1
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Shu Y, Truhlar DG. Generalized Semiclassical Ehrenfest Method: A Route to Wave Function-Free Photochemistry and Nonadiabatic Dynamics with Only Potential Energies and Gradients. J Chem Theory Comput 2024; 20:4396-4426. [PMID: 38819014 DOI: 10.1021/acs.jctc.4c00424] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/01/2024]
Abstract
We reconsider recent methods by which direct dynamics calculations of electronically nonadiabatic processes can be carried out while requiring only adiabatic potential energies and their gradients. We show that these methods can be understood in terms of a new generalization of the well-known semiclassical Ehrenfest method. This is convenient because it eliminates the need to evaluate electronic wave functions and their matrix elements along the mixed quantum-classical trajectories. The new approximations and procedures enabling this advance are the curvature-driven approximation to the time-derivative coupling, the generalized semiclassical Ehrenfest method, and a new gradient correction scheme called the time-derivative matrix (TDM) scheme. When spin-orbit coupling is present, one can carry out dynamics calculations in the fully adiabatic basis using potential energies and gradients calculated without spin-orbit coupling plus the spin-orbit coupling matrix elements. Even when spin-orbit coupling is neglected, the method is useful because it allows calculations by electronic structure methods for which nonadiabatic coupling vectors are unavailable. In order to place the new considerations in context, the article starts out with a review of background material on trajectory surface hopping, the semiclassical Ehrenfest scheme, and methods for incorporating decoherence. We consider both internal conversion and intersystem crossing. We also review several examples from our group of successful applications of the curvature-driven approximation.
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Affiliation(s)
- Yinan Shu
- Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431, United States
| | - Donald G Truhlar
- Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431, United States
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2
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Kang M, Nuomin H, Chowdhury SN, Yuly JL, Sun K, Whitlow J, Valdiviezo J, Zhang Z, Zhang P, Beratan DN, Brown KR. Seeking a quantum advantage with trapped-ion quantum simulations of condensed-phase chemical dynamics. Nat Rev Chem 2024; 8:340-358. [PMID: 38641733 DOI: 10.1038/s41570-024-00595-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 03/07/2024] [Indexed: 04/21/2024]
Abstract
Simulating the quantum dynamics of molecules in the condensed phase represents a longstanding challenge in chemistry. Trapped-ion quantum systems may serve as a platform for the analog-quantum simulation of chemical dynamics that is beyond the reach of current classical-digital simulation. To identify a 'quantum advantage' for these simulations, performance analysis of both analog-quantum simulation on noisy hardware and classical-digital algorithms is needed. In this Review, we make a comparison between a noisy analog trapped-ion simulator and a few choice classical-digital methods on simulating the dynamics of a model molecular Hamiltonian with linear vibronic coupling. We describe several simple Hamiltonians that are commonly used to model molecular systems, which can be simulated with existing or emerging trapped-ion hardware. These Hamiltonians may serve as stepping stones towards the use of trapped-ion simulators for systems beyond the reach of classical-digital methods. Finally, we identify dynamical regimes in which classical-digital simulations seem to have the weakest performance with respect to analog-quantum simulations. These regimes may provide the lowest hanging fruit to make the most of potential quantum advantages.
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Affiliation(s)
- Mingyu Kang
- Duke Quantum Center, Duke University, Durham, NC, USA.
- Department of Physics, Duke University, Durham, NC, USA.
| | - Hanggai Nuomin
- Department of Chemistry, Duke University, Durham, NC, USA
| | | | - Jonathon L Yuly
- Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, NJ, USA
| | - Ke Sun
- Duke Quantum Center, Duke University, Durham, NC, USA
- Department of Physics, Duke University, Durham, NC, USA
| | - Jacob Whitlow
- Duke Quantum Center, Duke University, Durham, NC, USA
- Department of Electrical and Computer Engineering, Duke University, Durham, NC, USA
| | - Jesús Valdiviezo
- Kenneth S. Pitzer Theory Center, University of California, Berkeley, CA, USA
- Department of Chemistry, University of California, Berkeley, CA, USA
- Departamento de Ciencias, Sección Química, Pontificia Universidad Católica del Perú, Lima, Peru
| | - Zhendian Zhang
- Department of Chemistry, Duke University, Durham, NC, USA
| | - Peng Zhang
- Department of Chemistry, Duke University, Durham, NC, USA
| | - David N Beratan
- Department of Physics, Duke University, Durham, NC, USA.
- Department of Chemistry, Duke University, Durham, NC, USA.
- Department of Biochemistry, Duke University, Durham, NC, USA.
| | - Kenneth R Brown
- Duke Quantum Center, Duke University, Durham, NC, USA.
- Department of Physics, Duke University, Durham, NC, USA.
- Department of Chemistry, Duke University, Durham, NC, USA.
- Department of Electrical and Computer Engineering, Duke University, Durham, NC, USA.
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3
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Ferreira J, Jin T, Mannhart J, Giamarchi T, Filippone M. Transport and Nonreciprocity in Monitored Quantum Devices: An Exact Study. PHYSICAL REVIEW LETTERS 2024; 132:136301. [PMID: 38613271 DOI: 10.1103/physrevlett.132.136301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/28/2023] [Revised: 01/03/2024] [Accepted: 01/25/2024] [Indexed: 04/14/2024]
Abstract
We study noninteracting fermionic systems undergoing continuous monitoring and driven by biased reservoirs. Averaging over the measurement outcomes, we derive exact formulas for the particle and heat flows in the system. We show that these currents feature competing elastic and inelastic components, which depend nontrivially on the monitoring strength γ. We highlight that monitor-induced inelastic processes lead to nonreciprocal currents, allowing one to extract work from measurements without active feedback control. We illustrate our formalism with two distinct monitoring schemes providing measurement-induced power or cooling. Optimal performances are found for values of the monitoring strength γ, which are hard to address with perturbative approaches.
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Affiliation(s)
- João Ferreira
- Department of Quantum Matter Physics, École de Physique University of Geneva, 1211 Geneva, Switzerland
| | - Tony Jin
- Department of Quantum Matter Physics, École de Physique University of Geneva, 1211 Geneva, Switzerland
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, USA
| | - Jochen Mannhart
- Max Planck Institute for Solid State Research, Heisenbergstrasse 1, 70569 Stuttgart, Germany
| | - Thierry Giamarchi
- Department of Quantum Matter Physics, École de Physique University of Geneva, 1211 Geneva, Switzerland
| | - Michele Filippone
- IRIG-MEM-L_Sim, Université Grenoble Alpes, CEA, Grenoble INP, Grenoble 38000, France
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4
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Begg SE, Hanai R. Quantum Criticality in Open Quantum Spin Chains with Nonreciprocity. PHYSICAL REVIEW LETTERS 2024; 132:120401. [PMID: 38579202 DOI: 10.1103/physrevlett.132.120401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/21/2023] [Revised: 12/26/2023] [Accepted: 02/20/2024] [Indexed: 04/07/2024]
Abstract
We investigate the impact of nonreciprocity on universality and critical phenomena in open quantum interacting many-body systems. Nonreciprocal open quantum systems often have an exotic spectral sensitivity to boundary conditions, known as the Liouvillian skin effect (LSE). By considering an open quantum XXZ spin chain that exhibits LSE, we demonstrate the existence of a universal scaling regime that is not affected by the presence of the LSE. We resolve the critical exponents, which differ from those of free fermions, via tensor network methods and demonstrate that observables exhibit a universal scaling collapse, irrespective of the reciprocity. We find that the LSE only becomes relevant when a healing length scale ξ_{heal} at the system's edge (which is different from the localization length of the eigenstate of the Liouvillian) exceeds the system size, allowing edge properties to dominate the physics. We expect this result to be a generic feature of nonreciprocal models in the vicinity of a critical point. The driven-dissipative quantum criticality we observe has no classical analog and stems from the existence of multiple dark states.
