1
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Chávez-Carlos J, Lezama TLM, Cortiñas RG, Venkatraman J, Devoret MH, Batista VS, Pérez-Bernal F, Santos LF. Spectral kissing and its dynamical consequences in the squeeze-driven Kerr oscillator. NPJ QUANTUM INFORMATION 2023; 9:76. [PMID: 38665256 PMCID: PMC11041765 DOI: 10.1038/s41534-023-00745-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 02/20/2023] [Accepted: 07/15/2023] [Indexed: 04/28/2024]
Abstract
Transmon qubits are the predominant element in circuit-based quantum information processing, such as existing quantum computers, due to their controllability and ease of engineering implementation. But more than qubits, transmons are multilevel nonlinear oscillators that can be used to investigate fundamental physics questions. Here, they are explored as simulators of excited state quantum phase transitions (ESQPTs), which are generalizations of quantum phase transitions to excited states. We show that the spectral kissing (coalescence of pairs of energy levels) experimentally observed in the effective Hamiltonian of a driven SNAIL-transmon is an ESQPT precursor. We explore the dynamical consequences of the ESQPT, which include the exponential growth of out-of-time-ordered correlators, followed by periodic revivals, and the slow evolution of the survival probability due to localization. These signatures of ESQPT are within reach for current superconducting circuits platforms and are of interest to experiments with cold atoms and ion traps.
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Affiliation(s)
| | | | - Rodrigo G. Cortiñas
- Department of Applied Physics and Physics, Yale University, New Haven, CT 06520 USA
| | | | - Michel H. Devoret
- Department of Applied Physics and Physics, Yale University, New Haven, CT 06520 USA
| | - Victor S. Batista
- Department of Chemistry, Yale University, P.O. Box 208107, New Haven, CT 06520-8107 USA
| | - Francisco Pérez-Bernal
- Departamento de Ciencias Integradas y Centro de Estudios Avanzados en Física, Matemáticas y Computación, Universidad de Huelva, Huelva, 21071 Spain
- Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, Fuentenueva s/n, 18071 Granada, Spain
| | - Lea F. Santos
- Department of Physics, University of Connecticut, Storrs, CT 06269 USA
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2
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Corps ÁL, Relaño A. Theory of Dynamical Phase Transitions in Quantum Systems with Symmetry-Breaking Eigenstates. PHYSICAL REVIEW LETTERS 2023; 130:100402. [PMID: 36962016 DOI: 10.1103/physrevlett.130.100402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/01/2022] [Revised: 10/03/2022] [Accepted: 02/16/2023] [Indexed: 06/18/2023]
Abstract
We present a theory for the two kinds of dynamical quantum phase transitions, termed DPT-I and DPT-II, based on a minimal set of symmetry assumptions. In the special case of collective systems with infinite-range interactions, both are triggered by excited-state quantum phase transitions. For quenches below the critical energy, the existence of an additional conserved charge, identifying the corresponding phase, allows for a nonzero value of the dynamical order parameter characterizing DPTs-I, and precludes the main mechanism giving rise to nonanalyticities in the return probability, trademark of DPTs-II. We propose a statistical ensemble describing the long-time averages of order parameters in DPTs-I, and provide a theoretical proof for the incompatibility of the main mechanism for DPTs-II with the presence of this additional conserved charge. Our results are numerically illustrated in the fully connected transverse-field Ising model, which exhibits both kinds of dynamical phase transitions. Finally, we discuss the applicability of our theory to systems with finite-range interactions, where the phenomenology of excited-state quantum phase transitions is absent. We illustrate our findings by means of numerical calculations with experimentally relevant initial states.
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Affiliation(s)
- Ángel L Corps
- Instituto de Estructura de la Materia, IEM-CSIC, Serrano 123, E-28006 Madrid, Spain
- Grupo Interdisciplinar de Sistemas Complejos (GISC), Universidad Complutense de Madrid, Avenida Complutense s/n, E-28040 Madrid, Spain
| | - Armando Relaño
- Grupo Interdisciplinar de Sistemas Complejos (GISC), Universidad Complutense de Madrid, Avenida Complutense s/n, E-28040 Madrid, Spain
- Departamento de Estructura de la Materia, Física Térmica y Electrónica, Universidad Complutense de Madrid, Avenida Complutense s/n, E-28040 Madrid, Spain
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3
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Gamito J, Khalouf-Rivera J, Arias JM, Pérez-Fernández P, Pérez-Bernal F. Excited-state quantum phase transitions in the anharmonic Lipkin-Meshkov-Glick model: Static aspects. Phys Rev E 2022; 106:044125. [PMID: 36397542 DOI: 10.1103/physreve.106.044125] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/10/2022] [Accepted: 08/15/2022] [Indexed: 06/16/2023]
Abstract
The basic Lipkin-Meshkov-Glick model displays a second-order ground-state quantum phase transition and an excited-state quantum phase transition (ESQPT). The inclusion of an anharmonic term in the Hamiltonian implies a second ESQPT of a different nature. We characterize this ESQPT using the mean field limit of the model. The alternative ESQPT, associated with the changes in the boundary of the finite Hilbert space of the system, can be properly described using the order parameter of the ground-state quantum phase transition, the energy gap between adjacent states, the participation ratio, and the quantum fidelity susceptibility.
