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Brenes M, Min B, Anto-Sztrikacs N, Bar-Gill N, Segal D. Bath-induced interactions and transient dynamics in open quantum systems at strong coupling: Effective Hamiltonian approach. J Chem Phys 2024; 160:244106. [PMID: 38916270 DOI: 10.1063/5.0207028] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/05/2024] [Accepted: 06/05/2024] [Indexed: 06/26/2024] Open
Abstract
Understanding the dynamics of dissipative quantum systems, particularly beyond the weak coupling approximation, is central to various quantum applications. While numerically exact methods provide accurate solutions, they often lack the analytical insight provided by theoretical approaches. In this study, we employ the recently developed method dubbed the effective Hamiltonian theory to understand the dynamics of system-bath configurations without resorting to a perturbative description of the system-bath coupling energy. Through a combination of mapping steps and truncation, the effective Hamiltonian theory offers both analytical insights into signatures of strong couplings in open quantum systems and a straightforward path for numerical simulations. To validate the accuracy of the method, we apply it to two canonical models: a single spin immersed in a bosonic bath and two noninteracting spins in a common bath. In both cases, we study the transient regime and the steady state limit at nonzero temperature and spanning system-bath interactions from the weak to the strong regime. By comparing the results of the effective Hamiltonian theory with numerically exact simulations, we show that although the former overlooks non-Markovian features in the transient equilibration dynamics, it correctly captures non-perturbative bath-generated couplings between otherwise non-interacting spins, as observed in their synchronization dynamics and correlations. Altogether, the effective Hamiltonian theory offers a powerful approach for understanding strong coupling dynamics and thermodynamics, capturing the signatures of such interactions in both relaxation dynamics and in the steady state limit.
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Affiliation(s)
- Marlon Brenes
- Department of Physics and Centre for Quantum Information and Quantum Control, University of Toronto, 60 Saint George St., Toronto, Ontario M5S 1A7, Canada
| | - Brett Min
- Department of Physics and Centre for Quantum Information and Quantum Control, University of Toronto, 60 Saint George St., Toronto, Ontario M5S 1A7, Canada
| | - Nicholas Anto-Sztrikacs
- Department of Physics and Centre for Quantum Information and Quantum Control, University of Toronto, 60 Saint George St., Toronto, Ontario M5S 1A7, Canada
| | - Nir Bar-Gill
- Department of Applied Physics, The Hebrew University of Jerusalem, Jerusalem, Israel
- The Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem, Israel
| | - Dvira Segal
- Department of Physics and Centre for Quantum Information and Quantum Control, University of Toronto, 60 Saint George St., Toronto, Ontario M5S 1A7, Canada
- Department of Chemistry, University of Toronto, 80 Saint George St., Toronto, Ontario M5S 3H6, Canada
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Yang C, Sheng J, Wu H. Anomalous thermodynamic cost of clock synchronization. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2024; 87:080501. [PMID: 38876094 DOI: 10.1088/1361-6633/ad5867] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/07/2024] [Accepted: 06/14/2024] [Indexed: 06/16/2024]
Abstract
Clock synchronization is critically important in positioning, navigation and timing systems. While its performance has been intensively studied in a wide range of disciplines, much less is known for the fundamental thermodynamics of clock synchronization‒what limits the precision and how to optimize the energy cost for clock synchronization. Here, we report the first experimental investigation of two stochastic autonomous clocks synchronization, unveiling the thermodynamic relation between the entropy cost and clock synchronization in an open cavity optomechanical system. Two interacting clocks are synchronized spontaneously owing to the disparate decay rates of hybrid modes by engineering the controllable cavity-mediated dissipative coupling. The measured dependence of the degree of synchronization on the overall entropy cost exhibits an unexpected non-monotonic characteristic, while the relation between the degree of synchronization and the entropy cost for the synchronization is monotonically decreasing. The investigation of transient dynamics of clock synchronization exposes a trade-off between energy and time consumption. Our results demonstrate the possibility of clock synchronization in an effective linear system, reveal the fundamental relation between clock synchronization and thermodynamics, and have a great potential for precision measurements, distributed quantum networks, and biological science.
