1
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Min B, Anto-Sztrikacs N, Brenes M, Segal D. Bath-Engineering Magnetic Order in Quantum Spin Chains: An Analytic Mapping Approach. PHYSICAL REVIEW LETTERS 2024; 132:266701. [PMID: 38996288 DOI: 10.1103/physrevlett.132.266701] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/15/2024] [Revised: 03/22/2024] [Accepted: 05/15/2024] [Indexed: 07/14/2024]
Abstract
Dissipative processes can drive different magnetic orders in quantum spin chains. Using a nonperturbative analytic mapping framework, we systematically show how to structure different magnetic orders in spin systems by controlling the locality of the attached baths. Our mapping approach reveals analytically the impact of spin-bath couplings, leading to the suppression of spin splittings, bath dressing and mixing of spin-spin interactions, and emergence of nonlocal ferromagnetic interactions between spins coupled to the same bath, which become long ranged for a global bath. Our general mapping method can be readily applied to a variety of spin models: we demonstrate (i) a bath-induced transition from antiferromagnetic (AFM) to ferromagnetic ordering in a Heisenberg spin chain, (ii) AFM to extended Neel phase ordering within a transverse-field Ising chain with pairwise couplings to baths, and (iii) a quantum phase transition in the fully connected Ising model. Our method is nonperturbative in the system-bath coupling. It holds for a variety of non-Markovian baths and it can be readily applied towards studying bath-engineered phases in frustrated or topological materials.
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Affiliation(s)
- Brett Min
- Department of Physics and Centre for Quantum Information and Quantum Control, University of Toronto, 60 Saint George Street, Toronto, Ontario, M5S 1A7, Canada
| | | | - Marlon Brenes
- Department of Physics and Centre for Quantum Information and Quantum Control, University of Toronto, 60 Saint George Street, Toronto, Ontario, M5S 1A7, Canada
| | - Dvira Segal
- Department of Physics and Centre for Quantum Information and Quantum Control, University of Toronto, 60 Saint George Street, Toronto, Ontario, M5S 1A7, Canada
- Department of Chemistry, University of Toronto, 80 Saint George Street, Toronto, Ontario, M5S 3H6, Canada
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2
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Ding D, Bai Z, Liu Z, Shi B, Guo G, Li W, Adams CS. Ergodicity breaking from Rydberg clusters in a driven-dissipative many-body system. SCIENCE ADVANCES 2024; 10:eadl5893. [PMID: 38437588 PMCID: PMC10911772 DOI: 10.1126/sciadv.adl5893] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/26/2023] [Accepted: 01/29/2024] [Indexed: 03/06/2024]
Abstract
It is challenging to probe ergodicity breaking trends of a quantum many-body system when dissipation inevitably damages quantum coherence originated from coherent coupling and dispersive two-body interactions. Rydberg atoms provide a test bed to detect emergent exotic many-body phases and nonergodic dynamics where the strong Rydberg atom interaction competes with and overtakes dissipative effects even at room temperature. Here, we report experimental evidence of a transition from ergodic toward ergodic breaking dynamics in driven-dissipative Rydberg atomic gases. The broken ergodicity is featured by the long-time phase oscillation, which is attributed to the formation of Rydberg excitation clusters in limit cycle phases. The broken symmetry in the limit cycle is a direct manifestation of many-body collective effects, which is verified experimentally by tuning atomic densities. The reported result reveals that Rydberg many-body systems are a promising candidate to probe ergodicity breaking dynamics, such as limit cycles, and enable the benchmark of nonequilibrium phase transition.
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Affiliation(s)
- Dongsheng Ding
- Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Zhengyang Bai
- State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200062, China
| | - Zongkai Liu
- Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Baosen Shi
- Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Guangcan Guo
- Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Weibin Li
- School of Physics and Astronomy, and Centre for the Mathematics and Theoretical Physics of Quantum Non-equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - C. Stuart Adams
- Department of Physics, Joint Quantum Centre (JQC) Durham-Newcastle, Durham University, South Road, Durham DH1 3LE, United Kingdom
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3
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Caleffi F, Capone M, Carusotto I. Collective Excitations of a Strongly Correlated Nonequilibrium Photon Fluid across the Insulator-Superfluid Phase Transition. PHYSICAL REVIEW LETTERS 2023; 131:193604. [PMID: 38000432 DOI: 10.1103/physrevlett.131.193604] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/26/2022] [Revised: 07/15/2023] [Accepted: 09/26/2023] [Indexed: 11/26/2023]
Abstract
We develop a Gutzwiller theory for the nonequilibrium steady states of a strongly interacting photon fluid driven by a non-Markovian incoherent pump. In particular, we explore the collective modes of the system across the out-of-equilibrium insulator-superfluid transition of the system, characterizing the diffusive Goldstone mode in the superfluid phase and the excitation of particles and holes in the insulating one. Observable features in the pump-and-probe optical response of the system are highlighted. Our predictions are experimentally accessible to state-of-the-art circuit-QED devices and open the way for the study of novel driven-dissipative many-body scenarios with no counterparts at equilibrium.
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Affiliation(s)
- Fabio Caleffi
- International School for Advanced Studies (SISSA), Via Bonomea 265, I-34136 Trieste, Italy
| | - Massimo Capone
- International School for Advanced Studies (SISSA), Via Bonomea 265, I-34136 Trieste, Italy
- CNR-IOM Democritos, Via Bonomea 265, I-34136 Trieste, Italy
| | - Iacopo Carusotto
- INO-CNR BEC Center and Dipartimento di Fisica, Università di Trento, Via Sommarive 14, I-38123 Povo, Italy
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4
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Kazemi J, Weimer H. Driven-Dissipative Rydberg Blockade in Optical Lattices. PHYSICAL REVIEW LETTERS 2023; 130:163601. [PMID: 37154665 DOI: 10.1103/physrevlett.130.163601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/30/2022] [Revised: 03/18/2023] [Accepted: 04/03/2023] [Indexed: 05/10/2023]
Abstract
While dissipative Rydberg gases exhibit unique possibilities to tune dissipation and interaction properties, very little is known about the quantum many-body physics of such long-range interacting open quantum systems. We theoretically analyze the steady state of a van der Waals interacting Rydberg gas in an optical lattice based on a variational treatment that also includes long-range correlations necessary to describe the physics of the Rydberg blockade, i.e., the inhibition of neighboring Rydberg excitations by strong interactions. In contrast to the ground state phase diagram, we find that the steady state undergoes a single first order phase transition from a blockaded Rydberg gas to a facilitation phase where the blockade is lifted. The first order line terminates in a critical point when including sufficiently strong dephasing, enabling a highly promising route to study dissipative criticality in these systems. In some regimes, we also find good quantitative agreement of the phase boundaries with previously employed short-range models, however, with the actual steady states exhibiting strikingly different behavior.