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Affiliation(s)
- J Gamito
- Departamento de Física Atómica, Molecular y Nuclear, Facultad de Física, Universidad de Sevilla, Apartado 1065, 41080 Sevilla, Spain
| | - J Khalouf-Rivera
- Departamento de Ciencias Integradas y Centro de Estudios Avanzados en Física, Matemáticas y Computación, Universidad de Huelva, Huelva 21071, Spain
| | - J M Arias
- Departamento de Física Atómica, Molecular y Nuclear, Facultad de Física, Universidad de Sevilla, Apartado 1065, 41080 Sevilla, Spain
- Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, Fuentenueva s/n, 18071 Granada, Spain
| | - P Pérez-Fernández
- Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, Fuentenueva s/n, 18071 Granada, Spain
- Departamento de Física Aplicada III, Escuela Técnica Superior de Ingeniería, Universidad de Sevilla, 41092 Sevilla, Spain
| | - F Pérez-Bernal
- Departamento de Ciencias Integradas y Centro de Estudios Avanzados en Física, Matemáticas y Computación, Universidad de Huelva, Huelva 21071, Spain
- Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, Fuentenueva s/n, 18071 Granada, Spain
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4
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Herrera Romero R, Bastarrachea-Magnani MA, Linares R. Critical Phenomena in Light-Matter Systems with Collective Matter Interactions. ENTROPY (BASEL, SWITZERLAND) 2022; 24:1198. [PMID: 36141084 PMCID: PMC9497676 DOI: 10.3390/e24091198] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 07/25/2022] [Revised: 08/20/2022] [Accepted: 08/23/2022] [Indexed: 06/16/2023]
Abstract
We study the quantum phase diagram and the onset of quantum critical phenomena in a generalized Dicke model that includes collective qubit-qubit interactions. By employing semiclassical techniques, we analyze the corresponding classical energy surfaces, fixed points, and the smooth Density of States as a function of the Hamiltonian parameters to determine quantum phase transitions in either the ground (QPT) or excited states (ESQPT). We unveil a rich phase diagram, the presence of new phases, and new transitions that result from varying the strength of the qubits interactions in independent canonical directions. We also find a correspondence between the phases emerging due to qubit interactions and those in their absence but with varying the strength of the non-resonant terms in the light-matter coupling. We expect our work to pave the way and stimulate the exploration of quantum criticality in systems combining matter-matter and light-matter interactions.
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5
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Mondal D, Sinha S, Sinha S. Quantum transitions, ergodicity, and quantum scars in the coupled top model. Phys Rev E 2022; 105:014130. [PMID: 35193322 DOI: 10.1103/physreve.105.014130] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/15/2021] [Accepted: 01/10/2022] [Indexed: 06/14/2023]
Abstract
We consider an interacting collective spin model known as coupled top (CT), exhibiting a rich variety of phenomena related to quantum transitions, ergodicity, and formation of quantum scars, discussed in our previous work [Mondal, Sinha, and Sinha, Phys. Rev. E 102, 020101(R) (2020)2470-004510.1103/PhysRevE.102.020101]. In this work, we present a detailed analysis of the different type of transitions in the CT model, and find their connection with the underlying collective spin dynamics. Apart from the quantum scarring phenomena, we also identify another source of deviation from ergodicity due to the presence of nonergodic multifractal states. The degree of ergodicity of the eigenstates across the energy band is quantified from the relative entanglement entropy as well as multifractal dimensions, which can be probed from nonequilibrium dynamics. Finally, we discuss the detection of nonergodic behavior and different types of quantum scars using "out-of-time-order correlators," which has relevance in the recent experiments.
