Semiclassical analysis of Bose–Hubbard dynamics

Veksler, Hagar; Fishman, Shmuel

doi:10.1088/1367-2630/17/5/053030

Cited by 35 publications

(32 citation statements)

References 53 publications

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“…"Tunneling" refers to linear coupling between the condensates (quadratic in operators) while "interactions" refer to a nonlinear self-particle quartic term. In this sense, Josephson's physics is a limiting case of the Bose-Hubbard model [14], although the name retained a strong bond with superconductors [15], possibly due to the important applications it found as a quantum interference device [16,17] or merely for historical reasons (the Josephson-Bardeen debate on the existence of the effect is one highlight of scientific controversies [18]). To mark this difference, one speaks of "Bosonic Josephson junctions" (BJJ) for bosonic implementations of the Josephson dynamics [19].…”

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confidence: 99%

Polaritonic Rabi and Josephson Oscillations

Rahmani

Laussy

2016

Sci Rep

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The dynamics of coupled condensates is a wide-encompassing problem with relevance to superconductors, BECs in traps, superfluids, etc. Here, we provide a unified picture of this fundamental problem that includes i) detuning of the free energies, ii) different self-interaction strengths and iii) finite lifetime of the modes. At such, this is particularly relevant for the dynamics of polaritons, both for their internal dynamics between their light and matter constituents, as well as for the more conventional dynamics of two spatially separated condensates. Polaritons are short-lived, interact only through their material fraction and are easily detuned. At such, they bring several variations to their atomic counterpart. We show that the combination of these parameters results in important twists to the phenomenology of the Josephson effect, such as the behaviour of the relative phase (running or oscillating) or the occurence of self-trapping. We undertake a comprehensive stability analysis of the fixed points on a normalized Bloch sphere, that allows us to provide a generalized criterion to identify the Rabi and Josephson regimes in presence of detuning and decay.

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confidence: 99%

Polaritonic Rabi and Josephson Oscillations

Rahmani

Laussy

2016

Sci Rep

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“…It is well known that the relationship between quantum and mean field descriptions of Bose gases is essentially quantum-classical correspondence [15][16][17] with 1/N (N is the total number of bosons) serves as effective Planck constant. Our results above can be straightforwardly applied to any system of Bose gas which is integrable as it was done for chaotic Bose system in Ref.…”

Section: Bose Gasesmentioning

confidence: 99%

“…In this work we study systematically the quantumclassical correspondence in integrable systems. We find * Electronic address: wubiao@pku.edu.cn that the quantum-classical correspondence is characterized by two time scales, Ehrenfest time τ and quantum revival time T r [13][14][15], as shown in Fig.1. According to this figure, for a fixed Planck constant, the wave packet dynamics is almost classical when the evolution time is shorter than the Ehrenfest time τ ; when the evolution time is longer than T r , quantum revival occurs and the wave packet dynamics can no longer be approximated by semiclassical approaches.…”

Section: Introductionmentioning

confidence: 97%

Quantum-classical correspondence in integrable systems

Zhao

2019

Sci. China Phys. Mech. Astron.

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We find that the quantum-classical correspondence in integrable systems is characterized by two time scales. One is the Ehrenfest time below which the system is classical; the other is the quantum revival time beyond which the system is fully quantum. In between, the quantum system can be well approximated by classical ensemble distribution in phase space. These results can be summarized in a diagram which we call Ehrenfest diagram. We derive an analytical expression for Ehrenfest time, which is proportional to −1/2 . According to our formula, the Ehrenfest time for the solar-earth system is about 10 26 times of the age of the solar system. We also find an analytical expression for the quantum revival time, which is proportional to −1 . Both time scales involve ω(I), the classical frequency as a function of classical action. Our results are numerically illustrated with two simple integrable models. In addition, we show that similar results exist for Bose gases, where 1/N serves as an effective Planck constant.

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“…The interactions between the bosons can be characterized by a dimensionless coupling parameter [36,[43][44][45][46][47][48] …”

Section: D Bose-hubbard Modelmentioning

confidence: 99%

Understanding quantum work in a quantum many-body system

Wang

Quan

2017

Phys. Rev. E

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Based on previous studies in a single-particle system in both the integrable [Jarzynski, Quan, and Rahav, Phys. Rev. X 5, 031038 (2015)] and the chaotic systems [Zhu, Gong, Wu, and Quan, Phys. Rev. E 93, 062108 (2016)], we study the the correspondence principle between quantum and classical work distributions in a quantum many-body system. Even though the interaction and the indistinguishability of identical particles increase the complexity of the system, we find that for a quantum many-body system the quantum work distribution still converges to its classical counterpart in the semiclassical limit. Our results imply that there exists a correspondence principle between quantum and classical work distributions in an interacting quantum many-body system, especially in the large particle number limit, and further justify the definition of quantum work via two-point energy measurements in quantum many-body systems.

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Semiclassical analysis of Bose–Hubbard dynamics

Cited by 35 publications

References 53 publications

Polaritonic Rabi and Josephson Oscillations

Polaritonic Rabi and Josephson Oscillations

Quantum-classical correspondence in integrable systems

Understanding quantum work in a quantum many-body system

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