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Affiliation(s)
- Javad Kazemi
- Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstraße 2, 30167 Hannover, Germany
| | - Hendrik Weimer
- Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstraße 2, 30167 Hannover, Germany and Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36 EW 7-1, 10623 Berlin, Germany
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5
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Singh VP, Weimer H. Driven-Dissipative Criticality within the Discrete Truncated Wigner Approximation. PHYSICAL REVIEW LETTERS 2022; 128:200602. [PMID: 35657854 DOI: 10.1103/physrevlett.128.200602] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/16/2021] [Accepted: 04/14/2022] [Indexed: 06/15/2023]
Abstract
We present an approach to the numerical simulation of open quantum many-body systems based on the semiclassical framework of the discrete truncated Wigner approximation. We establish a quantum jump formalism to integrate the quantum master equation describing the dynamics of the system, which we find to be exact in both the noninteracting limit and the limit where the system is described by classical rate equations. We apply our method to simulation of the paradigmatic dissipative Ising model, where we are able to capture the critical fluctuations of the system beyond the level of mean-field theory.
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Affiliation(s)
- Vijay Pal Singh
- Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstraße 2, 30167 Hannover, Germany
- Zentrum für Optische Quantentechnologien and Institut für Laserphysik, Universität Hamburg, 22761 Hamburg, Germany
| | - Hendrik Weimer
- Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstraße 2, 30167 Hannover, Germany
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6
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Rose DC, Macieszczak K, Lesanovsky I, Garrahan JP. Hierarchical classical metastability in an open quantum East model. Phys Rev E 2022; 105:044121. [PMID: 35590670 DOI: 10.1103/physreve.105.044121] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/25/2021] [Accepted: 03/18/2022] [Indexed: 06/15/2023]
Abstract
We study in detail an open quantum generalization of a classical kinetically constrained model-the East model-known to exhibit slow glassy dynamics stemming from a complex hierarchy of metastable states with distinct lifetimes. Using the recently introduced theory of classical metastability for open quantum systems, we show that the driven open quantum East model features a hierarchy of classical metastabilities at low temperature and weak driving field. We find that the effective long-time description of its dynamics not only is classical, but shares many properties with the classical East model, such as obeying an effective detailed balance condition and lacking static interactions between excitations, but with this occurring within a modified set of metastable phases which are coherent, and with an effective temperature that is dependent on the coherent drive.
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Affiliation(s)
- Dominic C Rose
- School of Physics and Astronomy, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
- Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
- Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom
| | - Katarzyna Macieszczak
- TCM Group, Cavendish Laboratory, University of Cambridge, J. J. Thomson Ave., Cambridge CB3 0HE, United Kingdom
| | - Igor Lesanovsky
- School of Physics and Astronomy, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
- Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
- Institut für Theoretische Physik, Universität Tübingen, Auf der Morgenstelle 14, 72076 Tübingen, Germany
| | - Juan P Garrahan
- School of Physics and Astronomy, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
- Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
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7
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Li Z, Claude F, Boulier T, Giacobino E, Glorieux Q, Bramati A, Ciuti C. Dissipative Phase Transition with Driving-Controlled Spatial Dimension and Diffusive Boundary Conditions. PHYSICAL REVIEW LETTERS 2022; 128:093601. [PMID: 35302789 DOI: 10.1103/physrevlett.128.093601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/19/2021] [Accepted: 02/01/2022] [Indexed: 06/14/2023]
Abstract
We investigate theoretically and experimentally a first-order dissipative phase transition, with diffusive boundary conditions and the ability to tune the spatial dimension of the system. The considered physical system is a planar semiconductor microcavity in the strong light-matter coupling regime, where polariton excitations are injected by a quasiresonant optical driving field. The spatial dimension of the system from 1D to 2D is tuned by designing the intensity profile of the driving field. We investigate the emergence of criticality by increasing the spatial size of the driven region. The system is nonlinear due to polariton-polariton interactions and the boundary conditions are diffusive because the polaritons can freely diffuse out of the driven region. We show that no phase transition occurs using a 1D driving geometry, while for a 2D geometry we do observe both in theory and experiments the emergence of a first-order phase transition. The demonstrated technique allows all-optical and in situ control of the system geometry, providing a versatile platform for exploring the many-body physics of photons.
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Affiliation(s)
- Zejian Li
- Laboratoire Matériaux et Phénomènes Quantiques (MPQ), Université de Paris, CNRS-UMR7162, Paris 75013, France
| | - Ferdinand Claude
- Laboratoire Kastler Brossel, Sorbonne Université, CNRS, ENS-Université PSL, Collège de France, Paris 75005, France
| | - Thomas Boulier
- Laboratoire Kastler Brossel, Sorbonne Université, CNRS, ENS-Université PSL, Collège de France, Paris 75005, France
| | - Elisabeth Giacobino
- Laboratoire Kastler Brossel, Sorbonne Université, CNRS, ENS-Université PSL, Collège de France, Paris 75005, France
| | - Quentin Glorieux
- Laboratoire Kastler Brossel, Sorbonne Université, CNRS, ENS-Université PSL, Collège de France, Paris 75005, France
| | - Alberto Bramati
- Laboratoire Kastler Brossel, Sorbonne Université, CNRS, ENS-Université PSL, Collège de France, Paris 75005, France
| | - Cristiano Ciuti
- Laboratoire Matériaux et Phénomènes Quantiques (MPQ), Université de Paris, CNRS-UMR7162, Paris 75013, France
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8
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Carollo F, Lesanovsky I. Nonequilibrium Dark Space Phase Transition. PHYSICAL REVIEW LETTERS 2022; 128:040603. [PMID: 35148125 DOI: 10.1103/physrevlett.128.040603] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/08/2021] [Revised: 09/22/2021] [Accepted: 01/06/2022] [Indexed: 06/14/2023]
Abstract
We introduce the concept of dark space phase transition, which may occur in open many-body quantum systems where irreversible decay, interactions, and quantum interference compete. Our study is based on a quantum many-body model that is inspired by classical nonequilibrium processes which feature phase transitions into an absorbing state, such as epidemic spreading. The possibility for different dynamical paths to interfere quantum mechanically results in collective dynamical behavior without classical counterpart. We identify two competing dark states, a trivial one corresponding to a classical absorbing state and an emergent one which is quantum coherent. We establish a nonequilibrium phase transition within this dark space that features a phenomenology which cannot be encountered in classical systems. Such emergent two-dimensional dark space may find technological applications, e.g., for the collective encoding of a quantum information.