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Affiliation(s)
- Debabrata Mondal
- Indian Institute of Science Education and Research-Kolkata, Mohanpur, Nadia-741246, India
| | - Sudip Sinha
- Indian Institute of Science Education and Research-Kolkata, Mohanpur, Nadia-741246, India
| | - S Sinha
- Indian Institute of Science Education and Research-Kolkata, Mohanpur, Nadia-741246, India
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6
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Gherardini S, Giachetti G, Ruffo S, Trombettoni A. Thermalization processes induced by quantum monitoring in multilevel systems. Phys Rev E 2021; 104:034114. [PMID: 34654093 DOI: 10.1103/physreve.104.034114] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/23/2021] [Accepted: 08/17/2021] [Indexed: 11/07/2022]
Abstract
We study the heat statistics of a multilevel N-dimensional quantum system monitored by a sequence of projective measurements. The late-time, asymptotic properties of the heat characteristic function are analyzed in the thermodynamic limit of a high, ideally infinite, number M of measurements (M→∞). In this context, the conditions allowing for an infinite-temperature thermalization (ITT), induced by the repeated monitoring of the quantum system, are discussed. We show that ITT is identified by the fixed point of a symmetric random matrix that models the stochastic process originated by the sequence of measurements. Such fixed point is independent on the nonequilibrium evolution of the system and its initial state. Exceptions to ITT, which we refer to as partial thermalization, take place when the observable of the intermediate measurements is commuting (or quasicommuting) with the Hamiltonian of the quantum system or when the time interval between measurements is smaller or comparable with the system energy scale (quantum Zeno regime). Results on the limit of infinite-dimensional Hilbert spaces (N→∞), describing continuous systems with a discrete spectrum, are also presented. We show that the order of the limits M→∞ and N→∞ matters: When N is fixed and M diverges, then ITT occurs. In the opposite case, the system becomes classical, so that the measurements are no longer effective in changing the state of the system. A nontrivial result is obtained fixing M/N^{2} where instead partial ITT occurs. Finally, an example of partial thermalization applicable to rotating two-dimensional gases is presented.
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Affiliation(s)
- S Gherardini
- SISSA and INFN, I-34136 Trieste, Italy.,Department of Physics and Astronomy and LENS, University of Florence, I-50019 Sesto Fiorentino, Italy.,CNR-IOM DEMOCRITOS Simulation Center, I-34136 Trieste, Italy
| | | | - S Ruffo
- SISSA and INFN, I-34136 Trieste, Italy.,Istituto dei Sistemi Complessi, Consiglio Nazionale delle Ricerche, I-50019 Sesto Fiorentino, Italy
| | - A Trombettoni
- SISSA and INFN, I-34136 Trieste, Italy.,CNR-IOM DEMOCRITOS Simulation Center, I-34136 Trieste, Italy.,Department of Physics, University of Trieste, I-34151 Trieste, Italy
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7
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Gonzalez D, Gutiérrez-Ruiz D, Vergara JD. Classical description of the parameter space geometry in the Dicke and Lipkin-Meshkov-Glick models. Phys Rev E 2021; 104:014113. [PMID: 34412288 DOI: 10.1103/physreve.104.014113] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/28/2021] [Accepted: 06/21/2021] [Indexed: 11/07/2022]
Abstract
We study the classical analog of the quantum metric tensor and its scalar curvature for two well-known quantum physics models. First, we analyze the geometry of the parameter space for the Dicke model with the aid of the classical and quantum metrics and find that, in the thermodynamic limit, they have the same divergent behavior near the quantum phase transition, as opposed to their corresponding scalar curvatures which are not divergent there. On the contrary, under resonance conditions, both scalar curvatures exhibit a divergence at the critical point. Second, we present the classical and quantum metrics for the Lipkin-Meshkov-Glick model in the thermodynamic limit and find a perfect agreement between them. We also show that the scalar curvature is only defined on one of the system's phases and that it approaches a negative constant value. Finally, we carry out a numerical analysis for the system's finite sizes, which clearly shows the precursors of the quantum phase transition in the metric and its scalar curvature and allows their characterization as functions of the parameters and of the system's size.
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Affiliation(s)
- Diego Gonzalez
- Departamento de Física, Cinvestav, Avenida Instituto Politécnico Nacional 2508, San Pedro Zacatenco, 07360, Gustavo A. Madero, Ciudad de México, Mexico.,Departamento de Física de Altas Energías, Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Apartado Postal 70-543, Ciudad de México, 04510, Mexico
| | - Daniel Gutiérrez-Ruiz
- Departamento de Física de Altas Energías, Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Apartado Postal 70-543, Ciudad de México, 04510, Mexico
| | - J David Vergara
- Departamento de Física de Altas Energías, Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Apartado Postal 70-543, Ciudad de México, 04510, Mexico
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8
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Feldmann P, Klempt C, Smerzi A, Santos L, Gessner M. Interferometric Order Parameter for Excited-State Quantum Phase Transitions in Bose-Einstein Condensates. PHYSICAL REVIEW LETTERS 2021; 126:230602. [PMID: 34170156 DOI: 10.1103/physrevlett.126.230602] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/04/2020] [Revised: 03/05/2021] [Accepted: 04/19/2021] [Indexed: 06/13/2023]
Abstract
Excited-state quantum phase transitions extend the notion of quantum phase transitions beyond the ground state. They are characterized by closing energy gaps amid the spectrum. Identifying order parameters for excited-state quantum phase transitions poses, however, a major challenge. We introduce a topological order parameter that distinguishes excited-state phases in a large class of mean-field models and can be accessed by interferometry in current experiments with spinor Bose-Einstein condensates. Our work opens a way for the experimental characterization of excited-state quantum phases in atomic many-body systems.