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Affiliation(s)
- Cheng Yang
- State Key Laboratory of Precision Spectroscopy, Institute of Quantum Science and Precision Measurement, East China Normal University, Shanghai 200062, People's Republic of China
| | - Jiteng Sheng
- State Key Laboratory of Precision Spectroscopy, Institute of Quantum Science and Precision Measurement, East China Normal University, Shanghai 200062, People's Republic of China
| | - Haibin Wu
- State Key Laboratory of Precision Spectroscopy, Institute of Quantum Science and Precision Measurement, East China Normal University, Shanghai 200062, People's Republic of China
- Shanghai Branch, Hefei National Laboratory, Shanghai 201315, People's Republic of China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, People's Republic of China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, People's Republic of China
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Schmolke F, Lutz E. Measurement-Induced Quantum Synchronization and Multiplexing. PHYSICAL REVIEW LETTERS 2024; 132:010402. [PMID: 38242665 DOI: 10.1103/physrevlett.132.010402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/12/2023] [Revised: 12/08/2023] [Accepted: 12/12/2023] [Indexed: 01/21/2024]
Abstract
Measurements are able to fundamentally affect quantum dynamics. We here show that a continuously measured quantum many-body system can undergo a spontaneous transition from asynchronous stochastic dynamics to noise-free stable synchronization at the level of single trajectories. We formulate general criteria for this quantum phenomenon to occur and demonstrate that the number of synchronized realizations can be controlled from none to all. We additionally find that ergodicity is typically broken, since time and ensemble averages may exhibit radically different synchronization behavior. We further introduce a quantum type of multiplexing that involves individual trajectories with distinct synchronization frequencies. Measurement-induced synchronization appears as a genuine nonclassical form of synchrony that exploits quantum superpositions.
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Affiliation(s)
- Finn Schmolke
- Institute for Theoretical Physics I, University of Stuttgart, D-70550 Stuttgart, Germany
| | - Eric Lutz
- Institute for Theoretical Physics I, University of Stuttgart, D-70550 Stuttgart, Germany
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Shortcut to synchronization in classical and quantum systems. Sci Rep 2023; 13:453. [PMID: 36624171 PMCID: PMC9829672 DOI: 10.1038/s41598-022-27130-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/26/2022] [Accepted: 12/26/2022] [Indexed: 01/11/2023] Open
Abstract
Synchronization is a major concept in nonlinear physics. In a large number of systems, it is observed at long times for a sinusoidal excitation. In this paper, we design a transiently non-sinusoidal driving to reach the synchronization regime more quickly. We exemplify an inverse engineering method to solve this issue on the classical Van der Pol oscillator. This approach cannot be directly transposed to the quantum case as the system is no longer point-like in phase space. We explain how to adapt our method by an iterative procedure to account for the finite-size quantum distribution in phase space. We show that the resulting driving yields a density matrix close to the synchronized one according to the trace distance. Our method provides an example of fast control of a nonlinear quantum system, and raises the question of the quantum speed limit concept in the presence of nonlinearities.
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Schmolke F, Lutz E. Noise-Induced Quantum Synchronization. PHYSICAL REVIEW LETTERS 2022; 129:250601. [PMID: 36608236 DOI: 10.1103/physrevlett.129.250601] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/06/2022] [Accepted: 11/17/2022] [Indexed: 06/17/2023]
Abstract
Synchronization is a widespread phenomenon in science and technology. Here, we study noise-induced synchronization in a quantum spin chain subjected to local Gaussian white noise. We demonstrate stable (anti)synchronization between the endpoint magnetizations of a quantum XY model with transverse field of arbitrary length. Remarkably, we show that noise applied to a single spin suffices to reach stable (anti)synchronization, and find that the two synchronized end spins are entangled. We additionally determine the optimal noise amplitude that leads to the fastest synchronization along the chain, and further compare the optimal synchronization speed to the fundamental Lieb-Robinson bound for information propagation.