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Affiliation(s)
- Federico Carollo
- Institut für Theoretische Physik, Eberhard Karls Universität Tübingen, Auf der Morgenstelle 14, 72076 Tübingen, Germany
| | - Igor Lesanovsky
- Institut für Theoretische Physik, Eberhard Karls Universität Tübingen, Auf der Morgenstelle 14, 72076 Tübingen, Germany
- School of Physics and Astronomy and Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, The University of Nottingham, Nottingham NG7 2RD, United Kingdom
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9
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Ferioli G, Glicenstein A, Robicheaux F, Sutherland RT, Browaeys A, Ferrier-Barbut I. Laser-Driven Superradiant Ensembles of Two-Level Atoms near Dicke Regime. PHYSICAL REVIEW LETTERS 2021; 127:243602. [PMID: 34951804 DOI: 10.1103/physrevlett.127.243602] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/28/2021] [Accepted: 11/03/2021] [Indexed: 06/14/2023]
Abstract
We report the experimental observation of a superradiant emission emanating from an elongated dense ensemble of laser cooled two-level atoms, with a radial extent smaller than the transition wavelength. In the presence of a strong driving laser, we observe that the system is superradiant along its symmmetry axis. This occurs even though the driving laser is orthogonal to the superradiance direction. This superradiance modifies the spontaneous emission, and, resultantly, the Rabi oscillations. We also investigate Dicke superradiance in the emission of an almost fully inverted system as a function of the atom number. The experimental results are in qualitative agreement with ab-initio, beyond-mean-field calculations.
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Affiliation(s)
- G Ferioli
- Université Paris-Saclay, Institut d'Optique Graduate School, CNRS, Laboratoire Charles Fabry, 91127, Palaiseau, France
| | - A Glicenstein
- Université Paris-Saclay, Institut d'Optique Graduate School, CNRS, Laboratoire Charles Fabry, 91127, Palaiseau, France
| | - F Robicheaux
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA
- Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette, Indiana 47907, USA
| | - R T Sutherland
- Department of Electrical and Computer Engineering, Department of Physics and Astronomy, University of Texas at San Antonio, San Antonio, Texas 78249, USA
| | - A Browaeys
- Université Paris-Saclay, Institut d'Optique Graduate School, CNRS, Laboratoire Charles Fabry, 91127, Palaiseau, France
| | - I Ferrier-Barbut
- Université Paris-Saclay, Institut d'Optique Graduate School, CNRS, Laboratoire Charles Fabry, 91127, Palaiseau, France
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10
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Pistorius T, Kazemi J, Weimer H. Quantum Many-Body Dynamics of Driven-Dissipative Rydberg Polaritons. PHYSICAL REVIEW LETTERS 2020; 125:263604. [PMID: 33449759 DOI: 10.1103/physrevlett.125.263604] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/25/2020] [Accepted: 11/30/2020] [Indexed: 06/12/2023]
Abstract
We study the propagation of strongly interacting Rydberg polaritons through an atomic medium in a one-dimensional optical lattice. We derive an effective single-band Hubbard model to describe the dynamics of the dark-state polaritons under realistic assumptions. Within this model, we analyze the driven-dissipative transport of polaritons through the system by considering a coherent drive on one side and by including the spontaneous emission of the metastable Rydberg state. Using a variational approach to solve the many-body problem, we find strong antibunching of the outgoing photons despite the losses from the Rydberg state decay.
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Affiliation(s)
- Tim Pistorius
- Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstraße 2, 30167 Hannover, Germany
| | - Javad Kazemi
- Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstraße 2, 30167 Hannover, Germany
| | - Hendrik Weimer
- Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstraße 2, 30167 Hannover, Germany
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11
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Landa H, Schiró M, Misguich G. Multistability of Driven-Dissipative Quantum Spins. PHYSICAL REVIEW LETTERS 2020; 124:043601. [PMID: 32058770 DOI: 10.1103/physrevlett.124.043601] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/30/2019] [Indexed: 06/10/2023]
Abstract
We study the dynamics of lattice models of quantum spins one-half, driven by a coherent drive and subject to dissipation. Generically the mean-field limit of these models manifests multistable parameter regions of coexisting steady states with different magnetizations. We introduce an efficient scheme accounting for the corrections to mean field by correlations at leading order, and benchmark this scheme using high-precision numerics based on matrix-product operators in one- and two-dimensional lattices. Correlations are shown to wash the mean-field bistability in dimension one, leading to a unique steady state. In dimension two and higher, we find that multistability is again possible, provided the thermodynamic limit of an infinitely large lattice is taken first with respect to the longtime limit. Variation of the system parameters results in jumps between the different steady states, each showing a critical slowing down in the convergence of perturbations towards the steady state. Experiments with trapped ions can realize the model and possibly answer open questions in the nonequilibrium many-body dynamics of these quantum systems, beyond the system sizes accessible to present numerics.
