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This research introduces a novel mean-field propagator method designed to accurately model complex interference, revival, and tunnelling dynamics in Bose-Hubbard systems. By extending standard variational principles with time-slicing procedures, the study offers a robust theoretical framework for simulating many-particle quantum states beyond simple approximations. The work advances our ability to predict breakdown phenomena in ultracold atomic gases within optical lattices, which is critical for developing scalable quantum simulation protocols.
Action on the Sphere: An Interfering Mean-Field Propagator for the Bose-Hubbard Dimer
arXiv:2606.30276v2 Announce Type: replace Abstract: The Bose-Hubbard system has been studied extensively both theoretically and experimentally, in particular in the context of ultracold atomic gases in optical lattices. Even in the two-mode case the many-particle dynamics display complex interference effects resulting in revival and breakdown phenomena as well as tunnelling. The most basic theoretical description is the mean-field approximation, which can be derived from a time-dependent variational principle assuming the many-particle wave function is an SU(2) coherent state. Here we build on this to construct a simple initial-value coherent state propagator, summing over mean-field trajectories and keeping track of their phases, given by the corresponding mean-field actions. This yields an approximation to the full time-dependent many-particle state, and is able to reproduce breakdown and revival dynamics. Applying a time-slicing procedure on top of this, we are able to accurately capture many-particle tunnelling effects. While in this paper we focus our analysis on the Bose-Hubbard dimer, the methods developed can be applied to more general SU(2) Hamiltonians, and can be extended to SU(M) systems.
Abstract:The Bose-Hubbard system has been studied extensively both theoretically and experimentally, in particular in the context of ultracold atomic gases in optical lattices. Even in the two-mode case the many-particle dynamics display complex interference effects resulting in revival and breakdown phenomena as well as tunnelling. The most basic theoretical description is the mean-field approximation, which can be derived from a time-dependent variational principle assuming the many-particle wave function is an SU(2) coherent state. Here we build on this to construct a simple initial-value coherent state propagator, summing over mean-field trajectories and keeping track of their phases, given by the corresponding mean-field actions. This yields an approximation to the full time-dependent many-particle state, and is able to reproduce breakdown and revival dynamics. Applying a time-slicing procedure on top of this, we are able to accurately capture many-particle tunnelling effects. While in this paper we focus our analysis on the Bose-Hubbard dimer, the methods developed can be applied to more general SU(2) Hamiltonians, and can be extended to SU(M) systems.
Quantum Physics (quant-ph); Quantum Gases (cond-mat.quant-gas); Mathematical Physics (math-ph)
arXiv:2606.30276 [quant-ph]
(or arXiv:2606.30276v2 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2606.30276 Focus to learn more arXiv-issued DOI via DataCite
J. Phys. A 59 (2026) 395302
https://doi.org/10.1088/1751-8121/aea277 Focus to learn more DOI(s) linking to related resources
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