Semiclassical quantization of an N-particle Bose-Hubbard model

Abstract

A semiclassical Bohr-Sommerfeld approximation is derived for an N-particle, two-mode Bose-Hubbard system modeling a Bose-Einstein condensate in a double-well potential. This semiclassical description is based on the `classical' dynamics of the mean-field Gross-Pitaevskii equation and is expected to be valid for large N. We demonstrate the possibility to reconstruct quantum properties of the N-particle system from the mean-field dynamics. The resulting semiclassical eigenvalues and eigenstates are found to be in very good agreement with the exact ones, even for small values of N, both for subcritical and supercritical particle interaction strength where tunneling has to be taken into account.

8 pages, 8 figures

References in corpus (5)

• Mean-field dynamics of a Bose-Einstein condensate in a time-dependent triple-well trap: Nonlinear eigenstates, Landau-Zener models and STIRAP
• Towards a Landau-Zener formula for an interacting Bose-Einstein condensate
• Commutability between Semiclassical Limit and Adiabatic Limit
• Semiclassical approach to Bose-Einstein condensates in a triple well potential
• Persistence of mean-field features in the energy spectrum of small arrays of Bose-Einstein condensates

Cited by in corpus (3)

• A non-Hermitian $PT-$symmetric Bose-Hubbard model: eigenvalue rings from unfolding higher-order exceptional points
• Mean-field dynamics of a non-Hermitian Bose-Hubbard dimer
• Non-Hermitian Hamiltonians of Lie algebraic type