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Affiliation(s)
- Haggai Landa
- Institut de Physique Théorique, Université Paris-Saclay, CEA, CNRS, 91191 Gif-sur-Yvette, France
| | - Marco Schiró
- JEIP, USR 3573 CNRS, Collège de France, PSL Research University, 11, place Marcelin Berthelot, 75231 Paris Cedex 05, France
| | - Grégoire Misguich
- Institut de Physique Théorique, Université Paris-Saclay, CEA, CNRS, 91191 Gif-sur-Yvette, France
- Laboratoire de Physique Théorique et Modélisation, CNRS UMR 8089, Université de Cergy-Pontoise, 95302 Cergy-Pontoise, France
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12
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Young JT, Gorshkov AV, Foss-Feig M, Maghrebi MF. Nonequilibrium Fixed Points of Coupled Ising Models. PHYSICAL REVIEW. X 2020; 10:10.1103/physrevx.10.011039. [PMID: 33364075 PMCID: PMC7756198 DOI: 10.1103/physrevx.10.011039] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Driven-dissipative systems are expected to give rise to nonequilibrium phenomena that are absent in their equilibrium counterparts. However, phase transitions in these systems generically exhibit an effectively classical equilibrium behavior in spite of their nonequilibrium origin. In this paper, we show that multicritical points in such systems lead to a rich and genuinely nonequilibrium behavior. Specifically, we investigate a driven-dissipative model of interacting bosons that possesses two distinct phase transitions: one from a high- to a low-density phase-reminiscent of a liquid-gas transition-and another to an antiferromagnetic phase. Each phase transition is described by the Ising universality class characterized by an (emergent or microscopic) ℤ 2 symmetry. However, they coalesce at a multicritical point, giving rise to a nonequilibrium model of coupled Ising-like order parameters described by a ℤ 2 × ℤ 2 symmetry. Using a dynamical renormalization-group approach, we show that a pair of nonequilibrium fixed points (NEFPs) emerge that govern the long-distance critical behavior of the system. We elucidate various exotic features of these NEFPs. In particular, we show that a generic continuous scale invariance at criticality is reduced to a discrete scale invariance. This further results in complex-valued critical exponents and spiraling phase boundaries, and it is also accompanied by a complex Liouvillian gap even close to the phase transition. As direct evidence of the nonequilibrium nature of the NEFPs, we show that the fluctuation-dissipation relation is violated at all scales, leading to an effective temperature that becomes "hotter" and "hotter" at longer and longer wavelengths. Finally, we argue that this nonequilibrium behavior can be observed in cavity arrays with cross-Kerr nonlinearities.
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Affiliation(s)
- Jeremy T. Young
- Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA
| | - Alexey V. Gorshkov
- 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
| | - Michael Foss-Feig
- United States Army Research Laboratory, Adelphi, Maryland 20783, USA
| | - Mohammad F. Maghrebi
- Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA
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13
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Carollo F, Gillman E, Weimer H, Lesanovsky I. Critical Behavior of the Quantum Contact Process in One Dimension. PHYSICAL REVIEW LETTERS 2019; 123:100604. [PMID: 31573316 DOI: 10.1103/physrevlett.123.100604] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/25/2019] [Indexed: 06/10/2023]
Abstract
The contact process is a paradigmatic classical stochastic system displaying critical behavior even in one dimension. It features a nonequilibrium phase transition into an absorbing state that has been widely investigated and shown to belong to the directed percolation universality class. When the same process is considered in a quantum setting, much less is known. So far, mainly semiclassical studies have been conducted and the nature of the transition in low dimensions is still a matter of debate. Also, from a numerical point of view, from which the system may look fairly simple-especially in one dimension-results are lacking. In particular, the presence of the absorbing state poses a substantial challenge, which appears to affect the reliability of algorithms targeting directly the steady state. Here we perform real-time numerical simulations of the open dynamics of the quantum contact process and shed light on the existence and on the nature of an absorbing state phase transition in one dimension. We find evidence for the transition being continuous and provide first estimates for the critical exponents. Beyond the conceptual interest, the simplicity of the quantum contact process makes it an ideal benchmark problem for scrutinizing numerical methods for open quantum nonequilibrium systems.
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Affiliation(s)
- Federico Carollo
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
- Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - Edward Gillman
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
- Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - Hendrik Weimer
- Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstrasse 2, 30167 Hannover, Germany
| | - Igor Lesanovsky
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
- Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
- Institut für Theoretische Physik, Universität Tübingen, Auf der Morgenstelle 14, 72076 Tübingen, Germany
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14
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Vicentini F, Biella A, Regnault N, Ciuti C. Variational Neural-Network Ansatz for Steady States in Open Quantum Systems. PHYSICAL REVIEW LETTERS 2019; 122:250503. [PMID: 31347877 DOI: 10.1103/physrevlett.122.250503] [Citation(s) in RCA: 36] [Impact Index Per Article: 7.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/28/2019] [Indexed: 06/10/2023]
Abstract
We present a general variational approach to determine the steady state of open quantum lattice systems via a neural-network approach. The steady-state density matrix of the lattice system is constructed via a purified neural-network Ansatz in an extended Hilbert space with ancillary degrees of freedom. The variational minimization of cost functions associated to the master equation can be performed using a Markov chain Monte Carlo sampling. As a first application and proof of principle, we apply the method to the dissipative quantum transverse Ising model.
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Affiliation(s)
- Filippo Vicentini
- Université de Paris, Laboratoire Matériaux et Phénomènes Quantiques, CNRS, F-75013, Paris, France
| | - Alberto Biella
- Université de Paris, Laboratoire Matériaux et Phénomènes Quantiques, CNRS, F-75013, Paris, France
| | - Nicolas Regnault
- Laboratoire de Physique de l'Ecole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, Sorbonne Paris Cité, F-75005, Paris, France
| | - Cristiano Ciuti
- Université de Paris, Laboratoire Matériaux et Phénomènes Quantiques, CNRS, F-75013, Paris, France
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15
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Nagy A, Savona V. Variational Quantum Monte Carlo Method with a Neural-Network Ansatz for Open Quantum Systems. PHYSICAL REVIEW LETTERS 2019; 122:250501. [PMID: 31347886 DOI: 10.1103/physrevlett.122.250501] [Citation(s) in RCA: 41] [Impact Index Per Article: 8.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/28/2019] [Indexed: 06/10/2023]
Abstract
The possibility to simulate the properties of many-body open quantum systems with a large number of degrees of freedom (d.o.f.) is the premise to the solution of several outstanding problems in quantum science and quantum information. The challenge posed by this task lies in the complexity of the density matrix increasing exponentially with the system size. Here, we develop a variational method to efficiently simulate the nonequilibrium steady state of Markovian open quantum systems based on variational Monte Carlo methods and on a neural network representation of the density matrix. Thanks to the stochastic reconfiguration scheme, the application of the variational principle is translated into the actual integration of the quantum master equation. We test the effectiveness of the method by modeling the two-dimensional dissipative XYZ spin model on a lattice.