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Affiliation(s)
- Finn Schmolke
- Institute for Theoretical Physics I, University of Stuttgart, D-70550 Stuttgart, Germany
| | - Eric Lutz
- Institute for Theoretical Physics I, University of Stuttgart, D-70550 Stuttgart, Germany
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Kato Y, Nakao H. Turing instability in quantum activator–inhibitor systems. Sci Rep 2022; 12:15573. [PMID: 36114210 PMCID: PMC9481611 DOI: 10.1038/s41598-022-19010-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/07/2022] [Accepted: 08/23/2022] [Indexed: 11/26/2022] Open
Abstract
Turing instability is a fundamental mechanism of nonequilibrium self-organization. However, despite the universality of its essential mechanism, Turing instability has thus far been investigated mostly in classical systems. In this study, we show that Turing instability can occur in a quantum dissipative system and analyze its quantum features such as entanglement and the effect of measurement. We propose a degenerate parametric oscillator with nonlinear damping in quantum optics as a quantum activator–inhibitor unit and demonstrate that a system of two such units can undergo Turing instability when diffusively coupled with each other. The Turing instability induces nonuniformity and entanglement between the two units and gives rise to a pair of nonuniform states that are mixed due to quantum noise. Further performing continuous measurement on the coupled system reveals the nonuniformity caused by the Turing instability. Our results extend the universality of the Turing mechanism to the quantum realm and may provide a novel perspective on the possibility of quantum nonequilibrium self-organization and its application in quantum technologies.
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Cabot A, Luca Giorgi G, Zambrini R. Synchronization and coalescence in a dissipative two-qubit system. Proc Math Phys Eng Sci 2021. [DOI: 10.1098/rspa.2020.0850] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
The possibility of detuned spins displaying synchronous oscillations in local observables is analysed in the presence of coupling, collective dissipation and incoherent pumping. We show that there exist two distinct scenarios in which synchronization can emerge, related respectively to the presence of a non-degenerate long-lived eigenmode and to the presence of a single-frequency regime. Both scenarios can arise by tuning parameters in this system, owing to the presence of coalascence. The former, known as transient synchronization, is here generalized in the presence of incoherent pumping, and is due to long-lasting coherences leading to a progressive frequency selection. On the other hand, in spite of the spins detuning, the dynamics can be governed by a single frequency. Still, we show that synchronization can be established only after a transient, when phase-locking arises. Spectral features of synchronization in these two scenarios are analysed for two-time correlations.
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Affiliation(s)
- Albert Cabot
- IFISC (UIB-CSIC), Instituto de Física Interdisciplinar y Sistemas Complejos, Palma de Mallorca, Spain
| | - Gian Luca Giorgi
- IFISC (UIB-CSIC), Instituto de Física Interdisciplinar y Sistemas Complejos, Palma de Mallorca, Spain
| | - Roberta Zambrini
- IFISC (UIB-CSIC), Instituto de Física Interdisciplinar y Sistemas Complejos, Palma de Mallorca, Spain
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Scholes GD. Polaritons and excitons: Hamiltonian design for enhanced coherence. Proc Math Phys Eng Sci 2020; 476:20200278. [PMID: 33223931 PMCID: PMC7655764 DOI: 10.1098/rspa.2020.0278] [Citation(s) in RCA: 28] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/20/2020] [Accepted: 09/21/2020] [Indexed: 12/11/2022] Open
Abstract
The primary questions motivating this report are: Are there ways to increase coherence and delocalization of excitation among many molecules at moderate electronic coupling strength? Coherent delocalization of excitation in disordered molecular systems is studied using numerical calculations. The results are relevant to molecular excitons, polaritons, and make connections to classical phase oscillator synchronization. In particular, it is hypothesized that it is not only the magnitude of electronic coupling relative to the standard deviation of energetic disorder that decides the limits of coherence, but that the structure of the Hamiltonian-connections between sites (or molecules) made by electronic coupling-is a significant design parameter. Inspired by synchronization phenomena in analogous systems of phase oscillators, some properties of graphs that define the structure of different Hamiltonian matrices are explored. The report focuses on eigenvalues and ensemble density matrices of various structured, random matrices. Some reasons for the special delocalization properties and robustness of polaritons in the single-excitation subspace (the star graph) are discussed. The key result of this report is that, for some classes of Hamiltonian matrix structure, coherent delocalization is not easily defeated by energy disorder, even when the electronic coupling is small compared to disorder.