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Affiliation(s)
- Samuel E Begg
- Asia Pacific Center for Theoretical Physics, Pohang 37673, Korea
| | - Ryo Hanai
- Asia Pacific Center for Theoretical Physics, Pohang 37673, Korea
- Center for Gravitational Physics and Quantum Information, Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan
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5
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Kawabata K, Sohal R, Ryu S. Lieb-Schultz-Mattis Theorem in Open Quantum Systems. PHYSICAL REVIEW LETTERS 2024; 132:070402. [PMID: 38427890 DOI: 10.1103/physrevlett.132.070402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/25/2023] [Revised: 10/26/2023] [Accepted: 01/18/2024] [Indexed: 03/03/2024]
Abstract
The Lieb-Schultz-Mattis (LSM) theorem provides a general constraint on quantum many-body systems and plays a significant role in the Haldane gap phenomena and topological phases of matter. Here, we extend the LSM theorem to open quantum systems and establish a general theorem that restricts the steady state and spectral gap of Liouvillians based solely on symmetry. Specifically, we demonstrate that the unique gapped steady state is prohibited when translation invariance and U(1) symmetry are simultaneously present for noninteger filling numbers. As an illustrative example, we find that no dissipative gap is open in the spin-1/2 dissipative Heisenberg model, while a dissipative gap can be open in the spin-1 counterpart-an analog of the Haldane gap phenomena in open quantum systems. Furthermore, we show that the LSM constraint manifests itself in a quantum anomaly of the dissipative form factor of Liouvillians. We also find the LSM constraints due to symmetry intrinsic to open quantum systems, such as Kubo-Martin-Schwinger symmetry. Our work leads to a unified understanding of phases and phenomena in open quantum systems.
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Affiliation(s)
- Kohei Kawabata
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
- Institute for Solid State Physics, University of Tokyo, Kashiwa, Chiba 277-8581, Japan
| | - Ramanjit Sohal
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - Shinsei Ryu
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
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6
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Catalano AG, Mattiotti F, Dubail J, Hagenmüller D, Prosen T, Franchini F, Pupillo G. Anomalous Diffusion in the Long-Range Haken-Strobl-Reineker Model. PHYSICAL REVIEW LETTERS 2023; 131:053401. [PMID: 37595217 DOI: 10.1103/physrevlett.131.053401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/15/2022] [Accepted: 07/17/2023] [Indexed: 08/20/2023]
Abstract
We analyze the propagation of excitons in a d-dimensional lattice with power-law hopping ∝1/r^{α} in the presence of dephasing, described by a generalized Haken-Strobl-Reineker model. We show that in the strong dephasing (quantum Zeno) regime the dynamics is described by a classical master equation for an exclusion process with long jumps. In this limit, we analytically compute the spatial distribution, whose shape changes at a critical value of the decay exponent α_{cr}=(d+2)/2. The exciton always diffuses anomalously: a superdiffusive motion is associated to a Lévy stable distribution with long-range algebraic tails for α≤α_{cr}, while for α>α_{cr} the distribution corresponds to a surprising mixed Gaussian profile with long-range algebraic tails, leading to the coexistence of short-range diffusion and long-range Lévy flights. In the many-exciton case, we demonstrate that, starting from a domain-wall exciton profile, algebraic tails appear in the distributions for any α, which affects thermalization: the longer the hopping range, the faster equilibrium is reached. Our results are directly relevant to experiments with cold trapped ions, Rydberg atoms, and supramolecular dye aggregates. They provide a way to realize an exclusion process with long jumps experimentally.
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Affiliation(s)
- A G Catalano
- University of Strasbourg and CNRS, CESQ and ISIS (UMR 7006), aQCess, 67000 Strasbourg, France
- Institut Ruđer Bošković, Bijenička cesta 54, 10000 Zagreb, Croatia
| | - F Mattiotti
- University of Strasbourg and CNRS, CESQ and ISIS (UMR 7006), aQCess, 67000 Strasbourg, France
| | - J Dubail
- University of Strasbourg and CNRS, CESQ and ISIS (UMR 7006), aQCess, 67000 Strasbourg, France
- Université de Lorraine and CNRS, LPCT (UMR 7019), 54000 Nancy, France
| | - D Hagenmüller
- University of Strasbourg and CNRS, CESQ and ISIS (UMR 7006), aQCess, 67000 Strasbourg, France
| | - T Prosen
- Faculty for Mathematics and Physics, University of Ljubljana, Jadranska ulica 19, 1000 Ljubljana, Slovenia
| | - F Franchini
- Institut Ruđer Bošković, Bijenička cesta 54, 10000 Zagreb, Croatia
| | - G Pupillo
- University of Strasbourg and CNRS, CESQ and ISIS (UMR 7006), aQCess, 67000 Strasbourg, France
- Institut Universitaire de France (IUF), 75000 Paris, France
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7
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Downing CA, Vidiella-Barranco A. Parametrically driving a quantum oscillator into exceptionality. Sci Rep 2023; 13:11004. [PMID: 37419917 PMCID: PMC10329046 DOI: 10.1038/s41598-023-37964-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/06/2023] [Accepted: 06/30/2023] [Indexed: 07/09/2023] Open
Abstract
The mathematical objects employed in physical theories do not always behave well. Einstein's theory of space and time allows for spacetime singularities and Van Hove singularities arise in condensed matter physics, while intensity, phase and polarization singularities pervade wave physics. Within dissipative systems governed by matrices, singularities occur at the exceptional points in parameter space whereby some eigenvalues and eigenvectors coalesce simultaneously. However, the nature of exceptional points arising in quantum systems described within an open quantum systems approach has been much less studied. Here we consider a quantum oscillator driven parametrically and subject to loss. This squeezed system exhibits an exceptional point in the dynamical equations describing its first and second moments, which acts as a borderland between two phases with distinctive physical consequences. In particular, we discuss how the populations, correlations, squeezed quadratures and optical spectra crucially depend on being above or below the exceptional point. We also remark upon the presence of a dissipative phase transition at a critical point, which is associated with the closing of the Liouvillian gap. Our results invite the experimental probing of quantum resonators under two-photon driving, and perhaps a reappraisal of exceptional and critical points within dissipative quantum systems more generally.
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Affiliation(s)
- C A Downing
- Department of Physics and Astronomy, University of Exeter, Exeter, EX4 4QL, UK.
| | - A Vidiella-Barranco
- Gleb Wataghin Institute of Physics, University of Campinas - UNICAMP, Campinas, SP, 13083-859, Brazil
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8
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Mori T, Shirai T. Symmetrized Liouvillian Gap in Markovian Open Quantum Systems. PHYSICAL REVIEW LETTERS 2023; 130:230404. [PMID: 37354419 DOI: 10.1103/physrevlett.130.230404] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/19/2022] [Revised: 04/24/2023] [Accepted: 05/23/2023] [Indexed: 06/26/2023]
Abstract
Markovian open quantum systems display complicated relaxation dynamics. The spectral gap of the Liouvillian characterizes the asymptotic decay rate toward the steady state, but it does not necessarily give a correct estimate of the relaxation time because the crossover time to the asymptotic regime may be too long. We here give a rigorous upper bound on the transient decay of autocorrelation functions in the steady state by introducing the symmetrized Liouvillian gap. The standard Liouvillian gap and the symmetrized one are identical in an equilibrium situation but differ from each other in the absence of the detailed balance condition. It is numerically shown that the symmetrized Liouvillian gap always gives a correct upper bound on the decay of the autocorrelation function, but the standard Liouvillian gap does not.
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Affiliation(s)
- Takashi Mori
- RIKEN Center for Emergent Matter Science (CEMS), Wako 351-0198, Japan
| | - Tatsuhiko Shirai
- Department of Computer Science and Communications Engineering, Waseda University, Tokyo 169-8555, Japan
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9
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Shu Y, Truhlar DG. Decoherence and Its Role in Electronically Nonadiabatic Dynamics. J Chem Theory Comput 2023; 19:380-395. [PMID: 36622843 PMCID: PMC9878713 DOI: 10.1021/acs.jctc.2c00988] [Citation(s) in RCA: 14] [Impact Index Per Article: 14.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/07/2022] [Indexed: 01/10/2023]
Abstract
Decoherence is the tendency of a time-evolved reduced density matrix for a subsystem to assume a form corresponding to a statistical ensemble of states rather than a coherent combination of pure-state wave functions. When a molecular process involves changes in the electronic state and the coordinates of the nuclei, as in ultraviolet or visible light photochemistry or electronically inelastic collisions, the reduced density matrix of the electronic subsystem suffers decoherence, due to its interaction with the nuclear subsystem. We present the background necessary to conceptualize this decoherence; in particular, we discuss the density matrix description of pure states and mixed states, and we discuss pointer states and decoherence time. We then discuss how decoherence is treated in the coherent switching with decay of mixing algorithm and the trajectory surface hopping method for semiclassical calculations of electronically nonadiabatic processes.