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Affiliation(s)
- Alexandra Nagy
- Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015, Lausanne, Switzerland
| | - Vincenzo Savona
- Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015, Lausanne, Switzerland
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16
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Gambetta FM, Carollo F, Marcuzzi M, Garrahan JP, Lesanovsky I. Discrete Time Crystals in the Absence of Manifest Symmetries or Disorder in Open Quantum Systems. PHYSICAL REVIEW LETTERS 2019; 122:015701. [PMID: 31012672 DOI: 10.1103/physrevlett.122.015701] [Citation(s) in RCA: 21] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/09/2018] [Indexed: 06/09/2023]
Abstract
We establish a link between metastability and a discrete time-crystalline phase in a periodically driven open quantum system. The mechanism we highlight requires neither the system to display any microscopic symmetry nor the presence of disorder, but relies instead on the emergence of a metastable regime. We investigate this in detail in an open quantum spin system, which is a canonical model for the exploration of collective phenomena in strongly interacting dissipative Rydberg gases. Here, a semiclassical approach reveals the emergence of a robust discrete time-crystalline phase in the thermodynamic limit in which metastability, dissipation, and interparticle interactions play a crucial role. We perform numerical simulations in order to investigate the dependence on the range of interactions, from all to all to short ranged, and the scaling with system size of the lifetime of the time crystal.
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Affiliation(s)
- F M Gambetta
- School of Physics and Astronomy, University of Nottingham, Nottingham, NG7 2RD, United Kingdom and Centre for the Mathematics and Theoretical Physics of Quantum Non-equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - F Carollo
- School of Physics and Astronomy, University of Nottingham, Nottingham, NG7 2RD, United Kingdom and Centre for the Mathematics and Theoretical Physics of Quantum Non-equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - M Marcuzzi
- School of Physics and Astronomy, University of Nottingham, Nottingham, NG7 2RD, United Kingdom and Centre for the Mathematics and Theoretical Physics of Quantum Non-equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - J P Garrahan
- School of Physics and Astronomy, University of Nottingham, Nottingham, NG7 2RD, United Kingdom and Centre for the Mathematics and Theoretical Physics of Quantum Non-equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - I Lesanovsky
- School of Physics and Astronomy, University of Nottingham, Nottingham, NG7 2RD, United Kingdom and Centre for the Mathematics and Theoretical Physics of Quantum Non-equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
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17
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Wade CG, Marcuzzi M, Levi E, Kondo JM, Lesanovsky I, Adams CS, Weatherill KJ. A terahertz-driven non-equilibrium phase transition in a room temperature atomic vapour. Nat Commun 2018; 9:3567. [PMID: 30177716 PMCID: PMC6120943 DOI: 10.1038/s41467-018-05597-4] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/06/2018] [Accepted: 07/16/2018] [Indexed: 11/25/2022] Open
Abstract
There are few demonstrated examples of phase transitions that may be driven directly by terahertz frequency electric fields, and those that are known require field strengths exceeding 1 MV cm-1. Here we report a non-equilibrium phase transition driven by a weak (≪1 V cm-1), continuous-wave terahertz electric field. The system consists of room temperature caesium vapour under continuous optical excitation to a high-lying Rydberg state, which is resonantly coupled to a nearby level by the terahertz electric field. We use a simple model to understand the underlying physical behaviour, and we demonstrate two protocols to exploit the phase transition as a narrowband terahertz detector: the first with a fast (20 μs) non-linear response to nano-Watts of incident radiation, and the second with a linearised response and effective noise equivalent power ≤1 pW Hz-1/2. The work opens the door to a class of terahertz devices controlled with low-field intensities and operating in a room temperature environment.
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Affiliation(s)
- C G Wade
- Joint Quantum Centre (JQC) Durham-Newcastle, Department of Physics, Durham University, Durham, DH1 3LE, UK.
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford, OX1 3PU, UK.
| | - M Marcuzzi
- School of Physics and Astronomy, University of Nottingham, Nottingham, NG7 2RD, UK
- Centre for the Mathematics and Theoretical Physics of Quantum Non-equilibrium Systems, University of Nottingham, Nottingham, NG7 2RD, UK
| | - E Levi
- School of Physics and Astronomy, University of Nottingham, Nottingham, NG7 2RD, UK
- Centre for the Mathematics and Theoretical Physics of Quantum Non-equilibrium Systems, University of Nottingham, Nottingham, NG7 2RD, UK
| | - J M Kondo
- Joint Quantum Centre (JQC) Durham-Newcastle, Department of Physics, Durham University, Durham, DH1 3LE, UK
| | - I Lesanovsky
- School of Physics and Astronomy, University of Nottingham, Nottingham, NG7 2RD, UK
- Centre for the Mathematics and Theoretical Physics of Quantum Non-equilibrium Systems, University of Nottingham, Nottingham, NG7 2RD, UK
| | - C S Adams
- Joint Quantum Centre (JQC) Durham-Newcastle, Department of Physics, Durham University, Durham, DH1 3LE, UK
| | - K J Weatherill
- Joint Quantum Centre (JQC) Durham-Newcastle, Department of Physics, Durham University, Durham, DH1 3LE, UK
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18
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Raghunandan M, Wrachtrup J, Weimer H. High-Density Quantum Sensing with Dissipative First Order Transitions. PHYSICAL REVIEW LETTERS 2018; 120:150501. [PMID: 29756853 DOI: 10.1103/physrevlett.120.150501] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/22/2017] [Indexed: 06/08/2023]
Abstract
The sensing of external fields using quantum systems is a prime example of an emergent quantum technology. Generically, the sensitivity of a quantum sensor consisting of N independent particles is proportional to sqrt[N]. However, interactions invariably occurring at high densities lead to a breakdown of the assumption of independence between the particles, posing a severe challenge for quantum sensors operating at the nanoscale. Here, we show that interactions in quantum sensors can be transformed from a nuisance into an advantage when strong interactions trigger a dissipative phase transition in an open quantum system. We demonstrate this behavior by analyzing dissipative quantum sensors based upon nitrogen-vacancy defect centers in diamond. Using both a variational method and a numerical simulation of the master equation describing the open quantum many-body system, we establish the existence of a dissipative first order transition that can be used for quantum sensing. We investigate the properties of this phase transition for two- and three-dimensional setups, demonstrating that the transition can be observed using current experimental technology. Finally, we show that quantum sensors based on dissipative phase transitions are particularly robust against imperfections such as disorder or decoherence, with the sensitivity of the sensor not being limited by the T_{2} coherence time of the device. Our results can readily be applied to other applications in quantum sensing and quantum metrology where interactions are currently a limiting factor.