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Affiliation(s)
- Polina Feldmann
- Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstraße 2, 30167 Hannover, Germany
| | - Carsten Klempt
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, 30167 Hannover, Germany
- Deutsches Zentrum für Luft- und Raumfahrt e.V. (DLR), Institut für Satellitengeodäsie und Inertialsensorik, c/o Leibniz Universität Hannover, DLR-SI, Callinstraße 36, 30167 Hannover, Germany
| | - Augusto Smerzi
- QSTAR, INO-CNR, and LENS, Largo Enrico Fermi 2, 50125 Firenze, Italy
| | - Luis Santos
- Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstraße 2, 30167 Hannover, Germany
| | - Manuel Gessner
- Laboratoire Kastler Brossel, ENS-Université PSL, CNRS, Sorbonne Université, Collège de France, 24 Rue Lhomond, 75005 Paris, France
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9
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Mzaouali Z, Puebla R, Goold J, El Baz M, Campbell S. Work statistics and symmetry breaking in an excited-state quantum phase transition. Phys Rev E 2021; 103:032145. [PMID: 33862795 DOI: 10.1103/physreve.103.032145] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/19/2021] [Accepted: 03/02/2021] [Indexed: 11/07/2022]
Abstract
We examine how the presence of an excited-state quantum phase transition manifests in the dynamics of a many-body system subject to a sudden quench. Focusing on the Lipkin-Meshkov-Glick model initialized in the ground state of the ferromagnetic phase, we demonstrate that the work probability distribution displays non-Gaussian behavior for quenches in the vicinity of the excited-state critical point. Furthermore, we show that the entropy of the diagonal ensemble is highly susceptible to critical regions, making it a robust and practical indicator of the associated spectral characteristics. We assess the role that symmetry breaking has on the ensuing dynamics, highlighting that its effect is only present for quenches beyond the critical point. Finally, we show that similar features persist when the system is initialized in an excited state and briefly explore the behavior for initial states in the paramagnetic phase.
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Affiliation(s)
- Zakaria Mzaouali
- ESMaR, Faculty of Sciences, Mohammed V University in Rabat, Morocco
| | - Ricardo Puebla
- Instituto de Física Fundamental, IFF-CSIC, Calle Serrano 113b, 28006 Madrid, Spain.,Centre for Theoretical Atomic, Molecular and Optical Physics, Queen's University Belfast, Belfast BT7 1NN, United Kingdom
| | - John Goold
- School of Physics, Trinity College Dublin, College Green, Dublin 2, Ireland
| | - Morad El Baz
- ESMaR, Faculty of Sciences, Mohammed V University in Rabat, Morocco
| | - Steve Campbell
- School of Physics, University College Dublin, Belfield, Dublin 4, Ireland.,Centre for Quantum Engineering, Science, and Technology, University College Dublin, Belfield, Dublin 4, Ireland
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10
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Guo SF, Chen F, Liu Q, Xue M, Chen JJ, Cao JH, Mao TW, Tey MK, You L. Faster State Preparation across Quantum Phase Transition Assisted by Reinforcement Learning. PHYSICAL REVIEW LETTERS 2021; 126:060401. [PMID: 33635691 DOI: 10.1103/physrevlett.126.060401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/19/2020] [Accepted: 01/12/2021] [Indexed: 06/12/2023]
Abstract
An energy gap develops near quantum critical point of quantum phase transition in a finite many-body (MB) system, facilitating the ground state transformation by adiabatic parameter change. In real application scenarios, however, the efficacy for such a protocol is compromised by the need to balance finite system lifetime with adiabaticity, as exemplified in a recent experiment that prepares three-mode balanced Dicke state near deterministically [Y.-Q. Zou et al., Proc. Natl. Acad. Sci. U.S.A. 115, 6381 (2018)PNASA60027-842410.1073/pnas.1715105115]. Instead of tracking the instantaneous ground state as unanimously required for most adiabatic crossing, this work reports a faster sweeping policy taking advantage of excited level dynamics. It is obtained based on deep reinforcement learning (DRL) from a multistep training scheme we develop. In the absence of loss, a fidelity ≥99% between prepared and the target Dicke state is achieved over a small fraction of the adiabatically required time. When loss is included, training is carried out according to an operational benchmark, the interferometric sensitivity of the prepared state instead of fidelity, leading to better sensitivity in about half of the previously reported time. Implemented in a Bose-Einstein condensate of ∼10^{4} ^{87}Rb atoms, the balanced three-mode Dicke state exhibiting an improved number squeezing of 13.02±0.20 dB is observed within 766 ms, highlighting the potential of DRL for quantum dynamics control and quantum state preparation in interacting MB systems.
