Adiabaticity when raising a uniform three-dimensional optical lattice in a bimodal Bose-Einstein condensate

Abstract

Using the time-dependent Bogoliubov approach, we study adiabaticity for a two-component Bose-Einstein condensate in a 3D time-dependent optical lattice with unit filling, in the superfluid and weakly interacting regime. We show that raising the lattice potential height can couple the ground state of the Bogoliubov Hamiltonian to excited states with two quasiparticles of opposite quasimomenta. In the symmetric case for interactions and density in the two components these represent sound waves where the two components oscillate out of phase. We find an analytic expression of the adiabatic time, its dependence on the fraction of atoms in each component and its scaling with the system size.

Producing and storing spin-squeezed states and Greenberger-Horne-Zeilinger states in a one-dimensional optical lattice

“…Here below, we give an approximate expression of χ in the static case, assuming that all the atoms are in the zero momentum mode that is the condensate mode in the noninteracting case. To this aim, we write the Bose-Hubbard Hamiltonian (3) in the momentum representation, âi = 1 √ M q e −iqxi âq and bi = 1 √ M q e −iqxi bq , and we keep only the zero momentum terms [41]. We obtain :…”