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Affiliation(s)
- Yinan Shu
- Department of Chemistry,
Chemical Theory Center, and Minnesota Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota55455-0431, United States
| | - Donald G. Truhlar
- Department of Chemistry,
Chemical Theory Center, and Minnesota Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota55455-0431, United States
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10
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Wellnitz D, Preisser G, Alba V, Dubail J, Schachenmayer J. Rise and Fall, and Slow Rise Again, of Operator Entanglement under Dephasing. PHYSICAL REVIEW LETTERS 2022; 129:170401. [PMID: 36332243 DOI: 10.1103/physrevlett.129.170401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/17/2022] [Accepted: 09/20/2022] [Indexed: 06/16/2023]
Abstract
The operator space entanglement entropy, or simply "operator entanglement" (OE), is an indicator of the complexity of quantum operators and of their approximability by matrix product operators (MPOs). We study the OE of the density matrix of 1D many-body models undergoing dissipative evolution. It is expected that, after an initial linear growth reminiscent of unitary quench dynamics, the OE should be suppressed by dissipative processes as the system evolves to a simple stationary state. Surprisingly, we find that this scenario breaks down for one of the most fundamental dissipative mechanisms: dephasing. Under dephasing, after the initial "rise and fall," the OE can rise again, increasing logarithmically at long times. Using a combination of MPO simulations for chains of infinite length and analytical arguments valid for strong dephasing, we demonstrate that this growth is inherent to a U(1) conservation law. We argue that in an XXZ spin model and a Bose-Hubbard model the OE grows universally as 1/4log_{2}t at long times and as 1/2log_{2}t for a Fermi-Hubbard model. We trace this behavior back to anomalous classical diffusion processes.
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Affiliation(s)
- D Wellnitz
- ISIS (UMR 7006) and CESQ, CNRS and Université de Strasbourg, 67000 Strasbourg, France
- IPCMS (UMR 7504), CNRS, 67000 Strasbourg, France
| | - G Preisser
- ISIS (UMR 7006) and CESQ, CNRS and Université de Strasbourg, 67000 Strasbourg, France
| | - V Alba
- Dipartimento di Fisica, Università di Pisa, and INFN Sezione di Pisa, Largo Bruno Pontecorvo 3, 56127 Pisa, Italy
| | - J Dubail
- ISIS (UMR 7006) and CESQ, CNRS and Université de Strasbourg, 67000 Strasbourg, France
- Université de Lorraine, CNRS, LPCT, F-54000 Nancy, France
| | - J Schachenmayer
- ISIS (UMR 7006) and CESQ, CNRS and Université de Strasbourg, 67000 Strasbourg, France
- IPCMS (UMR 7504), CNRS, 67000 Strasbourg, France
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11
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Gillard G, Clarke E, Chekhovich EA. Harnessing many-body spin environment for long coherence storage and high-fidelity single-shot qubit readout. Nat Commun 2022; 13:4048. [PMID: 35831368 PMCID: PMC9279416 DOI: 10.1038/s41467-022-31618-4] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/29/2022] [Accepted: 06/23/2022] [Indexed: 11/09/2022] Open
Abstract
There is a growing interest in hybrid solid-state quantum systems where nuclear spins, interfaced to the electron spin qubit, are used as quantum memory or qubit register. These approaches require long nuclear spin coherence, which until now seemed impossible owing to the disruptive effect of the electron spin. Here we study InGaAs semiconductor quantum dots, demonstrating millisecond-long collective nuclear spin coherence even under inhomogeneous coupling to the electron central spin. We show that the underlying decoherence mechanism is spectral diffusion induced by a fluctuating electron spin. These results provide new understanding of the many-body coherence in central spin systems, required for development of electron-nuclear spin qubits. As a demonstration, we implement a conditional gate that encodes electron spin state onto collective nuclear spin coherence, and use it for a single-shot readout of the electron spin qubit with >99% fidelity.
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Affiliation(s)
- George Gillard
- Department of Physics and Astronomy, University of Sheffield, Sheffield, S3 7RH, UK.
| | - Edmund Clarke
- Department of Electronic and Electrical Engineering, University of Sheffield, Sheffield, S1 3JD, UK
| | - Evgeny A Chekhovich
- Department of Physics and Astronomy, University of Sheffield, Sheffield, S3 7RH, UK.
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12
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Xue WT, Hu YM, Song F, Wang Z. Non-Hermitian Edge Burst. PHYSICAL REVIEW LETTERS 2022; 128:120401. [PMID: 35394323 DOI: 10.1103/physrevlett.128.120401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/04/2021] [Revised: 02/12/2022] [Accepted: 02/25/2022] [Indexed: 06/14/2023]
Abstract
We unveil an unexpected non-Hermitian phenomenon, dubbed edge burst, in non-Hermitian quantum dynamics. Specifically, in a class of non-Hermitian quantum walk in periodic lattices with open boundary condition, an exceptionally large portion of loss occurs at the system boundary. The physical origin of this edge burst is found to be an interplay between two unique non-Hermitian phenomena: non-Hermitian skin effect and imaginary gap closing. Furthermore, we establish a universal bulk-edge scaling relation underlying the non-Hermitian edge burst. Our predictions are experimentally accessible in various non-Hermitian systems including quantum-optical and cold-atom platforms.
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Affiliation(s)
- Wen-Tan Xue
- Institute for Advanced Study, Tsinghua University, Beijing 100084, China
| | - Yu-Min Hu
- Institute for Advanced Study, Tsinghua University, Beijing 100084, China
| | - Fei Song
- Institute for Advanced Study, Tsinghua University, Beijing 100084, China
| | - Zhong Wang
- Institute for Advanced Study, Tsinghua University, Beijing 100084, China
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13
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Cai Z. 1/3 Power-Law Universality Class out of Stochastic Driving in Interacting Systems. PHYSICAL REVIEW LETTERS 2022; 128:050601. [PMID: 35179931 DOI: 10.1103/physrevlett.128.050601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/11/2021] [Revised: 11/25/2021] [Accepted: 01/18/2022] [Indexed: 06/14/2023]
Abstract
In this Letter, we study the mean-field dynamics of a general class of many-body systems with stochastically fluctuating interactions. Our findings reveal a universal algebraic decay of the order parameter m(t)∼t^{-χ} with an exponent χ=1/3 that is independent of most system details including the strength of the stochastic driving, the energy spectrum of the undriven systems, the initial states, and even the driving protocols. It is shown that such a dynamical universality class can be understood as a consequence of a diffusive process with a time-dependent diffusion coefficient which is determined self-consistently during the evolution. The finite-size effect, as well as the relevance of our results with current experiments in high-finesse cavity QED systems are also discussed.
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Affiliation(s)
- Zi Cai
- Wilczek Quantum Center and Key Laboratory of Artificial Structures and Quantum Control, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China and Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
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14
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Haga T, Nakagawa M, Hamazaki R, Ueda M. Liouvillian Skin Effect: Slowing Down of Relaxation Processes without Gap Closing. PHYSICAL REVIEW LETTERS 2021; 127:070402. [PMID: 34459629 DOI: 10.1103/physrevlett.127.070402] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/07/2020] [Accepted: 07/21/2021] [Indexed: 06/13/2023]
Abstract
It is highly nontrivial to what extent we can deduce the relaxation behavior of a quantum dissipative system from the spectral gap of the Liouvillian that governs the time evolution of the density matrix. We investigate the relaxation processes of a quantum dissipative system that exhibits the Liouvillian skin effect, which means that the eigenmodes of the Liouvillian are localized exponentially close to the boundary of the system, and find that the timescale for the system to reach a steady state depends not only on the Liouvillian gap Δ, but also on the localization length ξ of the eigenmodes. In particular, we show that the longest relaxation time τ that is maximized over initial states and local observables is given by τ∼Δ^{-1}(1+L/ξ) with L being the system size. This implies that the longest relaxation time can diverge for L→∞ without gap closing.