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Affiliation(s)
- Meghana Raghunandan
- Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstraße 2, 30167 Hannover, Germany
| | - Jörg Wrachtrup
- 3. Physikalisches Institut, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
| | - Hendrik Weimer
- Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstraße 2, 30167 Hannover, Germany
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19
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Tscherbul TV, Brumer P. Non-equilibrium stationary coherences in photosynthetic energy transfer under weak-field incoherent illumination. J Chem Phys 2018; 148:124114. [PMID: 29604847 DOI: 10.1063/1.5028121] [Citation(s) in RCA: 20] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023] Open
Abstract
We present a theoretical study of the quantum dynamics of energy transfer in a model photosynthetic dimer excited by incoherent light and show that the interplay between incoherent pumping and phonon-induced relaxation, dephasing, and trapping leads to the emergence of non-equilibrium stationary states characterized by substantial stationary coherences in the energy basis. We obtain analytic expressions for these coherences in the limits of rapid dephasing of electronic excitations and of small excitonic coupling between the chromophores. The stationary coherences are maximized in the regime where the excitonic coupling is small compared to the trapping rate. We further show that the non-equilibrium coherences anti-correlate with the energy transfer efficiency in the regime of localized coupling to the reaction center and that no correlation exists under delocalized (Förster) trapping conditions.
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Affiliation(s)
- Timur V Tscherbul
- Department of Physics, University of Nevada, Reno, Nevada 89557, USA
| | - Paul Brumer
- Chemical Physics Theory Group, Department of Chemistry, and Center for Quantum Information and Quantum Control, University of Toronto, Toronto, Ontario M5S 3H6, Canada
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20
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Gangat AA, McCulloch IP, Kao YJ. Symmetry between repulsive and attractive interactions in driven-dissipative Bose-Hubbard systems. Sci Rep 2018; 8:3698. [PMID: 29487298 PMCID: PMC5829241 DOI: 10.1038/s41598-018-21845-5] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/13/2017] [Accepted: 02/12/2018] [Indexed: 11/29/2022] Open
Abstract
The driven-dissipative Bose-Hubbard model can be experimentally realized with either negative or positive onsite detunings, inter-site hopping energies, and onsite interaction energies. Here we use one-dimensional matrix product density operators to perform a fully quantum investigation of the dependence of the non-equilibrium steady states of this model on the signs of these parameters. Due to a symmetry in the Lindblad master equation, we find that simultaneously changing the sign of the interaction energies, hopping energies, and chemical potentials leaves the local boson number distribution and inter-site number correlations invariant, and the steady-state complex conjugated. This shows that all driven-dissipative phenomena of interacting bosons described by the Lindblad master equation, such as "fermionization" and "superbunching", can equivalently occur with attractive or repulsive interactions.
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Affiliation(s)
- Adil A Gangat
- Department of Physics, National Taiwan University, Taipei, 10607, Taiwan
| | - Ian P McCulloch
- ARC Centre of Excellence for Engineered Quantum Systems, School of Mathematics and Physics, The University of Queensland, St. Lucia, QLD 4072, Australia
| | - Ying-Jer Kao
- Department of Physics, National Taiwan University, Taipei, 10607, Taiwan.
- National Center for Theoretical Sciences, National Tsing Hua University, Hsinchu, 30013, Taiwan.
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21
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Foss-Feig M, Young JT, Albert VV, Gorshkov AV, Maghrebi MF. Solvable Family of Driven-Dissipative Many-Body Systems. PHYSICAL REVIEW LETTERS 2017; 119:190402. [PMID: 29219530 PMCID: PMC6467283 DOI: 10.1103/physrevlett.119.190402] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/25/2017] [Indexed: 05/28/2023]
Abstract
Exactly solvable models have played an important role in establishing the sophisticated modern understanding of equilibrium many-body physics. Conversely, the relative scarcity of solutions for nonequilibrium models greatly limits our understanding of systems away from thermal equilibrium. We study a family of nonequilibrium models, some of which can be viewed as dissipative analogues of the transverse-field Ising model, in that an effectively classical Hamiltonian is frustrated by dissipative processes that drive the system toward states that do not commute with the Hamiltonian. Surprisingly, a broad and experimentally relevant subset of these models can be solved efficiently. We leverage these solutions to compute the effects of decoherence on a canonical trapped-ion-based quantum computation architecture, and to prove a no-go theorem on steady-state phase transitions in a many-body model that can be realized naturally with Rydberg atoms or trapped ions.
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Affiliation(s)
- Michael Foss-Feig
- United States Army Research Laboratory, Adelphi, Maryland 20783, 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
| | - Jeremy T Young
- Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA
| | - Victor V Albert
- Yale Quantum Institute and Department of Physics, Yale University, New Haven, Connecticut 06520, USA
| | - Alexey V Gorshkov
- 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
- 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
- Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA
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22
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Kshetrimayum A, Weimer H, Orús R. A simple tensor network algorithm for two-dimensional steady states. Nat Commun 2017; 8:1291. [PMID: 29097666 PMCID: PMC5668304 DOI: 10.1038/s41467-017-01511-6] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/08/2016] [Accepted: 09/22/2017] [Indexed: 11/25/2022] Open
Abstract
Understanding dissipation in 2D quantum many-body systems is an open challenge which has proven remarkably difficult. Here we show how numerical simulations for this problem are possible by means of a tensor network algorithm that approximates steady states of 2D quantum lattice dissipative systems in the thermodynamic limit. Our method is based on the intuition that strong dissipation kills quantum entanglement before it gets too large to handle. We test its validity by simulating a dissipative quantum Ising model, relevant for dissipative systems of interacting Rydberg atoms, and benchmark our simulations with a variational algorithm based on product and correlated states. Our results support the existence of a first order transition in this model, with no bistable region. We also simulate a dissipative spin 1/2 XYZ model, showing that there is no re-entrance of the ferromagnetic phase. Our method enables the computation of steady states in 2D quantum lattice systems.
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Affiliation(s)
| | - Hendrik Weimer
- Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstr. 2, 30167, Hannover, Germany
| | - Román Orús
- Institute of Physics, Johannes Gutenberg University, 55099, Mainz, Germany.
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23
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Karabanov A, Rose DC, Köckenberger W, Garrahan JP, Lesanovsky I. Phase Transitions in Electron Spin Resonance Under Continuous Microwave Driving. PHYSICAL REVIEW LETTERS 2017; 119:150402. [PMID: 29077446 DOI: 10.1103/physrevlett.119.150402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/05/2017] [Indexed: 06/07/2023]
Abstract
We study an ensemble of strongly coupled electrons under continuous microwave irradiation interacting with a dissipative environment, a problem of relevance to the creation of highly polarized nonequilibrium states in nuclear magnetic resonance. We analyze the stationary states of the dynamics, described within a Lindblad master equation framework, at the mean-field approximation level. This approach allows us to identify steady-state phase transitions between phases of high and low polarization controlled by the distribution of disordered electronic interactions. We compare the mean-field predictions to numerically exact simulations of small systems and find good agreement. Our study highlights the possibility of observing collective phenomena, such as metastable states, phase transitions, and critical behavior, in appropriately designed paramagnetic systems. These phenomena occur in a low-temperature regime which is not theoretically tractable by conventional methods, e.g., the spin-temperature approach.
