Semiclassical quantization of an<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>N</mml:mi></mml:mrow></mml:math>-particle Bose-Hubbard model

Graefe, Eva-Maria; Korsch, Hans Jürgen

doi:10.1103/physreva.76.032116

Cited by 61 publications

(95 citation statements)

References 36 publications

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“…We will follow mainly Braun [12] and his discrete WKB method, as already applied to the double-well problem by Korsch et al [13]. The two-mode Bose-Hubbard Hamiltonian can be written in the Schwinger spin representation by transforming to angular momentum…”

Section: Semiclassical Descriptionmentioning

confidence: 99%

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Analytical results for Josephson dynamics of ultracold bosons

Simon

Strunz

2012

Phys. Rev. A

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We study the dynamics of ultracold Bosons in a double-well potential within the two-mode Bose-Hubbard model by means of semiclassical methods. By applying a WKB quantization we find analytical results for the energy spectrum, which are in excellent agreement with numerical exact results. They are valid in the energy range of plasma oscillations, both in the Rabi and the Josephson regime. Adopting the reflection principle and the Poisson summation formula we derive an analytical expression for the dynamics of the population imbalance depending on the few relevant parameters of the system only. This allows us to discuss its characteristic dynamics, especially the oscillation frequency, and the collapse-and revival time, as a function of the model parameters, leading to a deeper understanding of Josephson physics. We find that our fomulae match previous experimental observations.

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Section: Semiclassical Descriptionmentioning

confidence: 99%

“…Braun [12] and others [13,[23][24][25]. In [13], only the noninteracting case is investigated analytically.…”

Section: Semiclassical Descriptionmentioning

confidence: 99%

Analytical results for Josephson dynamics of ultracold bosons

Simon

Strunz

2012

Phys. Rev. A

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“…With N → ∞, one can replace the annihilation and creation operators by complex numbers [36,[48][49][50][51][52][53][54][55][56][57][58][59]:…”

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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“…Only recently the phase space region near the classical bifurcation was investigated experimentally with ultra cold 87 Rb atoms [41]. On the other hand the classical description has been the basis of successful semiclassical investigations [12][13][14][15][16][17][18][19] in the framework of WKB methods. Motivated by this preliminary work we want to move over to time-dependent semiclassical methods (namely the HK propagation) to describe the dynamics of the out-of-equilibrium ultracold bosons in the double-well potential.…”

Section: A Classical Descriptionmentioning

confidence: 99%

“…For the former, experiments exist which confirm the two-mode picture [35,41] on the one hand, and a number of articles dealing with the discussion of the consequences of the mean-field approximation and many-body corrections [10,11] on the other. Furthermore, (time-independent) semiclassical methods have been applied successfully to the two-mode model, with WKB methods leading the way [12][13][14][15][16][17][18][19], showing that semiclassical methods are a promising tool. In this article, we want to discuss the application of the (explicitly time-dependent) semiclassical Herman-Kluk propagator for ultracold bosons.…”

Section: Introductionmentioning

confidence: 99%

Time-dependent semiclassics for ultracold bosons

Simon

Strunz

2014

Phys. Rev. A

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We study the out-of-equilibrium dynamics of ultracold bosons in a double-and triple-well potential within the Bose-Hubbard model by means of the semiclassical Herman-Kluk propagator and compare the results to the frequently applied "classical dynamics" calculation in terms of the truncated Wigner approximation (TWA). For the double-well system we find the semiclassical results in excellent agreement with the numerically exact ones, while the TWA is not able to reproduce any revivals of the wave function. The triple-well system turns out to be more difficult to handle due to the irregularity of the corresponding classical phase space. Here, deviations of the TWA from the exact dynamics appear even for short times, while better agreement is obtained using the semiclassical approach presented in this article.

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Semiclassical quantization of anN-particle Bose-Hubbard model

Cited by 61 publications

References 36 publications

Analytical results for Josephson dynamics of ultracold bosons

Analytical results for Josephson dynamics of ultracold bosons

Understanding quantum work in a quantum many-body system

Time-dependent semiclassics for ultracold bosons

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