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Affiliation(s)
- Taiki Haga
- Department of Physics and Electronics, Osaka Prefecture University, Sakai-shi, Osaka 599-8531, Japan
- Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
| | - Masaya Nakagawa
- Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
| | - Ryusuke Hamazaki
- Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
- Nonequilibrium Quantum Statistical Mechanics RIKEN Hakubi Research Team, RIKEN Cluster for Pioneering Research (CPR), RIKEN iTHEMS, Wako, Saitama 351-0198, Japan
| | - Masahito Ueda
- Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
- RIKEN Center for Emergent Matter Science (CEMS), Wako, Saitama 351-0198, Japan
- Institute for Physics of Intelligence, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
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15
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Yuan D, Wang HR, Wang Z, Deng DL. Solving the Liouvillian Gap with Artificial Neural Networks. PHYSICAL REVIEW LETTERS 2021; 126:160401. [PMID: 33961454 DOI: 10.1103/physrevlett.126.160401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/03/2020] [Accepted: 03/30/2021] [Indexed: 06/12/2023]
Abstract
We propose a machine-learning inspired variational method to obtain the Liouvillian gap, which plays a crucial role in characterizing the relaxation time and dissipative phase transitions of open quantum systems. By using "spin bi-base mapping," we map the density matrix to a pure restricted-Boltzmann-machine (RBM) state and transform the Liouvillian superoperator to a rank-two non-Hermitian operator. The Liouvillian gap can be obtained by a variational real-time evolution algorithm under this non-Hermitian operator. We apply our method to the dissipative Heisenberg model in both one and two dimensions. For the isotropic case, we find that the Liouvillian gap can be analytically obtained and in one dimension even the whole Liouvillian spectrum can be exactly solved using the Bethe ansatz method. By comparing our numerical results with their analytical counterparts, we show that the Liouvillian gap could be accessed by the RBM approach efficiently to a desirable accuracy, regardless of the dimensionality and entanglement properties.
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Affiliation(s)
- Dong Yuan
- Center for Quantum Information, IIIS, Tsinghua University, Beijing 100084, People's Republic of China
- Department of Physics, Tsinghua University, Beijing 100084, People's Republic of China
| | - He-Ran Wang
- Department of Physics, Tsinghua University, Beijing 100084, People's Republic of China
- Institute for Advanced Study, Tsinghua University, Beijing 100084, People's Republic of China
| | - Zhong Wang
- Institute for Advanced Study, Tsinghua University, Beijing 100084, People's Republic of China
| | - Dong-Ling Deng
- Center for Quantum Information, IIIS, Tsinghua University, Beijing 100084, People's Republic of China
- Shanghai Qi Zhi Institute, 41st Floor, AI Tower, No. 701 Yunjin Road, Xuhui District, Shanghai 200232, China
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16
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Nakagawa M, Kawakami N, Ueda M. Exact Liouvillian Spectrum of a One-Dimensional Dissipative Hubbard Model. PHYSICAL REVIEW LETTERS 2021; 126:110404. [PMID: 33798340 DOI: 10.1103/physrevlett.126.110404] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/31/2020] [Accepted: 02/12/2021] [Indexed: 06/12/2023]
Abstract
A one-dimensional dissipative Hubbard model with two-body loss is shown to be exactly solvable. We obtain an exact eigenspectrum of a Liouvillian superoperator by employing a non-Hermitian extension of the Bethe-ansatz method. We find steady states, the Liouvillian gap, and an exceptional point that is accompanied by the divergence of the correlation length. A dissipative version of spin-charge separation induced by the quantum Zeno effect is also demonstrated. Our result presents a new class of exactly solvable Liouvillians of open quantum many-body systems, which can be tested with ultracold atoms subject to inelastic collisions.
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Affiliation(s)
- Masaya Nakagawa
- Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
| | - Norio Kawakami
- Department of Physics, Kyoto University, Kyoto 606-8502, Japan
| | - Masahito Ueda
- Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
- RIKEN Center for Emergent Matter Science (CEMS), Wako, Saitama 351-0198, Japan
- Institute for Physics of Intelligence, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
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17
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Bácsi Á, Moca CP, Zaránd G, Dóra B. Vaporization Dynamics of a Dissipative Quantum Liquid. PHYSICAL REVIEW LETTERS 2020; 125:266803. [PMID: 33449736 DOI: 10.1103/physrevlett.125.266803] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/03/2020] [Accepted: 12/07/2020] [Indexed: 06/12/2023]
Abstract
We investigate the stability of a Luttinger liquid, upon suddenly coupling it to a dissipative environment. Within the Lindblad equation, the environment couples to local currents and heats the quantum liquid up to infinite temperatures. The single particle density matrix reveals the fractionalization of fermionic excitations in the spatial correlations by retaining the initial noninteger power law exponents, accompanied by an exponential decay in time with an interaction dependent rate. The spectrum of the time evolved density matrix is gapped, which collapses gradually as -ln(t). The von Neumann entropy crosses over from the early time -tln(t) behavior to ln(t) growth for late times. The early time dynamics is captured numerically by performing simulations on spinless interacting fermions, using several numerically exact methods. Our results could be tested experimentally in bosonic Luttinger liquids.
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Affiliation(s)
- Ádám Bácsi
- MTA-BME Lendület Topology and Correlation Research Group, Budapest University of Technology and Economics, 1521 Budapest, Hungary
- Department of Mathematics and Computational Sciences, Széchenyi István University, 9026 Győr, Hungary
| | - Cătălin Paşcu Moca
- MTA-BME Quantum Dynamics and Correlations Research Group, Budapest University of Technology and Economics, 1521 Budapest, Hungary
- Department of Physics, University of Oradea, 410087 Oradea, Romania
| | - Gergely Zaránd
- MTA-BME Quantum Dynamics and Correlations Research Group, Budapest University of Technology and Economics, 1521 Budapest, Hungary
- BME-MTA Exotic Quantum Phases Research Group, Department of Theoretical Physics, Budapest University of Technology and Economics, 1521 Budapest, Hungary
| | - Balázs Dóra
- MTA-BME Lendület Topology and Correlation Research Group, Budapest University of Technology and Economics, 1521 Budapest, Hungary
- Department of Theoretical Physics, Budapest University of Technology and Economics, 1521 Budapest, Hungary
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18
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Finsterhölzl R, Katzer M, Knorr A, Carmele A. Using Matrix-Product States for Open Quantum Many-Body Systems: Efficient Algorithms for Markovian and Non-Markovian Time-Evolution. ENTROPY (BASEL, SWITZERLAND) 2020; 22:E984. [PMID: 33286753 PMCID: PMC7597300 DOI: 10.3390/e22090984] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 07/31/2020] [Revised: 08/28/2020] [Accepted: 09/01/2020] [Indexed: 11/20/2022]
Abstract
This paper presents an efficient algorithm for the time evolution of open quantum many-body systems using matrix-product states (MPS) proposing a convenient structure of the MPS-architecture, which exploits the initial state of system and reservoir. By doing so, numerically expensive re-ordering protocols are circumvented. It is applicable to systems with a Markovian type of interaction, where only the present state of the reservoir needs to be taken into account. Its adaption to a non-Markovian type of interaction between the many-body system and the reservoir is demonstrated, where the information backflow from the reservoir needs to be included in the computation. Also, the derivation of the basis in the quantum stochastic Schrödinger picture is shown. As a paradigmatic model, the Heisenberg spin chain with nearest-neighbor interaction is used. It is demonstrated that the algorithm allows for the access of large systems sizes. As an example for a non-Markovian type of interaction, the generation of highly unusual steady states in the many-body system with coherent feedback control is demonstrated for a chain length of N=30.
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Affiliation(s)
- Regina Finsterhölzl
- Institut für Theoretische Physik, Nichtlineare Optik und Quantenelektronik, Hardenbergstraße 36, 10623 Berlin, Germany; (M.K.); (A.K.); (A.C.)
