Analytical Expression of Ground State of Double-Well Bose-Einstein Condensates

Ai-Xi Chen, Li Deng

We derive an approximate analytical expression for the ground state of double-well BEC's, which reproduces highly accurately the numerical solution for the whole parameter regimes of the two-body repulsive interaction strength, the total number of atoms, and the hopping parameter.

D. Ananikian

Weizhu Bao, Yongyong Cai, Xinran Ruan

Bruno Juliá-Díaz, Joan Martorell, A. Polls

An analytical insight into the symmetry-breaking mechanisms underlying the transition from Josephson to self-trapping regimes in Bose-Einstein condensates is presented. We obtain expressions for the ground-state properties of the system of a gas of attractive bosons modeled by a two-site Bose-Hubbard Hamiltonian with an external bias. Simple formulas are found relating the appearance of fragmentation in the condensate with the large quantum fluctuations of the population imbalance occurring in the transition from the Josephson to the self-trapped regime.

Wattana Ratismith, Sigmund Heller, Virulh Sa‐Yakanit +1 more

A Bose–Einstein condensate in a double-well potential is considered by using the Feynman path integral theory combined with a variational approach. The system consists of N interacting bosons confined in the double well which is taken as a harmonic potential with a Gaussian barrier. The calculation is carried out within the first cumulant approximation measured with respect to the harmonic action containing variational parameters. Assuming a separable expression for the trial action corresponds to the usual mean field approximation. Performing the variational calculations, we obtain analytical results for the ground state energy and its condensate wavefunction. Using a projection onto the odd contributions, the first excited state energy and condensate wavefunction are determined, too. We find very good agreement with a full numerical solution of the Gross–Pitaevskii equation over the full range of potential parameters.

雅裕 高橋