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Affiliation(s)
- A Karabanov
- School of Physics and Astronomy, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom and Centre for the Mathematics and Theoretical Physics of Quantum Non-equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - D C Rose
- School of Physics and Astronomy, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom and Centre for the Mathematics and Theoretical Physics of Quantum Non-equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - W Köckenberger
- School of Physics and Astronomy, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom and Centre for the Mathematics and Theoretical Physics of Quantum Non-equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - J P Garrahan
- School of Physics and Astronomy, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom and Centre for the Mathematics and Theoretical Physics of Quantum Non-equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - I Lesanovsky
- School of Physics and Astronomy, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom and Centre for the Mathematics and Theoretical Physics of Quantum Non-equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
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24
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Gangat AA, I T, Kao YJ. Steady States of Infinite-Size Dissipative Quantum Chains via Imaginary Time Evolution. PHYSICAL REVIEW LETTERS 2017; 119:010501. [PMID: 28731760 DOI: 10.1103/physrevlett.119.010501] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/31/2016] [Indexed: 06/07/2023]
Abstract
Directly in the thermodynamic limit, we show how to combine local imaginary and real-time evolution of tensor networks to efficiently and accurately find the nonequilibrium steady states (NESSs) of one-dimensional dissipative quantum lattices governed by a local Lindblad master equation. The imaginary time evolution first bypasses any highly correlated portions of the real-time evolution trajectory by directly converging to the weakly correlated subspace of the NESS, after which, real-time evolution completes the convergence to the NESS with high accuracy. We demonstrate the power of the method with the dissipative transverse field quantum Ising chain. We show that a crossover of an order parameter shown to be smooth in previous finite-size studies remains smooth in the thermodynamic limit.
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Affiliation(s)
- Adil A Gangat
- Department of Physics, and Center for Theoretical Sciences, National Taiwan University, Taipei 10607, Taiwan
| | - Te I
- Department of Physics, and Center for Theoretical Sciences, National Taiwan University, Taipei 10607, Taiwan
| | - Ying-Jer Kao
- Department of Physics, and Center for Theoretical Sciences, National Taiwan University, Taipei 10607, Taiwan
- National Center for Theoretical Sciences, National Tsing Hua University, Hsinchu 30013, Taiwan
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25
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Foss-Feig M, Niroula P, Young JT, Hafezi M, Gorshkov AV, Wilson RM, Maghrebi MF. Emergent equilibrium in many-body optical bistability. PHYSICAL REVIEW. A 2017; 95:10.1103/PhysRevA.95.043826. [PMID: 31093586 PMCID: PMC6513354 DOI: 10.1103/physreva.95.043826] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Many-body systems constructed of quantum-optical building blocks can now be realized in experimental platforms ranging from exciton-polariton fluids to ultracold Rydberg gases, establishing a fascinating interface between traditional many-body physics and the driven-dissipative, nonequilibrium setting of cavity QED. At this interface, the standard techniques and intuitions of both fields are called into question, obscuring issues as fundamental as the role of fluctuations, dimensionality, and symmetry on the nature of collective behavior and phase transitions. Here, we study the driven-dissipative Bose-Hubbard model, a minimal description of numerous atomic, optical, and solid-state systems in which particle loss is countered by coherent driving. Despite being a lattice version of optical bistability, a foundational and patently nonequilibrium model of cavity QED, the steady state possesses an emergent equilibrium description in terms of a classical Ising model. We establish this picture by making new connections between traditional techniques from many-body physics (functional integrals) and quantum optics (the system-size expansion). To lowest order in a controlled expansion-organized around the experimentally relevant limit of weak interactions-the full quantum dynamics reduces to nonequilibrium Langevin equations, which support a phase transition described by model A of the Hohenberg-Halperin classification. Numerical simulations of the Langevin equations corroborate this picture, revealing that canonical behavior associated with the Ising model manifests readily in simple experimental observables.
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Affiliation(s)
- M Foss-Feig
- United States Army Research Laboratory, Adelphi, Maryland 20783, USA
- Joint Quantum Institute, NIST and University of Maryland, College Park, Maryland 20742, USA
- Joint Center for Quantum Information and Computer Science, NIST and University of Maryland, College Park, Maryland 20742, USA
| | - P Niroula
- Joint Quantum Institute, NIST and University of Maryland, College Park, Maryland 20742, USA
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - J T Young
- Joint Quantum Institute, NIST and University of Maryland, College Park, Maryland 20742, USA
| | - M Hafezi
- Joint Quantum Institute, NIST and University of Maryland, College Park, Maryland 20742, USA
- Department of Electrical and Computer Engineering and Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, Maryland 20742, USA
| | - A V Gorshkov
- Joint Quantum Institute, NIST and University of Maryland, College Park, Maryland 20742, USA
- Joint Center for Quantum Information and Computer Science, NIST and University of Maryland, College Park, Maryland 20742, USA
| | - R M Wilson
- Department of Physics, United States Naval Academy, Annapolis, Maryland 21402, USA
| | - M F Maghrebi
- Joint Quantum Institute, NIST and University of Maryland, College Park, Maryland 20742, USA
- Joint Center for Quantum Information and Computer Science, NIST and University of Maryland, College Park, Maryland 20742, USA
- Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA
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26
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Overbeck VR, Maghrebi MF, Gorshkov AV, Weimer H. Multicritical behavior in dissipative Ising models. PHYSICAL REVIEW. A 2017; 95:10.1103/PhysRevA.95.042133. [PMID: 31093585 PMCID: PMC6513333 DOI: 10.1103/physreva.95.042133] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/15/2023]
Abstract
We analyze theoretically the many-body dynamics of a dissipative Ising model in a transverse field using a variational approach. We find that the steady-state phase diagram is substantially modified compared to its equilibrium counterpart, including the appearance of a multicritical point belonging to a different universality class. Building on our variational analysis, we establish a field-theoretical treatment corresponding to a dissipative variant of a Ginzburg-Landau theory, which allows us to compute the upper critical dimension of the system. Finally, we present a possible experimental realization of the dissipative Ising model using ultracold Rydberg gases.
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Affiliation(s)
- Vincent R. Overbeck
- Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstraße 2, 30167 Hannover, Germany
| | - Mohammad F. Maghrebi
- Joint Quantum Institute and Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA
| | - Alexey V. Gorshkov
- Joint Quantum Institute and Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA
| | - Hendrik Weimer
- Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstraße 2, 30167 Hannover, Germany
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27
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Rose DC, Macieszczak K, Lesanovsky I, Garrahan JP. Metastability in an open quantum Ising model. Phys Rev E 2016; 94:052132. [PMID: 27967090 DOI: 10.1103/physreve.94.052132] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/22/2016] [Indexed: 06/06/2023]
Abstract
We apply a recently developed theory for metastability in open quantum systems to a one-dimensional dissipative quantum Ising model. Earlier results suggest this model features either a nonequilibrium phase transition or a smooth but sharp crossover, where the stationary state changes from paramagnetic to ferromagnetic, accompanied by strongly intermittent emission dynamics characteristic of first-order coexistence between dynamical phases. We show that for a range of parameters close to this transition or crossover point the dynamics of the finite system displays pronounced metastability, i.e., the system relaxes first to long-lived metastable states before eventual relaxation to the true stationary state. From the spectral properties of the quantum master operator we characterize the low-dimensional manifold of metastable states, which are shown to be probability mixtures of two, paramagnetic and ferromagnetic, metastable phases. We also show that for long times the dynamics can be approximated by a classical stochastic dynamics between the metastable phases that is directly related to the intermittent dynamics observed in quantum trajectories and thus the dynamical phases.
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Affiliation(s)
- Dominic C Rose
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
- Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - Katarzyna Macieszczak
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
- Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
- School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - Igor Lesanovsky
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
- Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - Juan P Garrahan
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
- Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
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28
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Sieberer LM, Buchhold M, Diehl S. Keldysh field theory for driven open quantum systems. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2016; 79:096001. [PMID: 27482736 DOI: 10.1088/0034-4885/79/9/096001] [Citation(s) in RCA: 84] [Impact Index Per Article: 10.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Recent experimental developments in diverse areas-ranging from cold atomic gases to light-driven semiconductors to microcavity arrays-move systems into the focus which are located on the interface of quantum optics, many-body physics and statistical mechanics. They share in common that coherent and driven-dissipative quantum dynamics occur on an equal footing, creating genuine non-equilibrium scenarios without immediate counterpart in equilibrium condensed matter physics. This concerns both their non-thermal stationary states and their many-body time evolution. It is a challenge to theory to identify novel instances of universal emergent macroscopic phenomena, which are tied unambiguously and in an observable way to the microscopic drive conditions. In this review, we discuss some recent results in this direction. Moreover, we provide a systematic introduction to the open system Keldysh functional integral approach, which is the proper technical tool to accomplish a merger of quantum optics and many-body physics, and leverages the power of modern quantum field theory to driven open quantum systems.
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Affiliation(s)
- L M Sieberer
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 7610001, Israel
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29
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Wilson RM, Mahmud KW, Hu A, Gorshkov AV, Hafezi M, Foss-Feig M. Collective phases of strongly interacting cavity photons. PHYSICAL REVIEW. A 2016; 94:10.1103/PhysRevA.94.033801. [PMID: 31098434 PMCID: PMC6515917 DOI: 10.1103/physreva.94.033801] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/28/2023]
Abstract
We study a coupled array of coherently driven photonic cavities, which maps onto a driven-dissipative XY spin- 1 2 model with ferromagnetic couplings in the limit of strong optical nonlinearities. Using a site-decoupled mean-field approximation, we identify steady-state phases with canted antiferromagnetic order, in addition to limit cycle phases, where oscillatory dynamics persist indefinitely. We also identify collective bistable phases, where the system supports two steady states among spatially uniform, antiferromagnetic, and limit cycle phases. We compare these mean-field results to exact quantum trajectory simulations for finite one-dimensional arrays. The exact results exhibit short-range antiferromagnetic order for parameters that have significant overlap with the mean-field phase diagram. In the mean-field bistable regime, the exact quantum dynamics exhibits real-time collective switching between macroscopically distinguishable states. We present a clear physical picture for this dynamics and establish a simple relationship between the switching times and properties of the quantum Liouvillian.
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Affiliation(s)
- Ryan M Wilson
- Department of Physics, The United States Naval Academy, Annapolis, Maryland 21402, USA
- Kavli Institute of Theoretical Physics, Santa Barbara, California 93106, USA
| | - Khan W Mahmud
- Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA
| | - Anzi Hu
- Department of Physics, American University, Washington, DC 20016, USA
| | - Alexey V Gorshkov
- Kavli Institute of Theoretical Physics, Santa Barbara, California 93106, 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 Hafezi
- Kavli Institute of Theoretical Physics, Santa Barbara, California 93106, USA
- Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA
- Department of Electrical Engineering and Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, Maryland 20742, USA
| | - Michael Foss-Feig
- Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA
- United States Army Research Laboratory, Adelphi, Maryland 20783, USA
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Maghrebi MF, Gorshkov AV. Nonequilibrium many-body steady states via Keldysh formalism. PHYSICAL REVIEW. B 2016; 93:10.1103/PhysRevB.93.014307. [PMID: 31093593 PMCID: PMC6513009 DOI: 10.1103/physrevb.93.014307] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/15/2023]
Abstract
Many-body systems with both coherent dynamics and dissipation constitute a rich class of models which are nevertheless much less explored than their dissipationless counterparts. The advent of numerous experimental platforms that simulate such dynamics poses an immediate challenge to systematically understand and classify these models. In particular, nontrivial many-body states emerge as steady states under nonequilibrium dynamics. While these states and their phase transitions have been studied extensively with mean-field theory, the validity of the mean-field approximation has not been systematically investigated. In this paper, we employ a field-theoretic approach based on the Keldysh formalism to study nonequilibrium phases and phase transitions in a variety of models. In all cases, a complete description via the Keldysh formalism indicates a partial or complete failure of the mean-field analysis. Furthermore, we find that an effective temperature emerges as a result of dissipation, and the universal behavior including the dynamics near the steady state is generically described by a thermodynamic universality class.
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Affiliation(s)
- Mohammad F. Maghrebi
- Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA and Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA
| | - Alexey V. Gorshkov
- Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA and Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA
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