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19
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20
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Johnson PM. The longer timescale excited state dynamics of isolated benzene. J Chem Phys 2020; 152:134307. [PMID: 32268755 DOI: 10.1063/5.0003908] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The excited state photodynamics of isolated benzene have been studied in the nanosecond range by two-step photoionization through various vibrations of the lowest singlet state, with imaging photoelectron spectroscopy detection. Photoelectron spectra are measured as a function of pump-probe delay time, and their time evolution is successfully compared to a biexponential decay function without regard to a particular kinetic model. The only reasonable kinetic model with only two exponentials is the one that involves an intersystem crossing from S1 to T1, although that model has previously been called into question by high-resolution studies that failed to find any singlet-triplet perturbations in Zeeman studies of the S1 spectrum. That contradiction remains unresolved.
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Affiliation(s)
- Philip M Johnson
- Department of Chemistry, Stony Brook University, Stony Brook, New York 11794-3400, USA
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21
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Ren J, Li Q, Li W, Cai Z, Wang X. Noise-Driven Universal Dynamics towards an Infinite Temperature State. PHYSICAL REVIEW LETTERS 2020; 124:130602. [PMID: 32302181 DOI: 10.1103/physrevlett.124.130602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/06/2019] [Revised: 01/17/2020] [Accepted: 03/09/2020] [Indexed: 06/11/2023]
Abstract
Dynamical universality is the observation that the dynamical properties of different systems might exhibit universal behavior that are independent of the system details. In this Letter, we study the longtime dynamics of a one-dimensional noisy quantum magnetic model, and find that even though the system is inevitably driven to an infinite temperature state, the relaxation dynamics towards such a featureless state can be highly nontrivial and universal. The effect of various mode-coupling mechanisms (external potential, disorder, interaction, and the interplay between them) as well as the conservation law on the longtime dynamics of the systems have been studied, and their relevance with current ultracold atomic experiments has been discussed.
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Affiliation(s)
- Jie Ren
- Department of Physics and Jiangsu Laboratory of Advanced Functional Material, Changshu Institute of Technology, Changshu 215500, China
- Key Laboratory of Artificial Structures and Quantum Control, Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, People's Republic of China
| | - Qiaoyi Li
- School of Physics, Key Laboratory of Micro-Nano Measurement-Manipulation and Physics (Ministry of Education), Beihang University, Beijing 100191, China
| | - Wei Li
- School of Physics, Key Laboratory of Micro-Nano Measurement-Manipulation and Physics (Ministry of Education), Beihang University, Beijing 100191, China
| | - Zi Cai
- Key Laboratory of Artificial Structures and Quantum Control, Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, People's Republic of China
- Wilczek Quantum Center, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Xiaoqun Wang
- Key Laboratory of Artificial Structures and Quantum Control, Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, People's Republic of China
- Beijing Computational Science Research Center, Beijing 100193, China
- Shenyang National Laboratory for Materials Science and T. D. Lee Institute, Shanghai Jiao Tong University, Shanghai 200240, China
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22
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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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23
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Can T, Oganesyan V, Orgad D, Gopalakrishnan S. Spectral Gaps and Midgap States in Random Quantum Master Equations. PHYSICAL REVIEW LETTERS 2019; 123:234103. [PMID: 31868445 DOI: 10.1103/physrevlett.123.234103] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/01/2019] [Indexed: 06/10/2023]
Abstract
We discuss the decay rates of chaotic quantum systems coupled to noise. We model both the Hamiltonian and the system-noise coupling by random N×N Hermitian matrices, and study the spectral properties of the resulting Liouvillian superoperator. We consider various random-matrix ensembles, and find that for all of them the asymptotic decay rate remains nonzero in the thermodynamic limit; i.e., the spectrum of the superoperator is gapped as N→∞. For finite N, the probability of finding a very small gap vanishes as P(Δ)∼Δ^{cN}, where c is insensitive to the dissipation strength. A sharp spectral transition takes place as the dissipation strength is increased: for dissipation beyond a critical strength, the slowest-decaying eigenvalues of the Liouvillian correspond to isolated "midgap" states. We give evidence that midgap states exist also for nonrandom system-noise coupling and discuss some experimental implications of the above results.
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Affiliation(s)
- Tankut Can
- Initiative for the Theoretical Sciences, The Graduate Center, CUNY, New York, New York 10012, USA
| | - Vadim Oganesyan
- Initiative for the Theoretical Sciences, The Graduate Center, CUNY, New York, New York 10012, USA
- Department of Physics and Astronomy, College of Staten Island, Staten Island, New York 10314, USA
| | - Dror Orgad
- Racah Institute of Physics, The Hebrew University, Jerusalem 91904, Israel
| | - Sarang Gopalakrishnan
- Initiative for the Theoretical Sciences, The Graduate Center, CUNY, New York, New York 10012, USA
- Department of Physics and Astronomy, College of Staten Island, Staten Island, New York 10314, USA
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24
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Berdanier W, Marino J, Altman E. Universal Dynamics of Stochastically Driven Quantum Impurities. PHYSICAL REVIEW LETTERS 2019; 123:230604. [PMID: 31868487 DOI: 10.1103/physrevlett.123.230604] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/25/2019] [Indexed: 06/10/2023]
Abstract
We show that the dynamics of a quantum impurity subject to a stochastic drive on one side and coupled to a quantum critical system on the other display a universal behavior inherited from the quantum critical scaling. Using boundary conformal field theory, we formulate a generic ansatz for the dynamical scaling form of the typical Loschmidt echo and corroborate it with exact numerical calculations in the case of a spin impurity driven by shot noise in a quantum Ising chain. We find that due to rare events the dynamics of the mean echo can follow very different dynamical scaling than the typical echo for certain classes of drives. Our results are insensitive to irrelevant perturbations of the bulk critical model and apply to all the microscopic models in the same universality class.
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Affiliation(s)
- William Berdanier
- Department of Physics, University of California, Berkeley, California 94720, USA
- Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106-4030, USA
| | - Jamir Marino
- Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106-4030, USA
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
- Department of Quantum Matter Physics, University of Geneva, 1211, Geneva, Switzerland
| | - Ehud Altman
- Department of Physics, University of California, Berkeley, California 94720, USA
- Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106-4030, USA
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25
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Song F, Yao S, Wang Z. Non-Hermitian Skin Effect and Chiral Damping in Open Quantum Systems. PHYSICAL REVIEW LETTERS 2019; 123:170401. [PMID: 31702238 DOI: 10.1103/physrevlett.123.170401] [Citation(s) in RCA: 57] [Impact Index Per Article: 11.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/24/2019] [Indexed: 06/10/2023]
Abstract
One of the unique features of non-Hermitian Hamiltonians is the non-Hermitian skin effect, namely, that the eigenstates are exponentially localized at the boundary of the system. For open quantum systems, a short-time evolution can often be well described by the effective non-Hermitian Hamiltonians, while long-time dynamics calls for the Lindblad master equations, in which the Liouvillian superoperators generate time evolution. In this Letter, we find that Liouvillian superoperators can exhibit the non-Hermitian skin effect, and uncover its unexpected physical consequences. It is shown that the non-Hermitian skin effect dramatically shapes the long-time dynamics, such that the damping in a class of open quantum systems is algebraic under periodic boundary conditions but exponential under open boundary conditions. Moreover, the non-Hermitian skin effect and non-Bloch bands cause a chiral damping with a sharp wave front. These phenomena are beyond the effective non-Hermitian Hamiltonians; instead, they belong to the non-Hermitian physics of full-fledged open quantum dynamics.
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Affiliation(s)
- Fei Song
- Institute for Advanced Study, Tsinghua University, Beijing 100084, China
| | - Shunyu Yao
- Institute for Advanced Study, Tsinghua University, Beijing 100084, China
| | - Zhong Wang
- Institute for Advanced Study, Tsinghua University, Beijing 100084, China
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26
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Gutiérrez R, Garrahan JP, Lesanovsky I. Physical swap dynamics, shortcuts to relaxation, and entropy production in dissipative Rydberg gases. Phys Rev E 2019; 100:012110. [PMID: 31499791 DOI: 10.1103/physreve.100.012110] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/03/2019] [Indexed: 11/07/2022]
Abstract
Dense Rydberg gases are out-of-equilibrium systems where strong density-density interactions give rise to effective kinetic constraints. They cause dynamic arrest associated with highly constrained many-body configurations, leading to slow relaxation and glassy behavior. Multicomponent Rydberg gases feature additional long-range interactions such as excitation exchange. These are analogous to particle swaps used to artificially accelerate relaxation in simulations of atomistic models of classical glass formers. In Rydberg gases, however, swaps are real physical processes, which provide dynamical shortcuts to relaxation. They permit the accelerated approach to stationarity in experiment and at the same time have an impact on the nonequilibrium stationary state. In particular, their interplay with radiative decay processes amplifies irreversibility of the dynamics, an effect which we quantify via the entropy production at stationarity. Our work highlights an intriguing analogy between real dynamical processes in Rydberg gases and artificial dynamics underlying advanced Monte Carlo methods. Moreover, it delivers a quantitative characterization of the dramatic effect swaps have on the structure and dynamics of their stationary state.