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Laskar AW, Adhikary P, Mondal S, Katiyar P, Vinjanampathy S, Ghosh S. Observation of Quantum Phase Synchronization in Spin-1 Atoms. PHYSICAL REVIEW LETTERS 2020; 125:013601. [PMID: 32678654 DOI: 10.1103/physrevlett.125.013601] [Citation(s) in RCA: 16] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/14/2019] [Revised: 04/10/2020] [Accepted: 05/29/2020] [Indexed: 06/11/2023]
Abstract
With growing interest in quantum technologies, possibilities of synchronizing quantum systems have garnered significant recent attention. In experiments with dilute ensemble of laser cooled spin-1 ^{87}Rb atoms, we observe phase difference of spin coherences to synchronize with phases of external classical fields. An initial limit-cycle state of a spin-1 atom localizes in phase space due to dark-state polaritons generated by classical two-photon tone fields. In particular, when the two couplings fields are out of phase, the limit-cycle state synchronizes only with two artificially engineered, anisotropic decay rates. Furthermore, we observe a blockade of synchronization due to quantum interference and emergence of Arnold-tongue-like features. Such anisotropic decay induced synchronization of spin-1 systems with no classical analog can provide insights in open quantum systems and find applications in synchronized quantum networks.
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Affiliation(s)
- Arif Warsi Laskar
- Department of Physics, Indian Institute of Technology-Kanpur, Uttar Pradesh 208016, India
| | - Pratik Adhikary
- Department of Physics, Indian Institute of Technology-Kanpur, Uttar Pradesh 208016, India
| | - Suprodip Mondal
- Department of Physics, Indian Institute of Technology-Kanpur, Uttar Pradesh 208016, India
| | - Parag Katiyar
- Department of Physics, Indian Institute of Technology-Kanpur, Uttar Pradesh 208016, India
| | - Sai Vinjanampathy
- Department of Physics, Indian Institute of Technology-Bombay, Powai, Mumbai 400076, India
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543 Singapore, Singapore
| | - Saikat Ghosh
- Department of Physics, Indian Institute of Technology-Kanpur, Uttar Pradesh 208016, India
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Eneriz H, Rossatto DZ, Cárdenas-López FA, Solano E, Sanz M. Degree of Quantumness in Quantum Synchronization. Sci Rep 2019; 9:19933. [PMID: 31882744 PMCID: PMC6934783 DOI: 10.1038/s41598-019-56468-x] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/20/2017] [Accepted: 12/02/2019] [Indexed: 11/09/2022] Open
Abstract
We introduce the concept of degree of quantumness in quantum synchronization, a measure of the quantum nature of synchronization in quantum systems. Following techniques from quantum information, we propose the number of non-commuting observables that synchronize as a measure of quantumness. This figure of merit is compatible with already existing synchronization measurements, and it captures different physical properties. We illustrate it in a quantum system consisting of two weakly interacting cavity-qubit systems, which are coupled via the exchange of bosonic excitations between the cavities. Moreover, we study the synchronization of the expectation values of the Pauli operators and we propose a feasible superconducting circuit setup. Finally, we discuss the degree of quantumness in the synchronization between two quantum van der Pol oscillators.
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Affiliation(s)
- H Eneriz
- Department of Physical Chemistry, University of the Basque Country UPV/EHU, Apartado 644, 48080, Bilbao, Spain
- LP2N, Laboratoire Photonique, Numérique et Nanosciences, Université Bordeaux-IOGS-CNRS:UMR 5298, 33400, Talence, France
| | - D Z Rossatto
- Departamento de Física, Universidade Federal de São Carlos, 13565-905, São Carlos, SP, Brazil.
- Universidade Estadual Paulista (Unesp), Campus Experimental de Itapeva, 18409-010, Itapeva, São Paulo, Brazil.
| | - F A Cárdenas-López
- International Center of Quantum Artificial Intelligence for Science and Technology (QuArtist) and Physics Department, Shanghai University, 200444, Shanghai, China
| | - E Solano
- Department of Physical Chemistry, University of the Basque Country UPV/EHU, Apartado 644, 48080, Bilbao, Spain
- International Center of Quantum Artificial Intelligence for Science and Technology (QuArtist) and Physics Department, Shanghai University, 200444, Shanghai, China
- IKERBASQUE, Basque Foundation for Science, Maria Diaz de Haro 3, 48013, Bilbao, Spain
| | - M Sanz
- Department of Physical Chemistry, University of the Basque Country UPV/EHU, Apartado 644, 48080, Bilbao, Spain.
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