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Affiliation(s)
- Shuai-Feng Guo
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
| | - Feng Chen
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
| | - Qi Liu
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
| | - Ming Xue
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
| | - Jun-Jie Chen
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
| | - Jia-Hao Cao
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
| | - Tian-Wei Mao
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
| | - Meng Khoon Tey
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
- Frontier Science Center for Quantum Information, Beijing, China
| | - Li You
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
- Frontier Science Center for Quantum Information, Beijing, China
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11
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Titum P, Maghrebi MF. Nonequilibrium Criticality in Quench Dynamics of Long-Range Spin Models. PHYSICAL REVIEW LETTERS 2020; 125:040602. [PMID: 32794797 DOI: 10.1103/physrevlett.125.040602] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/05/2019] [Revised: 06/07/2020] [Accepted: 06/19/2020] [Indexed: 06/11/2023]
Abstract
Long-range interacting spin systems are ubiquitous in physics and exhibit a variety of ground-state disorder-to-order phase transitions. We consider a prototype of infinite-range interacting models known as the Lipkin-Meshkov-Glick model describing the collective interaction of N spins and investigate the dynamical properties of fluctuations and correlations after a sudden quench of the Hamiltonian. Specifically, we focus on critical quenches, where the initial state and/or the postquench Hamiltonian are critical. Depending on the type of quench, we identify three distinct behaviors where both the short-time dynamics and the stationary state at long times are effectively thermal, quantum, and genuinely nonequilibrium, characterized by distinct universality classes and static and dynamical critical exponents. These behaviors can be identified by an infrared effective temperature that is finite, zero, and infinite (the latter scaling with the system size as N^{1/3}), respectively. The quench dynamics is studied through a combination of exact numerics and analytical calculations utilizing the nonequilibrium Keldysh field theory. Our results are amenable to realization in experiments with trapped-ion experiments where long-range interactions naturally arise.
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Affiliation(s)
- Paraj Titum
- Johns Hopkins University Applied Physics Laboratory, Laurel, Maryland 20723, USA
- Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA
- Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA
| | - Mohammad F Maghrebi
- Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA
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12
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Makhalov V, Satoor T, Evrard A, Chalopin T, Lopes R, Nascimbene S. Probing Quantum Criticality and Symmetry Breaking at the Microscopic Level. PHYSICAL REVIEW LETTERS 2019; 123:120601. [PMID: 31633983 DOI: 10.1103/physrevlett.123.120601] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/09/2019] [Indexed: 06/10/2023]
Abstract
We report on an experimental study of the Lipkin-Meshkov-Glick model of quantum spins interacting at infinite range in a transverse magnetic field, which exhibits a ferromagnetic phase transition in the thermodynamic limit. We use dysprosium atoms of electronic spin J=8, subjected to a quadratic Zeeman light shift, to simulate 2J=16 interacting spins 1/2. We probe the system microscopically using single magnetic sublevel resolution, giving access to the spin projection parity, which is the collective observable characterizing the underlying Z_{2} symmetry. We measure the thermodynamic properties and dynamical response of the system, and we study the quantum critical behavior around the transition point. In the ferromagnetic phase, we achieve coherent tunneling between symmetry-broken states, and we test the link between symmetry breaking and the appearance of a finite order parameter.