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Affiliation(s)
- Ricardo Gutiérrez
- Complex Systems Group & GISC, Universidad Rey Juan Carlos, 28933 Móstoles, Madrid, Spain
| | - 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
| | - 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
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27
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Carollo A, Spagnolo B, Valenti D. Uhlmann curvature in dissipative phase transitions. Sci Rep 2018; 8:9852. [PMID: 29959332 PMCID: PMC6026214 DOI: 10.1038/s41598-018-27362-9] [Citation(s) in RCA: 92] [Impact Index Per Article: 15.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/15/2018] [Accepted: 05/10/2018] [Indexed: 11/09/2022] Open
Abstract
A novel approach based on the Uhlmann curvature is introduced for the investigation of non-equilibrium steady-state quantum phase transitions (NESS-QPTs). Equilibrium phase transitions fall invariably into two markedly non-overlapping categories: classical phase transitions and quantum phase transitions. NESS-QPTs offer a unique arena where such a distinction fades off. We propose a method to reveal and quantitatively assess the quantum character of such critical phenomena. We apply this tool to a paradigmatic class of lattice fermion systems with local reservoirs, characterised by Gaussian non-equilibrium steady states. The relations between the behaviour of the Uhlmann curvature, the divergence of the correlation length, the character of the criticality and the dissipative gap are demonstrated. We argue that this tool can shade light upon the nature of non equilibrium steady state criticality in particular with regard to the role played by quantum vs classical fluctuations.
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Affiliation(s)
- Angelo Carollo
- Department of Physics and Chemistry, Group of Interdisciplinary Theoretical Physics, University of Palermo, Viale delle Scienze, Ed. 18, I-90128, Palermo, Italy. .,Radiophysics Department, Lobachevsky State University of Nizhni Novgorod, 23 Gagarin Avenue, Nizhni, Novgorod, 603950, Russia.
| | - Bernardo Spagnolo
- Department of Physics and Chemistry, Group of Interdisciplinary Theoretical Physics, University of Palermo, Viale delle Scienze, Ed. 18, I-90128, Palermo, Italy.,Radiophysics Department, Lobachevsky State University of Nizhni Novgorod, 23 Gagarin Avenue, Nizhni, Novgorod, 603950, Russia.,Istituto Nazionale di Fisica Nucleare, Sezione di Catania, Via S. Sofia 64, I-90123, Catania, Italy
| | - Davide Valenti
- Department of Physics and Chemistry, Group of Interdisciplinary Theoretical Physics, University of Palermo, Viale delle Scienze, Ed. 18, I-90128, Palermo, Italy.,Istituto di Biomedicina ed Immunologia Molecolare (IBIM) "Alberto Monroy", CNR, Via Ugo La Malfa 153, I-90146, Palermo, Italy
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28
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Symmetric Logarithmic Derivative of Fermionic Gaussian States. ENTROPY 2018; 20:e20070485. [PMID: 33265575 PMCID: PMC7513002 DOI: 10.3390/e20070485] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Subscribe] [Scholar Register] [Received: 05/21/2018] [Revised: 06/16/2018] [Accepted: 06/16/2018] [Indexed: 01/24/2023]
Abstract
In this article, we derive a closed form expression for the symmetric logarithmic derivative of Fermionic Gaussian states. This provides a direct way of computing the quantum Fisher Information for Fermionic Gaussian states. Applications range from quantum Metrology with thermal states to non-equilibrium steady states with Fermionic many-body systems.
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29
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Mathisen T, Larson J. Liouvillian of the Open STIRAP Problem. ENTROPY 2018; 20:e20010020. [PMID: 33265111 PMCID: PMC7512197 DOI: 10.3390/e20010020] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 10/25/2017] [Revised: 12/11/2017] [Accepted: 12/20/2017] [Indexed: 11/16/2022]
Abstract
With the corresponding Liouvillian as a starting point, we demonstrate two seemingly new phenomena of the STIRAP problem when subjected to irreversible losses. It is argued that both of these can be understood from an underlying Zeno effect, and in particular both can be viewed as if the environment assists the STIRAP population transfer. The first of these is found for relative strong dephasing, and, in the language of the Liouvillian, it is explained from the explicit form of the matrix generating the time-evolution; the coherence terms of the state decay off, which prohibits further population transfer. For pure dissipation, another Zeno effect is found, where the presence of a non-zero Liouvillian gap protects the system’s (adiabatic) state from non-adiabatic excitations. In contrast to full Zeno freezing of the evolution, which is often found in many problems without explicit time-dependence, here, the freezing takes place in the adiabatic basis such that the system still evolves but adiabatically.
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30
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Affiliation(s)
- Haibo Ma
- School of Chemistry and Chemical Engineering, Nanjing University, Nanjing, China
| | - Zhen Luo
- School of Chemistry and Chemical Engineering, Nanjing University, Nanjing, China
| | - Yao Yao
- Department of Physics, South China University of Technology, Guangzhou, China
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31
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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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32
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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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33
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Zhang G, Novais E, Baranger HU. Rescuing a Quantum Phase Transition with Quantum Noise. PHYSICAL REVIEW LETTERS 2017; 118:050402. [PMID: 28211744 DOI: 10.1103/physrevlett.118.050402] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/04/2016] [Indexed: 06/06/2023]
Abstract
We show that placing a quantum system in contact with an environment can enhance non-Fermi-liquid correlations, rather than destroy quantum effects, as is typical. The system consists of two quantum dots in series with two leads; the highly resistive leads couple charge flow through the dots to the electromagnetic environment, the source of quantum noise. While the charge transport inhibits a quantum phase transition, the quantum noise reduces charge transport and restores the transition. We find a non-Fermi-liquid intermediate fixed point for all strengths of the noise. For strong noise, it is similar to the intermediate fixed point of the two-impurity Kondo model.
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Affiliation(s)
- Gu Zhang
- Department of Physics, Duke University, P.O. Box 90305, Durham, North Carolina 27708, USA
| | - E Novais
- Centro de Ciíncias Naturais e Humanas, Universidade Federal do ABC, Santo Andrè, São Paulo 09210-580, Brazil
| | - Harold U Baranger
- Department of Physics, Duke University, P.O. Box 90305, Durham, North Carolina 27708, USA
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Everest B, Marcuzzi M, Garrahan JP, Lesanovsky I. Emergent kinetic constraints, ergodicity breaking, and cooperative dynamics in noisy quantum systems. Phys Rev E 2016; 94:052108. [PMID: 27967152 DOI: 10.1103/physreve.94.052108] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/07/2016] [Indexed: 06/06/2023]
Abstract
Kinetically constrained spin systems play an important role in understanding key properties of the dynamics of slowly relaxing materials, such as glasses. Recent experimental studies have revealed that manifest kinetic constraints govern the evolution of strongly interacting gases of highly excited atoms in a noisy environment. Motivated by this development we explore which types of kinetically constrained dynamics can generally emerge in quantum spin systems subject to strong noise and show how, in this framework, constraints are accompanied by conservation laws. We discuss an experimentally realizable case of a lattice gas, where the interplay between those and the geometry of the lattice leads to collective behavior and time-scale separation even at infinite temperature. This is in contrast to models of glass-forming substances which typically rely on low temperatures and the consequent suppression of thermal activation.
