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International Journal of Theoretical Physics

Quantum Two-breathers Formed by Ultracold Bosonic Atoms in Optical Lattices

Bing Tang

Published Jan 7, 2016• 4 citations
Publisher
DOI
10.1007/s10773-015-2903-9

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The dynamics and the energy spectrum of an ultracold gas of bosonic atoms in an optical lattice can be described by a Bose–Hubbard model for which the system parameters can be controlled by laser light. We study by means of the perturbation theory in addition to the numerical diagonalization, the energy spectrum and the related features of the band structures of the ultracold bosons in optical lattices containing a few number of quanta interacting with next-nearest neighbor interactions (NNNI) modeled by the Bose–Hubbard Hamiltonian. The energy spectra of such system display the bound states signature, which are analyzed in the first Brillouin zone for different wave numbers. The finding, i.e., quantum breathers, shows that their probabilities’ weight depends on the wave vector. The influence of NNNI on both the probabilities’ amplitude and the correlation function is also realized in case of a system with a small number of sites, respectively.
We analyze the decay of ultracold atoms from an optical lattice with loss from a single lattice site. If the initial state is dynamically stable, a suitable amount of dissipation can stabilize a Bose-Einstein condensate, such that it remains coherent even in the presence of strong interactions. A transition between two dynamical phases is observed if the initial state is dynamically unstable. This transition is analyzed here in detail. For strong interactions, the system relaxes to an entangled quantum state with remarkable statistical properties: The atoms bunch in a few ``breathers'' forming at random positions. Breathers at different positions are coherent, such that they can be used in precision quantum interferometry and other applications.