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Affiliation(s)
- Vasiliy Makhalov
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-PSL University, Sorbonne Université, 11 Place Marcelin Berthelot, 75005 Paris, France
| | - Tanish Satoor
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-PSL University, Sorbonne Université, 11 Place Marcelin Berthelot, 75005 Paris, France
| | - Alexandre Evrard
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-PSL University, Sorbonne Université, 11 Place Marcelin Berthelot, 75005 Paris, France
| | - Thomas Chalopin
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-PSL University, Sorbonne Université, 11 Place Marcelin Berthelot, 75005 Paris, France
| | - Raphael Lopes
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-PSL University, Sorbonne Université, 11 Place Marcelin Berthelot, 75005 Paris, France
| | - Sylvain Nascimbene
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-PSL University, Sorbonne Université, 11 Place Marcelin Berthelot, 75005 Paris, France
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13
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Analogies of the classical Euler top with a rotor to spin squeezing and quantum phase transitions in a generalized Lipkin-Meshkov-Glick model. Sci Rep 2018; 8:1984. [PMID: 29386576 PMCID: PMC5792583 DOI: 10.1038/s41598-018-20486-y] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/05/2017] [Accepted: 01/18/2018] [Indexed: 11/09/2022] Open
Abstract
We show that the classical model of Euler top (freely rotating, generally asymmetric rigid body), possibly supplemented with a rotor, corresponds to a generalized Lipkin-Meshkov-Glick (LMG) model describing phenomena of various branches of quantum physics. Classical effects such as free precession of a symmetric top, Feynman's wobbling plate, tennis-racket instability and the Dzhanibekov effect, attitude control of satellites by momentum wheels, or twisting somersault dynamics, have their counterparts in quantum effects that include spin squeezing by one-axis twisting and two-axis countertwisting, transitions between the Josephson and Rabi regimes of a Bose-Einstein condensate in a double-well potential, and other quantum critical phenomena. The parallels enable us to expand the range of explored quantum phase transitions in the generalized LMG model, as well as to present a classical analogy of the recently proposed LMG Floquet time crystal.
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14
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Pérez-Fernández P, Relaño A. From thermal to excited-state quantum phase transition: The Dicke model. Phys Rev E 2018; 96:012121. [PMID: 29347062 DOI: 10.1103/physreve.96.012121] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/26/2016] [Indexed: 11/07/2022]
Abstract
We study the thermodynamics of the full version of the Dicke model, including all the possible values of the total angular momentum j, with both microcanonical and canonical ensembles. We focus on both the excited-state quantum phase transition, appearing in the microcanonical description of the maximum angular momentum sector, j=N/2, and the thermal phase transition, which occurs when all the sectors are taken into account. We show that two different features characterize the full version of the Dicke model. If the system is in contact with a thermal bath and is described by means of the canonical ensemble, the parity symmetry becomes spontaneously broken at the critical temperature. In the microcanonical ensemble, and despite that all the logarithmic singularities which characterize the excited-state quantum phase transition are ruled out when all the j sectors are considered, there still exists a critical energy (or temperature) dividing the spectrum into two regions: one in which the parity symmetry can be broken, and another in which this symmetry is always well defined.
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Affiliation(s)
- P Pérez-Fernández
- Departamento de Física Aplicada III, Escuela Técnica Superior de Ingeniería, Universidad de Sevilla, Sevilla, Spain
| | - A Relaño
- Departamento de Física Aplicada I and GISC, Universidad Complutense de Madrid, Avenida Complutense s/n, 28040 Madrid, Spain
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15
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Kopylov W, Schaller G, Brandes T. Nonadiabatic dynamics of the excited states for the Lipkin-Meshkov-Glick model. Phys Rev E 2017; 96:012153. [PMID: 29347272 DOI: 10.1103/physreve.96.012153] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/27/2017] [Indexed: 06/07/2023]
Abstract
We theoretically investigate the impact of the excited state quantum phase transition on the adiabatic dynamics for the Lipkin-Meshkov-Glick model. Using a time-dependent protocol, we continuously change a model parameter and then discuss the scaling properties of the system especially close to the excited state quantum phase transition where we find that these depend on the energy eigenstate. On top, we show that the mean-field dynamics with the time-dependent protocol gives the correct scaling and expectation values in the thermodynamic limit even for the excited states.
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Affiliation(s)
- Wassilij Kopylov
- Institut für Theoretische Physik, Technische Universität Berlin, D-10623 Berlin, Germany
| | - Gernot Schaller
- Institut für Theoretische Physik, Technische Universität Berlin, D-10623 Berlin, Germany
| | - Tobias Brandes
- Institut für Theoretische Physik, Technische Universität Berlin, D-10623 Berlin, Germany
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Relaño A, Esebbag C, Dukelsky J. Excited-state quantum phase transitions in the two-spin elliptic Gaudin model. Phys Rev E 2016; 94:052110. [PMID: 27967097 DOI: 10.1103/physreve.94.052110] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/01/2016] [Indexed: 11/07/2022]
Abstract
We study the integrability of the two-spin elliptic Gaudin model for arbitrary values of the Hamiltonian parameters. The limit of a very large spin coupled to a small one is well described by a semiclassical approximation with just one degree of freedom. Its spectrum is divided into bands that do not overlap if certain conditions are fulfilled. In spite of the fact that there are no quantum phase transitions in each of the band heads, the bands show excited-state quantum phase transitions separating a region in which the parity symmetry is broken from another region in which time-reversal symmetry is broken. We derive analytical expressions for the critical energies in the semiclassical approximation, and confirm the results by means of exact diagonalizations for large systems.
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Affiliation(s)
- Armando Relaño
- Departamento de Física Aplicada I and GISC, Universidad Complutense de Madrid, Avenida Complutense s/n, 28040 Madrid, Spain
| | - Carlos Esebbag
- Departamento de Física y Matemáticas, Universidad de Alcalá, E-28871 Alcalá de Henares, Spain
| | - Jorge Dukelsky
- Instituto de Estructura de la Materia, Consejo Superior de Investigaciones Científicas, Serrano 123, E-28006 Madrid, Spain
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Castaños O, Calixto M, Pérez-Bernal F, Romera E. Identifying the order of a quantum phase transition by means of Wehrl entropy in phase space. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:052106. [PMID: 26651646 DOI: 10.1103/physreve.92.052106] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/25/2015] [Indexed: 06/05/2023]
Abstract
We propose a method to identify the order of a quantum phase transition by using area measures of the ground state in phase space. We illustrate our proposal by analyzing the well known example of the quantum cusp and four different paradigmatic boson models: Dicke, Lipkin-Meshkov-Glick, interacting boson model, and vibron model.
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Affiliation(s)
- Octavio Castaños
- Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Apartado Postal 70-543, 04510 Distrito Federal, Mexico
| | - Manuel Calixto
- Departamento de Matemática Aplicada, Facultad de Ciencias, Universidad de Granada, Fuentenueva s/n, 18071 Granada, Spain
| | - Francisco Pérez-Bernal
- Departamento de Física Aplicada, Facultad de Ciencias Experimentales, Universidad de Huelva, Campus del Carmen, Avenida de las Fuerzas Armadas s/n, 21071 Huelva, Spain
| | - Elvira Romera
- Departamento de Física Atómica, Molecular y Nuclear and Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, Fuentenueva s/n, 18071 Granada, Spain
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Bastidas VM, Pérez-Fernández P, Vogl M, Brandes T. Quantum criticality and dynamical instability in the kicked-top model. PHYSICAL REVIEW LETTERS 2014; 112:140408. [PMID: 24765930 DOI: 10.1103/physrevlett.112.140408] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/28/2013] [Indexed: 06/03/2023]
Abstract
We investigate precursors of critical behavior in the quasienergy spectrum due to the dynamical instability in the kicked top. Using a semiclassical approach, we analytically obtain a logarithmic divergence in the density of states, which is analogous to a continuous excited state quantum phase transition in undriven systems. We propose a protocol to observe the cusp behavior of the magnetization close to the critical quasienergy.
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Affiliation(s)
- Victor Manuel Bastidas
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany
| | - Pedro Pérez-Fernández
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany and Departamento de Física Aplicada III, Escuela Superior de Ingenieros, Universidad de Sevilla, Camino de los Descubrimientos s/n, ES-41092 Sevilla, Spain
| | - Malte Vogl
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany
| | - Tobias Brandes
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany
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Brown WG, Viola L. Convergence rates for arbitrary statistical moments of random quantum circuits. PHYSICAL REVIEW LETTERS 2010; 104:250501. [PMID: 20867353 DOI: 10.1103/physrevlett.104.250501] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/11/2009] [Revised: 05/21/2010] [Indexed: 05/29/2023]
Abstract
We consider a class of random quantum circuits where at each step a gate from a universal set is applied to a random pair of qubits, and determine how quickly averages of arbitrary finite-degree polynomials in the matrix elements of the resulting unitary converge to Haar measure averages. This is accomplished by mapping the superoperator that describes t order moments on n qubits to a multilevel SU(4^{t}) Lipkin-Meshkov-Glick Hamiltonian. We show that, for arbitrary fixed t, the ground-state manifold is exactly spanned by factorized eigenstates and, under the assumption that a mean-field ansatz accurately describes the low-lying excitations, the spectral gap scales as 1/n in the thermodynamic limit. Our results imply that random quantum circuits yield an efficient implementation of ϵ approximate unitary t designs.
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Affiliation(s)
- Winton G Brown
- Department of Physics and Astronomy, Dartmouth College, 6127 Wilder Laboratory, Hanover, New Hampshire 03755, USA
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Figueiredo MC, Cotta TM, Pellegrino GQ. Classical analysis of quantum phase transitions in a bilayer model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 81:012104. [PMID: 20365415 DOI: 10.1103/physreve.81.012104] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/06/2009] [Indexed: 05/29/2023]
Abstract
In this Brief Report we extend the classical analysis performed on the schematic model proposed in [T. Moreira, G. Q. Pellegrino, J. G. Peixoto de Faria, M. C. Nemes, F. Camargo, and A. F. R. Toledo Piza, Phys. Rev. E 77, 051102 (2008)] concerning quantum phase transitions in a bilayer system. We show that appropriate integrations along the classical periodic orbits reproduce with excellent agreement both the quantum spectrum and the expected mean value for the number of excitons in the system, quantities which are directly related to the observed boson-fermion quantum phase transition.
