Collective Excitation and Quantum Depletion of a Bose–Einstein Condensate in a Periodic Array of Quantum Wells
XUE Rui1,2,3,4, LI Wei-Dong5, LIANG Zhao-Xin6**
1Key Laboratory of Instrumentation Science and Dynamic Measurement, North University of China, Taiyuan 030051 2National Key Laboratory for Electronic Measurement Technology, North University of China, Taiyuan 030051 3Department of Physics, North University of China, Taiyuan 030051 4Engineering Technology Research Center of Shanxi Province for Opto-Electronic Information and Instrument, North University of China, Taiyuan 030051 5Institute of Theoretical Physics and Department of Physics, Shanxi University, Taiyuan 030006 6Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016
Abstract：With the help of a set of exact closed-form solutions to the stationary Gross–Pitaevskii (GP) equation, we calculate the collective excitation and quantum depletion of a weakly interacting Bose gas in the presence of a periodic array of quantum wells. The excitation spectrum (Bogoliubov spectrum) is obtained from the solution of the linearized time-dependent GP equation, which develops energy bands ?ωj( p) periodic in quasi-momentum space. Moreover, we calculate the excitation strengths Zj( p) relative to the density operator and then the dynamic structure factor S( p,ω). Accordingly, the analytical expressions of quantum depletion of the system are obtained. We find that the quantum depletion is enhanced when the interatomic interactions become larger and the potential is sufficiently deep. The conditions for the possible experimental realization of our scenario are also proposed.
(Tunneling, Josephson effect, Bose-Einstein condensates in periodic potentials, solitons, vortices, and topological excitations)
引用本文:
. [J]. 中国物理快报, 2014, 31(03): 30302-030302.
XUE Rui, LI Wei-Dong, LIANG Zhao-Xin. Collective Excitation and Quantum Depletion of a Bose–Einstein Condensate in a Periodic Array of Quantum Wells. Chin. Phys. Lett., 2014, 31(03): 30302-030302.
2014, Vol. 31 
