Cold Bosons in Optical Lattices

Abstract

Basic properties of cold Bose atoms in optical lattices are reviewed. The main principles of correct self-consistent description of arbitrary systems with Bose-Einstein condensate are formulated. Theoretical methods for describing regular periodic lattices are presented. A special attention is paid to the discussion of Bose-atom properties in the frame of the boson Hubbard model. Optical lattices with arbitrary strong disorder, induced by random potentials, are treated. Possible applications of cold atoms in optical lattices are discussed, with an emphasis of their usefulness for quantum information processing and quantum computing. An important feature of the present review article, distinguishing it from other review works, is that theoretical fundamentals here are not just mentioned in brief, but are thoroughly explained. This makes it easy for the reader to follow the principal points without the immediate necessity of resorting to numerous publications in the field.

Enhancing laser sideband cooling in one-dimensional optical lattices via the dipole interaction

“…( 11) describes processes where no photons are lost from the system, either because none are emitted, or because one is emitted but is reabsorbed before time ