Affiliation(s)
- He-Guang Xu
- School of Physics, Dalian University of Technology, 116024 Dalian, China
| | - Jiasen Jin
- School of Physics, Dalian University of Technology, 116024 Dalian, China
| | - G D M Neto
- Department of Physics, Zhejiang Normal University, Jinhua 321004, China
| | - Norton G de Almeida
- Instituto de Física, Universidade Federal de Goiás, 74.001-970, Goiânia, Goiás, Brazil
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5
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Villaseñor D, Barberis-Blostein P. Analysis of chaos and regularity in the open Dicke model. Phys Rev E 2024; 109:014206. [PMID: 38366466 DOI: 10.1103/physreve.109.014206] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/10/2023] [Accepted: 11/22/2023] [Indexed: 02/18/2024]
Abstract
We present an analysis of chaos and regularity in the open Dicke model, when dissipation is due to cavity losses. Due to the infinite Liouville space of this model, we also introduce a criterion to numerically find a complex spectrum which approximately represents the system spectrum. The isolated Dicke model has a well-defined classical limit with two degrees of freedom. We select two case studies where the classical isolated system shows regularity and where chaos appears. To characterize the open system as regular or chaotic, we study regions of the complex spectrum taking windows over the absolute value of its eigenvalues. Our results for this infinite-dimensional system agree with the Grobe-Haake-Sommers (GHS) conjecture for Markovian dissipative open quantum systems, finding the expected 2D Poisson distribution for regular regimes, and the distribution of the Ginibre unitary ensemble (GinUE) for the chaotic ones, respectively.
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Affiliation(s)
- David Villaseñor
- Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, C.P. 04510 CDMX, Mexico
| | - Pablo Barberis-Blostein
- Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, C.P. 04510 CDMX, Mexico
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6
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Gietka K, Hotter C, Ritsch H. Unique Steady-State Squeezing in a Driven Quantum Rabi Model. PHYSICAL REVIEW LETTERS 2023; 131:223604. [PMID: 38101370 DOI: 10.1103/physrevlett.131.223604] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/22/2023] [Accepted: 11/06/2023] [Indexed: 12/17/2023]
Abstract
Squeezing is essential to many quantum technologies and our understanding of quantum physics. Here, we show a novel type of steady-state squeezing that can be generated in the closed and open quantum Rabi as well as Dicke model. To this end, we eliminate the spin dynamics which effectively leads to an abstract harmonic oscillator whose eigenstates are squeezed with respect to the noninteracting harmonic oscillator. By driving the system, we generate squeezing which has the unique property of time-independent uncertainties and squeezed dynamics. Such squeezing might find applications in continuous backaction evading measurements and should already be observable in optomechanical systems and Coulomb crystals.
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Affiliation(s)
- Karol Gietka
- Institut für Theoretische Physik, Universität Innsbruck, A-6020 Innsbruck, Austria
| | - Christoph Hotter
- 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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7
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Giachetti G, Defenu N. Entanglement propagation and dynamics in non-additive quantum systems. Sci Rep 2023; 13:12388. [PMID: 37524738 PMCID: PMC10390585 DOI: 10.1038/s41598-023-37984-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/03/2023] [Accepted: 06/30/2023] [Indexed: 08/02/2023] Open
Abstract
The prominent collective character of long-range interacting quantum systems makes them promising candidates for quantum technological applications. Yet, lack of additivity overthrows the traditional picture for entanglement scaling and transport, due to the breakdown of the common mechanism based on excitations propagation and confinement. Here, we describe the dynamics of the entanglement entropy in many-body quantum systems with a diverging contribution to the internal energy from the long-range two body potential. While in the strict thermodynamic limit entanglement dynamics is shown to be suppressed, a rich mosaic of novel scaling regimes is observed at intermediate system sizes, due to the possibility to trigger multiple resonant modes in the global dynamics. Quantitative predictions on the shape and timescales of entanglement propagation are made, paving the way to the observation of these phases in current quantum simulators. This picture is connected and contrasted with the case of local many body systems subject to Floquet driving.
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Affiliation(s)
- Guido Giachetti
- SISSA and INFN Sezione di Trieste, Via Bonomea 265, 34136, Trieste, Italy
| | - Nicolò Defenu
- Institut für Theoretische Physik, ETH Zürich, Wolfgang-Pauli-Str. 27, Zurich, Switzerland.
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8
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Villaseñor D, Pilatowsky-Cameo S, Bastarrachea-Magnani MA, Lerma-Hernández S, Santos LF, Hirsch JG. Chaos and Thermalization in the Spin-Boson Dicke Model. ENTROPY (BASEL, SWITZERLAND) 2022; 25:8. [PMID: 36673156 PMCID: PMC9857936 DOI: 10.3390/e25010008] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/14/2022] [Revised: 12/13/2022] [Accepted: 12/14/2022] [Indexed: 06/17/2023]
Abstract
We present a detailed analysis of the connection between chaos and the onset of thermalization in the spin-boson Dicke model. This system has a well-defined classical limit with two degrees of freedom, and it presents both regular and chaotic regions. Our studies of the eigenstate expectation values and the distributions of the off-diagonal elements of the number of photons and the number of excited atoms validate the diagonal and off-diagonal eigenstate thermalization hypothesis (ETH) in the chaotic region, thus ensuring thermalization. The validity of the ETH reflects the chaotic structure of the eigenstates, which we corroborate using the von Neumann entanglement entropy and the Shannon entropy. Our results for the Shannon entropy also make evident the advantages of the so-called "efficient basis" over the widespread employed Fock basis when investigating the unbounded spectrum of the Dicke model. The efficient basis gives us access to a larger number of converged states than what can be reached with the Fock basis.
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Affiliation(s)
- David Villaseñor
- Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Apdo. Postal 70-543, Mexico City 04510, Mexico
- Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, Mexico City 04510, Mexico
| | - Saúl Pilatowsky-Cameo
- Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - Miguel A. Bastarrachea-Magnani
- Departamento de Física, Universidad Autónoma Metropolitana-Iztapalapa, Av. Ferrocarril San Rafael Atlixco 186, Mexico City 09340, Mexico
| | - Sergio Lerma-Hernández
- Facultad de Física, Universidad Veracruzana, Circuito Aguirre Beltrán s/n, Xalapa 91000, Mexico
| | - Lea F. Santos
- Department of Physics, University of Connecticut, Storrs, CT 06269, USA
| | - Jorge G. Hirsch
- Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Apdo. Postal 70-543, Mexico City 04510, Mexico
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9
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Mei QX, Li BW, Wu YK, Cai ML, Wang Y, Yao L, Zhou ZC, Duan LM. Experimental Realization of the Rabi-Hubbard Model with Trapped Ions. PHYSICAL REVIEW LETTERS 2022; 128:160504. [PMID: 35522503 DOI: 10.1103/physrevlett.128.160504] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/09/2021] [Revised: 03/26/2022] [Accepted: 03/31/2022] [Indexed: 06/14/2023]
Abstract
Quantum simulation provides important tools in studying strongly correlated many-body systems with controllable parameters. As a hybrid of two fundamental models in quantum optics and in condensed matter physics, the Rabi-Hubbard model demonstrates rich physics through the competition between local spin-boson interactions and long-range boson hopping. Here, we report an experimental realization of the Rabi-Hubbard model using up to 16 trapped ions and present a controlled study of its equilibrium properties and quantum dynamics. We observe the ground-state quantum phase transition by slowly quenching the coupling strength, and measure the quantum dynamical evolution in various parameter regimes. With the magnetization and the spin-spin correlation as probes, we verify the prediction of the model Hamiltonian by comparing theoretical results in small system sizes with experimental observations. For larger-size systems of 16 ions and 16 phonon modes, the effective Hilbert space dimension exceeds 2^{57}, whose dynamics is intractable for classical supercomputers.
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Affiliation(s)
- Q-X Mei
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, People's Republic of China
| | - B-W Li
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, People's Republic of China
| | - Y-K Wu
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, People's Republic of China
| | - M-L Cai
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, People's Republic of China
- HYQ Co., Ltd., Beijing, 100176, People's Republic of China
| | - Y Wang
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, People's Republic of China
| | - L Yao
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, People's Republic of China
- HYQ Co., Ltd., Beijing, 100176, People's Republic of China
| | - Z-C Zhou
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, People's Republic of China
| | - L-M Duan
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, People's Republic of China
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10
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Zhao J, Hwang MJ. Frustrated Superradiant Phase Transition. PHYSICAL REVIEW LETTERS 2022; 128:163601. [PMID: 35522483 DOI: 10.1103/physrevlett.128.163601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/02/2021] [Accepted: 03/08/2022] [Indexed: 06/14/2023]
Abstract
Frustration occurs when a system cannot find a lowest-energy configuration due to conflicting constraints. We show that a frustrated superradiant phase transition occurs when the ground-state superradiance of cavity fields due to local light-matter interactions cannot simultaneously minimize the positive photon hopping energies. We solve the Dicke trimer model on a triangle motif with both negative and positive hopping energies and show that the latter results in a sixfold degenerate ground-state manifold in which the translational symmetry is spontaneously broken. In the frustrated superradiant phase, we find that two sets of diverging time and fluctuation scales coexist, one governed by the mean-field critical exponent and another by a novel critical exponent. The latter is associated with the fluctuation in the difference of local order parameters and gives rise to site-dependent photon number critical exponents, which may serve as an experimental probe for the frustrated superradiant phase. We provide a qualitative explanation for the emergence of unconventional critical scalings and demonstrate that they are generic properties of the frustrated superradiant phase at the hand of a one-dimensional Dicke lattice with an odd number of sites. The mechanism for the frustrated superradiant phase transition discovered here applies to any lattice geometries where the antiferromagnetic ordering of neighboring sites are incompatible and therefore our work paves the way toward the exploration of frustrated phases of coupled light and matter.
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Affiliation(s)
- Jinchen Zhao
- Division of Natural and Applied Sciences, Duke Kunshan University, Kunshan, Jiangsu 215300, China
| | - Myung-Joong Hwang
- Division of Natural and Applied Sciences, Duke Kunshan University, Kunshan, Jiangsu 215300, China
- Zu Chongzhi Center for Mathematics and Computational Science, Duke Kunshan University, Kunshan, Jiangsu 215300, China
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11
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Chen X, Wu Z, Jiang M, Lü XY, Peng X, Du J. Experimental quantum simulation of superradiant phase transition beyond no-go theorem via antisqueezing. Nat Commun 2021; 12:6281. [PMID: 34725347 PMCID: PMC8560888 DOI: 10.1038/s41467-021-26573-5] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/29/2021] [Accepted: 09/24/2021] [Indexed: 11/09/2022] Open
Abstract
The superradiant phase transition in thermal equilibrium is a fundamental concept bridging statistical physics and electrodynamics, which has never been observed in real physical systems since the first proposal in the 1970s. The existence of this phase transition in cavity quantum electrodynamics systems is still subject of ongoing debates due to the no-go theorem induced by the so-called A2 term. Moreover, experimental conditions to study this phase transition are hard to achieve with current accessible technology. Based on the platform of nuclear magnetic resonance, here we experimentally simulate the occurrence of an equilibrium superradiant phase transition beyond no-go theorem by introducing the antisqueezing effect. The mechanism relies on that the antisqueezing effect recovers the singularity of the ground state via exponentially enhancing the zero point fluctuation of system. The strongly entangled and squeezed Schrödinger cat states of spins are achieved experimentally in the superradiant phase, which may play an important role in fundamental tests of quantum theory and implementations of quantum metrology. Quantum simulation allows to investigate otherwise inaccessible physical scenarios. Here, the authors simulate a quantum Rabi model using nuclear spins, including the A2 term and an anti-squeezing term, which allows them to see signatures of a superradiant phase transition in the simulated system.
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Affiliation(s)
- Xi Chen
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, 230026, China.,CAS Key Laboratory of Microscale Magnetic Resonance, University of Science and Technology of China, Hefei, 230026, China.,Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, 230026, China
| | - Ze Wu
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, 230026, China.,CAS Key Laboratory of Microscale Magnetic Resonance, University of Science and Technology of China, Hefei, 230026, China.,Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, 230026, China
| | - Min Jiang
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, 230026, China.,CAS Key Laboratory of Microscale Magnetic Resonance, University of Science and Technology of China, Hefei, 230026, China.,Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, 230026, China
| | - Xin-You Lü
- School of physics, Huazhong University of Science and Technology, Wuhan, 430074, China.
| | - Xinhua Peng
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, 230026, China. .,CAS Key Laboratory of Microscale Magnetic Resonance, University of Science and Technology of China, Hefei, 230026, China. .,Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, 230026, China.
| | - Jiangfeng Du
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, 230026, China.,CAS Key Laboratory of Microscale Magnetic Resonance, University of Science and Technology of China, Hefei, 230026, China.,Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, 230026, China
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12
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Giachetti G, Defenu N, Ruffo S, Trombettoni A. Berezinskii-Kosterlitz-Thouless Phase Transitions with Long-Range Couplings. PHYSICAL REVIEW LETTERS 2021; 127:156801. [PMID: 34678026 DOI: 10.1103/physrevlett.127.156801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/17/2021] [Accepted: 08/16/2021] [Indexed: 06/13/2023]
Abstract
The Berezinskii-Kosterlitz-Thouless (BKT) transition is the paradigmatic example of a topological phase transition without symmetry breaking, where a quasiordered phase, characterized by a power-law scaling of the correlation functions at low temperature, is disrupted by the proliferation of topological excitations above the critical temperature T_{BKT}. In this Letter, we consider the effect of long-range decaying couplings ∼r^{-2-σ} on the BKT transition. After pointing out the relevance of this nontrivial problem, we discuss the phase diagram, which is far richer than the corresponding short-range one. It features-for 7/4<σ<2-a quasiordered phase in a finite temperature range T_{c}<T<T_{BKT}, which occurs between a symmetry broken phase for T<T_{c} and a disordered phase for T>T_{BKT}. The transition temperature T_{c} displays unique universal features quite different from those of the traditional, short-range XY model. Given the universal nature of our findings, they may be observed in current experimental realizations in 2D atomic, molecular, and optical quantum systems.
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Affiliation(s)
- Guido Giachetti
- SISSA and INFN Sezione di Trieste, Via Bonomea 265, I-34136 Trieste, Italy
| | - Nicolò Defenu
- Institute for Theoretical Physics, ETH Zürich, Wolfgang-Pauli-Strasse 27, 8093 Zürich, Switzerland
| | - Stefano Ruffo
- SISSA and INFN Sezione di Trieste, Via Bonomea 265, I-34136 Trieste, Italy and Istituto dei Sistemi Complessi, Consiglio Nazionale delle Ricerche, Via Madonna del Piano 10, I-50019 Sesto Fiorentino, Italy
| | - Andrea Trombettoni
- Department of Physics, University of Trieste, Strada Costiera 11, I-34151 Trieste, Italy, SISSA and INFN Sezione di Trieste, Via Bonomea 265, I-34136 Trieste, Italy, and CNR-IOM DEMOCRITOS Simulation Center, Via Bonomea 265, I-34136 Trieste, Italy
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13
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Mao ZC, Xu YZ, Mei QX, Zhao WD, Jiang Y, Wang Y, Chang XY, He L, Yao L, Zhou ZC, Wu YK, Duan LM. Experimental Realization of Multi-ion Sympathetic Cooling on a Trapped Ion Crystal. PHYSICAL REVIEW LETTERS 2021; 127:143201. [PMID: 34652176 DOI: 10.1103/physrevlett.127.143201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/27/2021] [Accepted: 08/30/2021] [Indexed: 06/13/2023]
Abstract
Trapped ions are one of the leading platforms in quantum information science. For quantum computing with large circuit depth and quantum simulation with long evolution time, it is of crucial importance to cool large ion crystals at runtime without affecting the internal states of the computational qubits, thus the necessity of sympathetic cooling. Here, we report multi-ion sympathetic cooling on a long ion chain using a narrow cooling beam focused on two adjacent ions, and optimize the choice of the cooling ions according to the collective oscillation modes of the chain. We show that, by cooling a small fraction of ions, cooling effects close to the global Doppler cooling limit can be achieved. This experiment therefore demonstrates an important enabling step for quantum information processing with large ion crystals.
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Affiliation(s)
- Z-C Mao
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, People's Republic of China
| | - Y-Z Xu
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, People's Republic of China
| | - Q-X Mei
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, People's Republic of China
| | - W-D Zhao
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, People's Republic of China
| | - Y Jiang
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, People's Republic of China
| | - Y Wang
- School of Physics, Peking University, Beijing 100871, People's Republic of China
| | - X-Y Chang
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, People's Republic of China
| | - L He
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, People's Republic of China
| | - L Yao
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, People's Republic of China
| | - Z-C Zhou
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, People's Republic of China
- Beijing Academy of Quantum Information Sciences, Beijing 100193, People's Republic of China
| | - Y-K Wu
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, People's Republic of China
| | - L-M Duan
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, People's Republic of China
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14
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Gilmore KA, Affolter M, Lewis-Swan RJ, Barberena D, Jordan E, Rey AM, Bollinger JJ. Quantum-enhanced sensing of displacements and electric fields with two-dimensional trapped-ion crystals. Science 2021; 373:673-678. [PMID: 34353950 DOI: 10.1126/science.abi5226] [Citation(s) in RCA: 23] [Impact Index Per Article: 7.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/15/2021] [Accepted: 06/25/2021] [Indexed: 11/02/2022]
Abstract
Fully controllable ultracold atomic systems are creating opportunities for quantum sensing, yet demonstrating a quantum advantage in useful applications by harnessing entanglement remains a challenging task. Here, we realize a many-body quantum-enhanced sensor to detect displacements and electric fields using a crystal of ~150 trapped ions. The center-of-mass vibrational mode of the crystal serves as a high-Q mechanical oscillator, and the collective electronic spin serves as the measurement device. By entangling the oscillator and collective spin and controlling the coherent dynamics via a many-body echo, a displacement is mapped into a spin rotation while avoiding quantum back-action and thermal noise. We achieve a sensitivity to displacements of 8.8 ± 0.4 decibels below the standard quantum limit and a sensitivity for measuring electric fields of 240 ± 10 nanovolts per meter in 1 second. Feasible improvements should enable the use of trapped ions in searches for dark matter.
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Affiliation(s)
- Kevin A Gilmore
- Center for Theory of Quantum Matter, University of Colorado, Boulder, CO 80309, USA. .,Homer L. Dodge Department of Physics and Astronomy, University of Oklahoma, Norman, OK 73019, USA.,National Institute of Standards and Technology, Boulder, CO 80305, USA.,Department of Physics, University of Colorado, Boulder, CO 80309, USA
| | - Matthew Affolter
- Center for Theory of Quantum Matter, University of Colorado, Boulder, CO 80309, USA.,National Institute of Standards and Technology, Boulder, CO 80305, USA
| | - Robert J Lewis-Swan
- National Institute of Standards and Technology, Boulder, CO 80305, USA.,Department of Physics, University of Colorado, Boulder, CO 80309, USA.,Homer L. Dodge Department of Physics and Astronomy, University of Oklahoma, Norman, OK 73019, USA.,Center for Quantum Research and Technology, University of Oklahoma, Norman, OK 73019, USA
| | - Diego Barberena
- Center for Quantum Research and Technology, University of Oklahoma, Norman, OK 73019, USA.,JILA, NIST, and Department of Physics, University of Colorado, Boulder, CO 80309, USA.,JILA, NIST, and Department of Physics, University of Colorado, Boulder, CO 80309, USA.,Center for Theory of Quantum Matter, University of Colorado, Boulder, CO 80309, USA
| | - Elena Jordan
- Center for Theory of Quantum Matter, University of Colorado, Boulder, CO 80309, USA.,National Institute of Standards and Technology, Boulder, CO 80305, USA
| | - Ana Maria Rey
- Center for Quantum Research and Technology, University of Oklahoma, Norman, OK 73019, USA. .,JILA, NIST, and Department of Physics, University of Colorado, Boulder, CO 80309, USA.,JILA, NIST, and Department of Physics, University of Colorado, Boulder, CO 80309, USA.,Center for Theory of Quantum Matter, University of Colorado, Boulder, CO 80309, USA
| | - John J Bollinger
- Center for Theory of Quantum Matter, University of Colorado, Boulder, CO 80309, USA. .,National Institute of Standards and Technology, Boulder, CO 80305, USA
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15
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Villaseñor D, Pilatowsky-Cameo S, Bastarrachea-Magnani MA, Lerma-Hernández S, Hirsch JG. Quantum localization measures in phase space. Phys Rev E 2021; 103:052214. [PMID: 34134277 DOI: 10.1103/physreve.103.052214] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/15/2021] [Accepted: 04/23/2021] [Indexed: 11/07/2022]
Abstract
Measuring the degree of localization of quantum states in phase space is essential for the description of the dynamics and equilibration of quantum systems, but this topic is far from being understood. There is no unique way to measure localization, and individual measures can reflect different aspects of the same quantum state. Here we present a general scheme to define localization in measure spaces, which is based on what we call Rényi occupations, from which any measure of localization can be derived. We apply this scheme to the four-dimensional unbounded phase space of the interacting spin-boson Dicke model. In particular, we make a detailed comparison of two localization measures based on the Husimi function in the regime where the model is chaotic, namely, one that projects the Husimi function over the finite phase space of the spin and another that uses the Husimi function defined over classical energy shells. We elucidate the origin of their differences, showing that in unbounded spaces the definition of maximal delocalization requires a bounded reference subspace, with different selections leading to contextual answers.
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Affiliation(s)
- D Villaseñor
- Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Apartado Postal 70-543, CP 04510 Ciudad de México, Mexico
| | - S Pilatowsky-Cameo
- Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Apartado Postal 70-543, CP 04510 Ciudad de México, Mexico
| | - M A Bastarrachea-Magnani
- Departamento de Física, Universidad Autónoma Metropolitana-Iztapalapa, San Rafael Atlixco 186, CP 09340 Ciudad de México, Mexico
| | - S Lerma-Hernández
- Facultad de Física, Universidad Veracruzana, Circuito Aguirre Beltrán s/n, CP 91000 Xalapa, Veracruz, Mexico
| | - J G Hirsch
- Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Apartado Postal 70-543, CP 04510 Ciudad de México, Mexico
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16
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Shapiro DS. Transport of pseudothermal photons through an anharmonic cavity. Sci Rep 2021; 11:8328. [PMID: 33859246 PMCID: PMC8050331 DOI: 10.1038/s41598-021-87536-w] [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: 09/19/2020] [Accepted: 03/31/2021] [Indexed: 11/14/2022] Open
Abstract
Under nonequilibrium conditions, quantum optical systems reveal unusual properties that might be distinct from those in condensed matter. The fundamental reason is that photonic eigenstates can have arbitrary occupation numbers, whereas in electronic systems these are limited by the Pauli principle. Here, we address the steady-state transport of pseudothermal photons between two waveguides connected through a cavity with Bose–Hubbard interaction between photons. One of the waveguides is subjected to a broadband incoherent pumping. We predict a continuous transition between the regimes of Lorentzian and Gaussian chaotic light emitted by the cavity. The rich variety of nonequilibrium transport regimes is revealed by the zero-frequency noise. There are three limiting cases, in which the noise-current relation is characterized by a power-law, \documentclass[12pt]{minimal}
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\begin{document}$$S\propto J^\gamma$$\end{document}S∝Jγ. The Lorentzian light corresponds to Breit-Wigner-like transmission and \documentclass[12pt]{minimal}
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\begin{document}$$\gamma =2$$\end{document}γ=2. The Gaussian regime corresponds to many-body transport with the shot noise (\documentclass[12pt]{minimal}
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\begin{document}$$\gamma =1$$\end{document}γ=1) at large currents; at low currents, however, we find an unconventional exponent \documentclass[12pt]{minimal}
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\begin{document}$$\gamma =3/2$$\end{document}γ=3/2 indicating a nontrivial interplay between multi-photon transitions and incoherent pumping. The nonperturbative solution for photon dephasing is obtained in the framework of the Keldysh field theory and Caldeira-Leggett effective action. These findings might be relevant for experiments on photon blockade in superconducting qubits, thermal states transfer, and photon statistics probing.
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Affiliation(s)
- Dmitriy S Shapiro
- Dukhov Research Institute of Automatics (VNIIA), Moscow, Russia, 127055. .,Department of Physics, National Research University Higher School of Economics, Moscow, Russia, 101000. .,Laboratory of Superconducting Metamaterials, National University of Science and Technology MISiS, Moscow, Russia, 119049. .,V. A. Kotel'nikov Institute of Radio Engineering and Electronics, Russian Academy of Sciences, Moscow, Russia, 125009.
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17
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Kelly SP, Rey AM, Marino J. Effect of Active Photons on Dynamical Frustration in Cavity QED. PHYSICAL REVIEW LETTERS 2021; 126:133603. [PMID: 33861099 DOI: 10.1103/physrevlett.126.133603] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/18/2020] [Accepted: 03/05/2021] [Indexed: 06/12/2023]
Abstract
We study the far-from-equilibrium dynamical regimes of a many-body spin-boson model with disordered couplings relevant for cavity QED and trapped ion experiments, using the discrete truncated Wigner approximation. We focus on the dynamics of spin observables upon varying the disorder strength and the frequency of the photons, finding that the latter can considerably alter the structure of the system's dynamical responses. When the photons evolve at a similar rate as the spins, they can induce qualitatively distinct frustrated dynamics characterized by either logarithmic or algebraically slow relaxation. The latter illustrates resilience of glassylike dynamics in the presence of active photonic degrees of freedom, suggesting that disordered quantum many-body systems with resonant photons or phonons can display a rich diagram of nonequilibrium responses, with near future applications for quantum information science.
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Affiliation(s)
- Shane P Kelly
- Institut für Physik, Johannes Gutenberg Universität Mainz, D-55099 Mainz, Germany
| | - Ana Maria Rey
- JILA, NIST, Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
- Center for Theory of Quantum Matter, University of Colorado, Boulder, Colorado 80309, USA
| | - Jamir Marino
- Institut für Physik, Johannes Gutenberg Universität Mainz, D-55099 Mainz, Germany
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18
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Pilatowsky-Cameo S, Villaseñor D, Bastarrachea-Magnani MA, Lerma-Hernández S, Santos LF, Hirsch JG. Ubiquitous quantum scarring does not prevent ergodicity. Nat Commun 2021; 12:852. [PMID: 33558492 PMCID: PMC7870831 DOI: 10.1038/s41467-021-21123-5] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/18/2020] [Accepted: 01/13/2021] [Indexed: 11/11/2022] Open
Abstract
In a classically chaotic system that is ergodic, any trajectory will be arbitrarily close to any point of the available phase space after a long time, filling it uniformly. Using Born’s rules to connect quantum states with probabilities, one might then expect that all quantum states in the chaotic regime should be uniformly distributed in phase space. This simplified picture was shaken by the discovery of quantum scarring, where some eigenstates are concentrated along unstable periodic orbits. Despite that, it is widely accepted that most eigenstates of chaotic models are indeed ergodic. Our results show instead that all eigenstates of the chaotic Dicke model are actually scarred. They also show that even the most random states of this interacting atom-photon system never occupy more than half of the available phase space. Quantum ergodicity is achievable only as an ensemble property, after temporal averages are performed. It is generally believed that most eigenstates of quantum chaotic models are ergodic. In this work, the authors disprove this by showing that all eigenstates of the Dicke model in the chaotic regime are scarred, and that ergodicity is an ensemble property, achievable only in the temporal average.
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Affiliation(s)
- Saúl Pilatowsky-Cameo
- Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Mexico City, Mexico
| | - David Villaseñor
- Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Mexico City, Mexico
| | - Miguel A Bastarrachea-Magnani
- Department of Physics and Astronomy, Aarhus University, Ny Munkegade, Aarhus C, Denmark.,Departamento de Física, Universidad Autónoma Metropolitana-Iztapalapa, Mexico City, Mexico
| | - Sergio Lerma-Hernández
- Facultad de Física, Universidad Veracruzana, Circuito Aguirre Beltrán s/n, Xalapa, Veracruz, Mexico
| | - Lea F Santos
- Department of Physics, Yeshiva University, New York, NY, USA.
| | - Jorge G Hirsch
- Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Mexico City, Mexico.
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19
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Lewis-Swan RJ, Muleady SR, Rey AM. Detecting Out-of-Time-Order Correlations via Quasiadiabatic Echoes as a Tool to Reveal Quantum Coherence in Equilibrium Quantum Phase Transitions. PHYSICAL REVIEW LETTERS 2020; 125:240605. [PMID: 33412057 DOI: 10.1103/physrevlett.125.240605] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/11/2020] [Revised: 09/09/2020] [Accepted: 10/26/2020] [Indexed: 06/12/2023]
Abstract
We propose a new dynamical method to connect equilibrium quantum phase transitions and quantum coherence using out-of-time-order correlations (OTOCs). Adopting the iconic Lipkin-Meshkov-Glick and transverse-field Ising models as illustrative examples, we show that an abrupt change in coherence and entanglement of the ground state across a quantum phase transition is observable in the spectrum of multiple quantum coherence intensities, which are a special type of OTOC. We also develop a robust protocol to obtain the relevant OTOCs using quasi-adiabatic quenches through the ground state phase diagram. Our scheme allows for the detection of OTOCs without time reversal of coherent dynamics, making it applicable and important for a broad range of current experiments where time reversal cannot be achieved by inverting the sign of the underlying Hamiltonian.
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Affiliation(s)
- R J Lewis-Swan
- Homer L. Dodge Department of Physics and Astronomy, The University of Oklahoma, Norman, Oklahoma 73019, USA
- JILA, NIST, Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
- Center for Theory of Quantum Matter, University of Colorado, Boulder, Colorado 80309, USA
| | - S R Muleady
- JILA, NIST, Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
- Center for Theory of Quantum Matter, University of Colorado, Boulder, Colorado 80309, USA
| | - A M Rey
- JILA, NIST, Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
- Center for Theory of Quantum Matter, University of Colorado, Boulder, Colorado 80309, USA
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20
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Reiter F, Nguyen TL, Home JP, Yelin SF. Cooperative Breakdown of the Oscillator Blockade in the Dicke Model. PHYSICAL REVIEW LETTERS 2020; 125:233602. [PMID: 33337189 DOI: 10.1103/physrevlett.125.233602] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/20/2018] [Revised: 03/30/2020] [Accepted: 10/02/2020] [Indexed: 06/12/2023]
Abstract
The Dicke model, which describes the coupling of an ensemble of spins to a harmonic oscillator, is known for its superradiant phase transition, which can both be observed in the ground state in a purely Hamiltonian setting, as well as in the steady state of an open-system Dicke model with dissipation. We demonstrate that, in addition, the dissipative Dicke model can undergo a second phase transition to a nonstationary phase, characterized by unlimited heating of the harmonic oscillator. Identifying the mechanism of the phase transition and deriving the scaling of the critical coupling with the system size we conclude that the novel phase transition can be understood as a cooperative breakdown of the oscillator blockade which otherwise prevents higher excitation of the system. We discuss an implementation with trapped ions and investigate the role of cooling, by which the breakdown can be suppressed.
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Affiliation(s)
- Florentin Reiter
- Department of Physics, Harvard University, 17 Oxford Street, Cambridge, Massachusetts 02138, USA
- Institute for Quantum Electronics, ETH Zürich, Otto-Stern-Weg 1, 8093 Zürich, Switzerland
| | - Thanh Long Nguyen
- Institute for Quantum Electronics, ETH Zürich, Otto-Stern-Weg 1, 8093 Zürich, Switzerland
| | - Jonathan P Home
- Institute for Quantum Electronics, ETH Zürich, Otto-Stern-Weg 1, 8093 Zürich, Switzerland
| | - Susanne F Yelin
- Department of Physics, Harvard University, 17 Oxford Street, Cambridge, Massachusetts 02138, USA
- Department of Physics, University of Connecticut, Storrs, Connecticut 06269, USA
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21
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Wang Q, Robnik M. Statistical properties of the localization measure of chaotic eigenstates in the Dicke model. Phys Rev E 2020; 102:032212. [PMID: 33075891 DOI: 10.1103/physreve.102.032212] [Citation(s) in RCA: 16] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/15/2020] [Accepted: 08/25/2020] [Indexed: 05/16/2023]
Abstract
The quantum localization is one of the remarkable phenomena in the studies of quantum chaos and plays an important role in various contexts. Thus, an understanding of the properties of quantum localization is essential. In spite of much effort dedicated to investigating the manifestations of localization in the time-dependent systems, the features of localization in time-independent systems are still less explored, particularly in quantum systems which correspond to the classical systems with smooth Hamiltonian. In this work, we present such a study for a quantum many-body system, namely, the Dicke model. The classical counterpart of the Dicke model is given by a smooth Hamiltonian with two degrees of freedom. We examine the signatures of localization in its chaotic eigenstates. We show that the entropy localization measure, which is defined in terms of the information entropy of Husimi distribution, behaves linearly with the participation number, a measure of the degree of localization of a quantum state. We further demonstrate that the localization measure probability distribution is well described by the β distribution. We also find that the averaged localization measure is linearly related to the level repulsion exponent, a widely used quantity to characterize the localization in chaotic eigenstates. Our findings extend the previous results in billiards to the quantum many-body system with classical counterpart described by a smooth Hamiltonian, and they indicate that the properties of localized chaotic eigenstates are universal.
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Affiliation(s)
- Qian Wang
- CAMTP-Center for Applied Mathematics and Theoretical Physics, University of Maribor, Mladinska 3, SI-2000 Maribor, Slovenia
- Department of Physics, Zhejiang Normal University, Jinhua 321004, China
| | - Marko Robnik
- CAMTP-Center for Applied Mathematics and Theoretical Physics, University of Maribor, Mladinska 3, SI-2000 Maribor, Slovenia
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22
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Garbe L, Wade P, Minganti F, Shammah N, Felicetti S, Nori F. Dissipation-induced bistability in the two-photon Dicke model. Sci Rep 2020; 10:13408. [PMID: 32770061 PMCID: PMC7414202 DOI: 10.1038/s41598-020-69704-6] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/09/2019] [Accepted: 07/13/2020] [Indexed: 11/09/2022] Open
Abstract
The Dicke model is a paradigmatic quantum-optical model describing the interaction of a collection of two-level systems with a single bosonic mode. Effective implementations of this model made it possible to observe the emergence of superradiance, i.e., cooperative phenomena arising from the collective nature of light-matter interactions. Via reservoir engineering and analogue quantum simulation techniques, current experimental platforms allow us not only to implement the Dicke model but also to design more exotic interactions, such as the two-photon Dicke model. In the Hamiltonian case, this model presents an interesting phase diagram characterized by two quantum criticalities: a superradiant phase transition and a spectral collapse, that is, the coalescence of discrete energy levels into a continuous band. Here, we investigate the effects of both qubit and photon dissipation on the phase transition and on the instability induced by the spectral collapse. Using a mean-field decoupling approximation, we analytically obtain the steady-state expectation values of the observables signaling a symmetry breaking, identifying a first-order phase transition from the normal to the superradiant phase. Our stability analysis unveils a very rich phase diagram, which features stable, bistable, and unstable phases depending on the dissipation rate.
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Affiliation(s)
- Louis Garbe
- Laboratoire Matériaux et Phénomènes Quantiques, Sorbonne Paris Cité, CNRS UMR 7162, Université de Paris, 75013, Paris, France.
- Theoretical Quantum Physics Laboratory, RIKEN Cluster for Pioneering Research, Wako-shi, Saitama, 351-0198, Japan.
| | - Peregrine Wade
- Laboratoire Matériaux et Phénomènes Quantiques, Sorbonne Paris Cité, CNRS UMR 7162, Université de Paris, 75013, Paris, France
| | - Fabrizio Minganti
- Theoretical Quantum Physics Laboratory, RIKEN Cluster for Pioneering Research, Wako-shi, Saitama, 351-0198, Japan
| | - Nathan Shammah
- Theoretical Quantum Physics Laboratory, RIKEN Cluster for Pioneering Research, Wako-shi, Saitama, 351-0198, Japan
- Unitary Fund, 340 S Lemon Ave. 7770, Walnut, CA, 91789, USA
| | - Simone Felicetti
- Departamento de Física Teórica de la Materia Condensada and Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, 28049, Madrid, Spain
- Istituto di Fotonica e Nanotecnologie, Consiglio Nazionale delle Ricerche (IFN-CNR), Piazza Leonardo da Vinci 32, 20133, Milano, Italy
| | - Franco Nori
- Theoretical Quantum Physics Laboratory, RIKEN Cluster for Pioneering Research, Wako-shi, Saitama, 351-0198, Japan
- Physics Department, The University of Michigan, Ann Arbor, MI, 48109-1040, USA
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23
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Zhu HJ, Xu K, Zhang GF, Liu WM. Finite-Component Multicriticality at the Superradiant Quantum Phase Transition. PHYSICAL REVIEW LETTERS 2020; 125:050402. [PMID: 32794842 DOI: 10.1103/physrevlett.125.050402] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/28/2020] [Accepted: 07/08/2020] [Indexed: 06/11/2023]
Abstract
We demonstrate the existence of finite-component multicriticality in a qubit-boson model where biased qubits collectively coupled to a single-mode bosonic field. The interplay between biases and boson-qubit coupling produces a rich phase diagram which shows multiple superradiant phases and phase boundaries of different orders. In particular, multiple phases become indistinguishable in appropriate bias configurations, which is the signature of multicriticality. A series of universality classes characterizing these multicritical points are identified. Moreover, we present a trapped-ion realization with the potential to explore multicritical phenomena experimentally using a small number of ions. The results open a novel way to probe multicritical universality classes in experiments.
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Affiliation(s)
- Han-Jie Zhu
- Key Laboratory of Micro-Nano Measurement-Manipulation and Physics (Ministry of Education), School of Physics, Beihang University, Xueyuan Road No. 37, Beijing 100191, China
| | - Kai Xu
- Key Laboratory of Micro-Nano Measurement-Manipulation and Physics (Ministry of Education), School of Physics, Beihang University, Xueyuan Road No. 37, Beijing 100191, China
| | - Guo-Feng Zhang
- Key Laboratory of Micro-Nano Measurement-Manipulation and Physics (Ministry of Education), School of Physics, Beihang University, Xueyuan Road No. 37, Beijing 100191, China
| | - Wu-Ming Liu
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
- Songshan Lake Materials Laboratory, Dongguan, Guangdong 523808, China
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24
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Lysne NK, Kuper KW, Poggi PM, Deutsch IH, Jessen PS. Small, Highly Accurate Quantum Processor for Intermediate-Depth Quantum Simulations. PHYSICAL REVIEW LETTERS 2020; 124:230501. [PMID: 32603170 DOI: 10.1103/physrevlett.124.230501] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/13/2019] [Revised: 05/01/2020] [Accepted: 05/11/2020] [Indexed: 06/11/2023]
Abstract
Analog quantum simulation is widely considered a step on the path to fault tolerant quantum computation. With current noisy hardware, the accuracy of an analog simulator will degrade after just a few time steps, especially when simulating complex systems likely to exhibit quantum chaos. Here we describe a quantum simulator based on the combined electron-nuclear spins of individual Cs atoms, and its use to run high fidelity simulations of three different model Hamiltonians for >100 time steps. While not scalable to exponentially large Hilbert spaces, it provides the accuracy and programmability required to explore the interplay between dynamics, imperfections, and accuracy in quantum simulation.
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Affiliation(s)
- Nathan K Lysne
- Center for Quantum Information and Control, Wyant College of Optical Sciences, University of Arizona, Tucson, Arizona 85721, USA
| | - Kevin W Kuper
- Center for Quantum Information and Control, Wyant College of Optical Sciences, University of Arizona, Tucson, Arizona 85721, USA
| | - Pablo M Poggi
- Center for Quantum Information and Control, Department of Physics and Astronomy, University of New Mexico, Albuquerque, New Mexico 87131, USA
| | - Ivan H Deutsch
- Center for Quantum Information and Control, Department of Physics and Astronomy, University of New Mexico, Albuquerque, New Mexico 87131, USA
| | - Poul S Jessen
- Center for Quantum Information and Control, Wyant College of Optical Sciences, University of Arizona, Tucson, Arizona 85721, USA
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25
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Lewis-Swan RJ, Barberena D, Muniz JA, Cline JRK, Young D, Thompson JK, Rey AM. Protocol for Precise Field Sensing in the Optical Domain with Cold Atoms in a Cavity. PHYSICAL REVIEW LETTERS 2020; 124:193602. [PMID: 32469538 DOI: 10.1103/physrevlett.124.193602] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/07/2019] [Accepted: 04/08/2020] [Indexed: 06/11/2023]
Abstract
In the context of quantum metrology, optical cavity-QED platforms have primarily been focused on the generation of entangled atomic spin states useful for next-generation frequency and time standards. Here, we report a complementary application: the use of optical cavities to generate nonclassical states of light for electric field sensing below the standard quantum limit. We show that cooperative atom-light interactions in the strong collective coupling regime can be used to engineer generalized atom-light cat states which enable quantum enhanced sensing of small displacements of the cavity field even in the presence of photon loss. We demonstrate that metrological gains of 10-20 dB below the standard quantum limit are within reach for current cavity-QED systems operating with long-lived alkaline-earth atoms.
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Affiliation(s)
- Robert J Lewis-Swan
- JILA, NIST, Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
- Center for Theory of Quantum Matter, University of Colorado, Boulder, Colorado 80309, USA
| | - Diego Barberena
- JILA, NIST, Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
- Center for Theory of Quantum Matter, University of Colorado, Boulder, Colorado 80309, USA
| | - Juan A Muniz
- JILA, NIST, Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
| | - Julia R K Cline
- JILA, NIST, Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
| | - Dylan Young
- JILA, NIST, Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
| | - James K Thompson
- JILA, NIST, Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
| | - Ana Maria Rey
- JILA, NIST, Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
- Center for Theory of Quantum Matter, University of Colorado, Boulder, Colorado 80309, USA
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26
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Hauke P, Katzgraber HG, Lechner W, Nishimori H, Oliver WD. Perspectives of quantum annealing: methods and implementations. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2020; 83:054401. [PMID: 32235066 DOI: 10.1088/1361-6633/ab85b8] [Citation(s) in RCA: 48] [Impact Index Per Article: 12.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/02/2023]
Abstract
Quantum annealing is a computing paradigm that has the ambitious goal of efficiently solving large-scale combinatorial optimization problems of practical importance. However, many challenges have yet to be overcome before this goal can be reached. This perspectives article first gives a brief introduction to the concept of quantum annealing, and then highlights new pathways that may clear the way towards feasible and large scale quantum annealing. Moreover, since this field of research is to a strong degree driven by a synergy between experiment and theory, we discuss both in this work. An important focus in this article is on future perspectives, which complements other review articles, and which we hope will motivate further research.
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Affiliation(s)
- Philipp Hauke
- INO-CNR BEC Center and Department of Physics, University of Trento, 38123Povo (TN), Italy. Kirchhoff-Institute for Physics, Heidelberg University, 69120 Heidelberg, Germany. Institute for Theoretical Physics, Heidelberg University, 69120 Heidelberg, Germany
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27
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Pilatowsky-Cameo S, Chávez-Carlos J, Bastarrachea-Magnani MA, Stránský P, Lerma-Hernández S, Santos LF, Hirsch JG. Positive quantum Lyapunov exponents in experimental systems with a regular classical limit. Phys Rev E 2020; 101:010202. [PMID: 32069677 DOI: 10.1103/physreve.101.010202] [Citation(s) in RCA: 32] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/06/2019] [Indexed: 06/10/2023]
Abstract
Quantum chaos refers to signatures of classical chaos found in the quantum domain. Recently, it has become common to equate the exponential behavior of out-of-time order correlators (OTOCs) with quantum chaos. The quantum-classical correspondence between the OTOC exponential growth and chaos in the classical limit has indeed been corroborated theoretically for some systems and there are several projects to do the same experimentally. The Dicke model, in particular, which has a regular and a chaotic regime, is currently under intense investigation by experiments with trapped ions. We show, however, that for experimentally accessible parameters, OTOCs can grow exponentially also when the Dicke model is in the regular regime. The same holds for the Lipkin-Meshkov-Glick model, which is integrable and also experimentally realizable. The exponential behavior in these cases are due to unstable stationary points, not to chaos.
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Affiliation(s)
- Saúl Pilatowsky-Cameo
- Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Apdo. Postal 70-543, C.P. 04510 CDMX, Mexico
| | - Jorge Chávez-Carlos
- Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Apdo. Postal 70-543, C.P. 04510 CDMX, Mexico
| | | | - Pavel Stránský
- Faculty of Mathematics and Physics, Charles University, V Holešovičkách 2, Prague 180 00, Czech Republic
| | - Sergio Lerma-Hernández
- Facultad de Física, Universidad Veracruzana, Circuito Aguirre Beltrán s/n, C.P. 91000 Xalapa, Mexico
| | - Lea F Santos
- Department of Physics, Yeshiva University, New York, New York 10016, USA
| | - Jorge G Hirsch
- Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Apdo. Postal 70-543, C.P. 04510 CDMX, Mexico
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28
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Palmero M, Simón MÁ, Poletti D. Towards Generation of Cat States in Trapped Ions Set-Ups via FAQUAD Protocols and Dynamical Decoupling. ENTROPY 2019. [PMCID: PMC7514552 DOI: 10.3390/e21121207] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
The high fidelity generation of strongly entangled states of many particles, such as cat states, is a particularly demanding challenge. One approach is to drive the system, within a certain final time, as adiabatically as possible, in order to avoid the generation of unwanted excitations. However, excitations can also be generated by the presence of dissipative effects such as dephasing. Here we compare the effectiveness of Local Adiabatic and the FAst QUasi ADiabatic protocols in achieving a high fidelity for a target superposition state both with and without dephasing. In particular, we consider trapped ions set-ups in which each spin interacts with all the others with the uniform coupling strength or with a power-law coupling. In order to mitigate the effects of dephasing, we complement the adiabatic protocols with dynamical decoupling and we test its effectiveness. The protocols we study could be readily implemented with state-of-the-art techniques.
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Affiliation(s)
- Mikel Palmero
- Science and Math Cluster, Singapore University of Technology and Design, 8 Somapah Road, Singapore 487372, Singapore
- Correspondence: (M.P.); (D.P.)
| | - Miguel Ángel Simón
- Departamento de Química-Física, Universidad del País Vasco UPV-EHU, B. Sarriena s/n, 48940 Leioa, Spain;
| | - Dario Poletti
- Science and Math Cluster, Singapore University of Technology and Design, 8 Somapah Road, Singapore 487372, Singapore
- Engineering Product Development, Singapore University of Technology and Design, 8 Somapah Road, Singapore 487372, Singapore
- Correspondence: (M.P.); (D.P.)
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29
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Unifying scrambling, thermalization and entanglement through measurement of fidelity out-of-time-order correlators in the Dicke model. Nat Commun 2019; 10:1581. [PMID: 30952845 PMCID: PMC6450886 DOI: 10.1038/s41467-019-09436-y] [Citation(s) in RCA: 36] [Impact Index Per Article: 7.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/24/2018] [Accepted: 03/05/2019] [Indexed: 11/08/2022] Open
Abstract
Scrambling is the process by which information stored in local degrees of freedom spreads over the many-body degrees of freedom of a quantum system, becoming inaccessible to local probes and apparently lost. Scrambling and entanglement can reconcile seemingly unrelated behaviors including thermalization of isolated quantum systems and information loss in black holes. Here, we demonstrate that fidelity out-of-time-order correlators (FOTOCs) can elucidate connections between scrambling, entanglement, ergodicity and quantum chaos (butterfly effect). We compute FOTOCs for the paradigmatic Dicke model, and show they can measure subsystem Rényi entropies and inform about quantum thermalization. Moreover, we illustrate why FOTOCs give access to a simple relation between quantum and classical Lyapunov exponents in a chaotic system without finite-size effects. Our results open a path to experimental use FOTOCs to explore scrambling, bounds on quantum information processing and investigation of black hole analogs in controllable quantum systems. The scrambling of quantum information in a many-body system leads to the emergence of statistical mechanics and chaotic behaviour. Here the authors establish quantitative relationships between experimentally-measureable correlators, the Rényi entropy and Lyapunov exponents in the Dicke model.
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30
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Chávez-Carlos J, López-Del-Carpio B, Bastarrachea-Magnani MA, Stránský P, Lerma-Hernández S, Santos LF, Hirsch JG. Quantum and Classical Lyapunov Exponents in Atom-Field Interaction Systems. PHYSICAL REVIEW LETTERS 2019; 122:024101. [PMID: 30720302 DOI: 10.1103/physrevlett.122.024101] [Citation(s) in RCA: 44] [Impact Index Per Article: 8.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/27/2018] [Revised: 09/19/2018] [Indexed: 06/09/2023]
Abstract
The exponential growth of the out-of-time-ordered correlator (OTOC) has been proposed as a quantum signature of classical chaos. The growth rate is expected to coincide with the classical Lyapunov exponent. This quantum-classical correspondence has been corroborated for the kicked rotor and the stadium billiard, which are one-body chaotic systems. The conjecture has not yet been validated for realistic systems with interactions. We make progress in this direction by studying the OTOC in the Dicke model, where two-level atoms cooperatively interact with a quantized radiation field. For parameters where the model is chaotic in the classical limit, the OTOC increases exponentially in time with a rate that closely follows the classical Lyapunov exponent.
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Affiliation(s)
- Jorge Chávez-Carlos
- Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Apdo. Postal 70-543, C.P. 04510 Cd. Mx., México
| | - B López-Del-Carpio
- Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Apdo. Postal 70-543, C.P. 04510 Cd. Mx., México
| | | | - Pavel Stránský
- Faculty of Mathematics and Physics, Charles University, V Holešovičkách 2, Prague 180 00, Czech Republic
| | - Sergio Lerma-Hernández
- Facultad de Física, Universidad Veracruzana, Circuito Aguirre Beltrán s/n, Xalapa, Veracruz 91000, Mexico
| | - Lea F Santos
- Department of Physics, Yeshiva University, New York, New York 10016, USA
| | - Jorge G Hirsch
- Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Apdo. Postal 70-543, C.P. 04510 Cd. Mx., México
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31
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Defenu N, Enss T, Kastner M, Morigi G. Dynamical Critical Scaling of Long-Range Interacting Quantum Magnets. PHYSICAL REVIEW LETTERS 2018; 121:240403. [PMID: 30608754 DOI: 10.1103/physrevlett.121.240403] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/30/2018] [Indexed: 06/09/2023]
Abstract
Slow quenches of the magnetic field across the paramagnetic-ferromagnetic phase transition of spin systems produce heat. In systems with short-range interactions the heat exhibits universal power-law scaling as a function of the quench rate, known as Kibble-Zurek scaling. In this work we analyze slow quenches of the magnetic field in the Lipkin-Meshkov-Glick (LMG) model, which describes fully connected quantum spins. We analytically determine the quantum contribution to the residual heat as a function of the quench rate δ by means of a Holstein-Primakoff expansion about the mean-field value. Unlike in the case of short-range interactions, scaling laws in the LMG model are only found for a ramp starting or ending at the critical point. If instead the ramp is symmetric, as in the typical Kibble-Zurek scenario, then the number of excitations exhibits a crossover behavior as a function of δ and tends to a constant in the thermodynamic limit. Previous, and seemingly contradictory, theoretical studies are identified as specific limits of this dynamics. Our results can be tested on several experimental platforms, including quantum gases and trapped ions.
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Affiliation(s)
- Nicolò Defenu
- Institut für Theoretische Physik, Universität Heidelberg, D-69120 Heidelberg, Germany
| | - Tilman Enss
- Institut für Theoretische Physik, Universität Heidelberg, D-69120 Heidelberg, Germany
| | - Michael Kastner
- Institute of Theoretical Physics, Department of Physics, University of Stellenbosch, Stellenbosch 7600, South Africa
- National Institute for Theoretical Physics (NITheP), Stellenbosch 7600, South Africa
| | - Giovanna Morigi
- Theoretische Physik, Universität des Saarlandes, D-66123 Saarbrücken, Germany
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