Semiclassical quantization of an N-particle Bose-Hubbard model

Details Semiclassical quantization of an N-particle Bose-Hubbard model Semiclassical quantization of an N-particle Bose-Hubbard model

2006-11-03

arxiv.org/abs/quant-ph/0611040v2

Phys.Rev.A 76 (2007) 032116

Physics

Quantum Physics

8 pages, 8 figures

Scientific paper

10.1103/PhysRevA.76.032116

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.

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