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Affiliation(s)
- Mariane Camargos Figueiredo
- Departamento de Engenharia Elétrica, Centro Federal de Educação Tecnológica de Minas Gerais, Belo Horizonte, MG, Brazil
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Caneva T, Fazio R, Santoro GE. Quantum annealing of an infinite-range transverse-field Ising model. ACTA ACUST UNITED AC 2009. [DOI: 10.1088/1742-6596/143/1/012004] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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22
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Cejnar P, Stránský P. Impact of quantum phase transitions on excited-level dynamics. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 78:031130. [PMID: 18851016 DOI: 10.1103/physreve.78.031130] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/25/2008] [Revised: 07/23/2008] [Indexed: 05/26/2023]
Abstract
The influence of quantum phase transitions on the evolution of excited levels in the critical parameter region is discussed. The analysis is performed for one- and two-dimensional systems with first- and second-order ground-state transitions. Examples include the cusp and nuclear collective Hamiltonians. Applications in systems of higher dimensions are possible.
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Affiliation(s)
- Pavel Cejnar
- Institute of Particle and Nuclear Physics, Faculty of Mathematics and Physics, Charles University, V Holesovickách 2, 18000 Prague, Czech Republic
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Ribeiro P, Vidal J, Mosseri R. Exact spectrum of the Lipkin-Meshkov-Glick model in the thermodynamic limit and finite-size corrections. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 78:021106. [PMID: 18850785 DOI: 10.1103/physreve.78.021106] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/27/2008] [Indexed: 05/26/2023]
Abstract
The spectrum of the Lipkin-Meshkov-Glick model is exactly derived in the thermodynamic limit by means of a spin-coherent-state formalism. In the first step, a classical analysis allows one to distinguish between four distinct regions in the parameter space according to the nature of the singularities arising in the classical energy surface; these correspond to spectral critical points. The eigenfunctions are then analyzed more precisely in terms of the associated roots of the Majorana polynomial, leading to exact expressions for the density of states in the thermodynamic limit. Finite-size effects are also analyzed, leading in particular to logarithmic corrections near the singularities occurring in the spectrum. Finally, we also compute expectation values of the spin operators in a semiclassical analysis in order to illustrate some subtle effects occurring in one region of the parameter space.
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Affiliation(s)
- Pedro Ribeiro
- Laboratoire de Physique Théorique de la Matière Condensée, CNRS UMR 7600, Université Pierre et Marie Curie, 4 Place Jussieu, 75252 Paris Cedex 05, France.
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Cejnar P, Heinze S, Macek M. Coulomb analogy for non-Hermitian degeneracies near quantum phase transitions. PHYSICAL REVIEW LETTERS 2007; 99:100601. [PMID: 17930380 DOI: 10.1103/physrevlett.99.100601] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/11/2007] [Indexed: 05/25/2023]
Abstract
Degeneracies near the real axis in a complex-extended parameter space of a Hermitian Hamiltonian are studied. We present a method to measure distributions of such degeneracies on the Riemann sheet of a selected level and apply it in classification of quantum phase transitions. The degeneracies are shown to behave similarly as complex zeros of a partition function.
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Affiliation(s)
- Pavel Cejnar
- Institute of Particle and Nuclear Physics, Faculty of Mathematics and Physics, Charles University, V Holesovickách 2, 180 00 Prague, Czech Republic
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Ribeiro P, Vidal J, Mosseri R. Thermodynamical limit of the Lipkin-Meshkov-Glick model. PHYSICAL REVIEW LETTERS 2007; 99:050402. [PMID: 17930734 DOI: 10.1103/physrevlett.99.050402] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/19/2007] [Indexed: 05/25/2023]
Abstract
A method based on the analysis of the Majorana polynomial roots is introduced to compute the spectrum of the Lipkin-Meshkov-Glick model in the thermodynamical limit. A rich structure made of four qualitatively different regions is revealed in the parameter space, whereas the ground state study distinguishes between only two phases.
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Affiliation(s)
- Pedro Ribeiro
- Laboratoire de Physique Théorique de la Matière Condensée, CNRS UMR 7600, Université Pierre et Marie Curie, 4 Place Jussieu, 75252 Paris Cedex 05, France
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Cejnar P, Macek M, Heinze S, Jolie J, Dobeš J. Monodromy and excited-state quantum phase transitions in integrable systems: collective vibrations of nuclei. ACTA ACUST UNITED AC 2006. [DOI: 10.1088/0305-4470/39/31/l01] [Citation(s) in RCA: 101] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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