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Affiliation(s)
- B Everest
- 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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35
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Medvedyeva MV, Essler FHL, Prosen T. Exact Bethe Ansatz Spectrum of a Tight-Binding Chain with Dephasing Noise. PHYSICAL REVIEW LETTERS 2016; 117:137202. [PMID: 27715082 DOI: 10.1103/physrevlett.117.137202] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/20/2016] [Indexed: 06/06/2023]
Abstract
We construct an exact map between a tight-binding model on any bipartite lattice in the presence of dephasing noise and a Hubbard model with imaginary interaction strength. In one dimension, the exact many-body Liouvillian spectrum can be obtained by application of the Bethe ansatz method. We find that both the nonequilibrium steady state and the leading decay modes describing the relaxation at late times are related to the η-pairing symmetry of the Hubbard model. We show that there is a remarkable relation between the time evolution of an arbitrary k-point correlation function in the dissipative system and k-particle states of the corresponding Hubbard model.
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Affiliation(s)
- Mariya V Medvedyeva
- Physics Department, Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana 1000, Slovenia
| | - Fabian H L Essler
- The Rudolf Peierls Centre for Theoretical Physics, Oxford University, Oxford OX1 3NP, United Kingdom
| | - Tomaž Prosen
- Physics Department, Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana 1000, Slovenia
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36
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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: 73] [Impact Index Per Article: 9.1] [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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37
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Macieszczak K, Guţă M, Lesanovsky I, Garrahan JP. Towards a Theory of Metastability in Open Quantum Dynamics. PHYSICAL REVIEW LETTERS 2016; 116:240404. [PMID: 27367368 DOI: 10.1103/physrevlett.116.240404] [Citation(s) in RCA: 40] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/14/2016] [Indexed: 06/06/2023]
Abstract
By generalizing concepts from classical stochastic dynamics, we establish the basis for a theory of metastability in Markovian open quantum systems. Partial relaxation into long-lived metastable states-distinct from the asymptotic stationary state-is a manifestation of a separation of time scales due to a splitting in the spectrum of the generator of the dynamics. We show here how to exploit this spectral structure to obtain a low dimensional approximation to the dynamics in terms of motion in a manifold of metastable states constructed from the low-lying eigenmatrices of the generator. We argue that the metastable manifold is in general composed of disjoint states, noiseless subsystems, and decoherence-free subspaces.
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Affiliation(s)
- Katarzyna Macieszczak
- School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, United Kingdom
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - Mădălin Guţă
- 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
| | - Juan P Garrahan
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
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38
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Werner AH, Jaschke D, Silvi P, Kliesch M, Calarco T, Eisert J, Montangero S. Positive Tensor Network Approach for Simulating Open Quantum Many-Body Systems. PHYSICAL REVIEW LETTERS 2016; 116:237201. [PMID: 27341253 DOI: 10.1103/physrevlett.116.237201] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/05/2015] [Indexed: 06/06/2023]
Abstract
Open quantum many-body systems play an important role in quantum optics and condensed matter physics, and capture phenomena like transport, the interplay between Hamiltonian and incoherent dynamics, and topological order generated by dissipation. We introduce a versatile and practical method to numerically simulate one-dimensional open quantum many-body dynamics using tensor networks. It is based on representing mixed quantum states in a locally purified form, which guarantees that positivity is preserved at all times. Moreover, the approximation error is controlled with respect to the trace norm. Hence, this scheme overcomes various obstacles of the known numerical open-system evolution schemes. To exemplify the functioning of the approach, we study both stationary states and transient dissipative behavior, for various open quantum systems ranging from few to many bodies.
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Affiliation(s)
- A H Werner
- Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany
| | - D Jaschke
- Institute for Complex Quantum Systems & Center for Integrated Quantum Science and Technologies (IQST), Universität Ulm, 89069 Ulm, Germany
- Department of Physics, Colorado School of Mines, Golden, Colorado 80401, USA
| | - P Silvi
- Institute for Complex Quantum Systems & Center for Integrated Quantum Science and Technologies (IQST), Universität Ulm, 89069 Ulm, Germany
| | - M Kliesch
- Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany
| | - T Calarco
- Institute for Complex Quantum Systems & Center for Integrated Quantum Science and Technologies (IQST), Universität Ulm, 89069 Ulm, Germany
| | - J Eisert
- Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany
| | - S Montangero
- Institute for Complex Quantum Systems & Center for Integrated Quantum Science and Technologies (IQST), Universität Ulm, 89069 Ulm, Germany
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39
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Žnidarič M. Dissipative Remote-State Preparation in an Interacting Medium. PHYSICAL REVIEW LETTERS 2016; 116:030403. [PMID: 26849578 DOI: 10.1103/physrevlett.116.030403] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/21/2015] [Indexed: 06/05/2023]
Abstract
Standard quantum state preparation methods work by preparing a required state locally and then distributing it to a distant location by a free-space propagation. We instead study procedures of preparing a target state at a remote location in the presence of an interacting background medium on which no control is required, manipulating only local dissipation. In mathematical terms, we characterize a set of reduced steady states stabilizable by local dissipation. An explicit local method is proposed by which one can construct a wanted one-site reduced steady state at an arbitrary remote site in a lattice of any size and geometry. In the chain geometry we also prove uniqueness of such a steady state. We demonstrate that the convergence time to fixed precision is smaller than the inverse gap, and we study robustness of the scheme in different medium interactions.
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Affiliation(s)
- Marko Žnidarič
- Physics Department, Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana SI-1000, Slovenia
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40
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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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41
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Gutiérrez R, Garrahan JP, Lesanovsky I. Self-similar nonequilibrium dynamics of a many-body system with power-law interactions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:062144. [PMID: 26764669 DOI: 10.1103/physreve.92.062144] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/21/2015] [Indexed: 06/05/2023]
Abstract
The influence of power-law interactions on the dynamics of many-body systems far from equilibrium is much less explored than their effect on static and thermodynamic properties. To gain insight into this problem we introduce and analyze here an out-of-equilibrium deposition process in which the deposition rate of a given particle depends as a power law on the distance to previously deposited particles. This model draws its relevance from recent experimental progress in the domain of cold atomic gases, which are studied in a setting where atoms that are excited to high-lying Rydberg states interact through power-law potentials that translate into power-law excitation rates. The out-of-equilibrium dynamics of this system turns out to be surprisingly rich. It features a self-similar evolution which leads to a characteristic power-law time dependence of observables such as the particle concentration, and results in a scale invariance of the structure factor. Our findings show that in dissipative Rydberg gases out of equilibrium the characteristic distance among excitations-often referred to as the blockade radius-is not a static but rather a dynamic quantity.
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Affiliation(s)
- Ricardo Gutiérrez
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - Juan P Garrahan
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - Igor Lesanovsky
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
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42
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Žnidarič M. Relaxation times of dissipative many-body quantum systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:042143. [PMID: 26565204 DOI: 10.1103/physreve.92.042143] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/30/2015] [Indexed: 06/05/2023]
Abstract
We study relaxation times, also called mixing times, of quantum many-body systems described by a Lindblad master equation. We in particular study the scaling of the spectral gap with the system length, the so-called dynamical exponent, identifying a number of transitions in the scaling. For systems with bulk dissipation we generically observe different scaling for small and for strong dissipation strength, with a critical transition strength going to zero in the thermodynamic limit. We also study a related phase transition in the largest decay mode. For systems with only boundary dissipation we show a generic bound that the gap cannot be larger than ∼1/L. In integrable systems with boundary dissipation one typically observes scaling of ∼1/L(3), while in chaotic ones one can have faster relaxation with the gap scaling as ∼1/L and thus saturating the generic bound. We also observe transition from exponential to algebraic gap in systems with localized modes.
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Affiliation(s)
- Marko Žnidarič
- Physics Department, Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana, Slovenia
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43
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Sciolla B, Poletti D, Kollath C. Two-time correlations probing the dynamics of dissipative many-body quantum systems: aging and fast relaxation. PHYSICAL REVIEW LETTERS 2015; 114:170401. [PMID: 25978211 DOI: 10.1103/physrevlett.114.170401] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/18/2014] [Indexed: 06/04/2023]
Abstract
We use two-time correlation functions to study the complex dynamics of dissipative many-body quantum systems. In order to measure, understand, and categorize these correlations we extend the framework of the adiabatic elimination method. We show that, for the same parameters and times, two-time correlations can display two distinct behaviors depending on the observable considered: a fast exponential decay or a much slower dynamics. We exemplify these findings by studying strongly interacting bosons in a double well subjected to phase noise. While the single-particle correlations decay exponentially fast with time, the density-density correlations display slow aging dynamics. We also show that this slow relaxation regime is robust against particle losses. Additionally, we use the developed framework to show that the dynamic properties of dissipatively engineered states can be drastically different from their Hamiltonian counterparts.
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Affiliation(s)
- Bruno Sciolla
- University of Bonn, HISKP, Nussallee 14-16, 53115 Bonn, Germany
| | - Dario Poletti
- Singapore University of Technology and Design, 8 Somapah Road, Singapore 487372 Singapore
- MajuLab, CNRS-UNS-NUS-NTU International Joint Research Unit, Singapore UMI 3654, Singapore
| | - Corinna Kollath
- University of Bonn, HISKP, Nussallee 14-16, 53115 Bonn, Germany
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44
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Cai Z, Schollwöck U, Pollet L. Identifying a bath-induced bose liquid in interacting spin-boson models. PHYSICAL REVIEW LETTERS 2014; 113:260403. [PMID: 25615290 DOI: 10.1103/physrevlett.113.260403] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/02/2014] [Indexed: 06/04/2023]
Abstract
We study the ground state phase diagram of a one-dimensional hard-core bosonic model with nearest-neighbor interactions (XXZ model) where every site is coupled Ohmically to an independent but identical reservoir, hereby generalizing spin-boson models to interacting spin-boson systems. We show that a bath-induced Bose liquid phase can occur in the ground state phase diagram away from half filling. This phase is compressible, gapless, and conducting but not superfluid. At half filling, only a Luttinger liquid and a charge density wave are found. The phase transition between them is of Kosterlitz-Thouless type where the Luttinger parameter takes a nonuniversal value. The applied quantum Monte Carlo method can be used for all open bosonic and unfrustrated spin systems, regardless of their dimension, filling factor, and spectrum of the dissipation as long as the quantum system couples to the bath via the density operators.
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Affiliation(s)
- Zi Cai
- Department of Physics and Arnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilians-Universität München, Theresienstrasse 37, 80333 Munich, Germany and Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, 6020 Innsbruck, Austria
| | - Ulrich Schollwöck
- Department of Physics and Arnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilians-Universität München, Theresienstrasse 37, 80333 Munich, Germany
| | - Lode Pollet
- Department of Physics and Arnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilians-Universität München, Theresienstrasse 37, 80333 Munich, Germany
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45
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Kliesch M, Gross D, Eisert J. Matrix-product operators and states: NP-hardness and undecidability. PHYSICAL REVIEW LETTERS 2014; 113:160503. [PMID: 25361243 DOI: 10.1103/physrevlett.113.160503] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/06/2014] [Indexed: 06/04/2023]
Abstract
Tensor network states constitute an important variational set of quantum states for numerical studies of strongly correlated systems in condensed-matter physics, as well as in mathematical physics. This is specifically true for finitely correlated states or matrix-product operators, designed to capture mixed states of one-dimensional quantum systems. It is a well-known open problem to find an efficient algorithm that decides whether a given matrix-product operator actually represents a physical state that in particular has no negative eigenvalues. We address and answer this question by showing that the problem is provably undecidable in the thermodynamic limit and that the bounded version of the problem is NP-hard (nondeterministic-polynomial-time hard) in the system size. Furthermore, we discuss numerous connections between tensor network methods and (seemingly) different concepts treated before in the literature, such as hidden Markov models and tensor trains.
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Affiliation(s)
- M Kliesch
- QMIO Group, Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany
| | - D Gross
- Physikalisches Institut and Freiburg Center for Data Analysis and Modeling, Universität Freiburg, 79104 Freiburg, Germany
| | - J Eisert
- QMIO Group, Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany
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46
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Creatore C, Fazio R, Keeling J, Türeci HE. Quench dynamics of a disordered array of dissipative coupled cavities. Proc Math Phys Eng Sci 2014; 470:20140328. [PMID: 25197253 DOI: 10.1098/rspa.2014.0328] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/22/2014] [Accepted: 06/17/2014] [Indexed: 11/12/2022] Open
Abstract
We investigate the mean-field dynamics of a system of interacting photons in an array of coupled cavities in the presence of dissipation and disorder. We follow the evolution of an initially prepared Fock state, and show how the interplay between dissipation and disorder affects the coherence properties of the cavity emission, and show that these properties can be used as signatures of the many-body phase of the whole array.
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Affiliation(s)
- C Creatore
- Cavendish Laboratory , University of Cambridge , CB3 0HE Cambridge UK
| | - R Fazio
- NEST , Scuola Normale Superiore and Istituto Nanoscienze-CNR , I-56127 Pisa Italy
| | - J Keeling
- Scottish Universities Physics Alliance , School of Physics and Astronomy, University of St Andrews , St Andrews KY16 9SS UK
| | - H E Türeci
- Department of Electrical Engineering , Princeton University , Princeton, NJ08544 USA
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47
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Perturbative approach to Markovian open quantum systems. Sci Rep 2014; 4:4887. [PMID: 24811607 PMCID: PMC4013940 DOI: 10.1038/srep04887] [Citation(s) in RCA: 69] [Impact Index Per Article: 6.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/21/2014] [Accepted: 04/15/2014] [Indexed: 11/09/2022] Open
Abstract
The exact treatment of Markovian open quantum systems, when based on numerical diagonalization of the Liouville super-operator or averaging over quantum trajectories, is severely limited by Hilbert space size. Perturbation theory, standard in the investigation of closed quantum systems, has remained much less developed for open quantum systems where a direct application to the Lindblad master equation is desirable. We present such a perturbative treatment which will be useful for an analytical understanding of open quantum systems and for numerical calculation of system observables which would otherwise be impractical.
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48
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Banchi L, Giorda P, Zanardi P. Quantum information-geometry of dissipative quantum phase transitions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:022102. [PMID: 25353417 DOI: 10.1103/physreve.89.022102] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/29/2013] [Indexed: 06/04/2023]
Abstract
A general framework for analyzing the recently discovered phase transitions in the steady state of dissipation-driven open quantum systems is still lacking. To fill this gap, we extend the so-called fidelity approach to quantum phase transitions to open systems whose steady state is a Gaussian fermionic state. We endow the manifold of correlation matrices of steady states with a metric tensor g measuring the distinguishability distance between solutions corresponding to a different set of control parameters. The phase diagram can then be mapped out in terms of the scaling behavior of g and connections with the Liouvillean gap and the model correlation functions unveiled. We argue that the fidelity approach, thanks to its differential-geometric and information-theoretic nature, provides insights into dissipative quantum critical phenomena as well as a general and powerful strategy to explore them.
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Affiliation(s)
- Leonardo Banchi
- Institute for Scientific Interchange Foundation, Via Alassio 11/c, 10126 Torino, Italy
| | - Paolo Giorda
- Institute for Scientific Interchange Foundation, Via Alassio 11/c, 10126 Torino, Italy
| | - Paolo Zanardi
- Department of Physics and Astronomy, and Center for Quantum Information Science & Technology, University of Southern California, Los Angeles, California 90089-0484, USA and Centre for Quantum Technologies, National University of Singapore, 2 Science Drive 3, Singapore 117542
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49
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Poletti D, Barmettler P, Georges A, Kollath C. Emergence of glasslike dynamics for dissipative and strongly interacting bosons. PHYSICAL REVIEW LETTERS 2013; 111:195301. [PMID: 24266477 DOI: 10.1103/physrevlett.111.195301] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/19/2012] [Revised: 05/20/2013] [Indexed: 06/02/2023]
Abstract
We study the dynamics of a strongly interacting bosonic quantum gas in an optical lattice potential under the effect of a dissipative environment. We show that the interplay between the dissipative process and the Hamiltonian evolution leads to an unconventional dynamical behavior of local number fluctuations. In particular, we show, both analytically and numerically, the emergence of an anomalous diffusive evolution in configuration space at short times and, at long times, an unconventional dynamics dominated by rare events. Such rare events, common in disordered and frustrated systems, are due here to strong interactions. This complex two-stage dynamics reveals information on the level structure of the strongly interacting gas.
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Affiliation(s)
- Dario Poletti
- Singapore University of Technology and Design, 20 Dover Drive 138682, Singapore
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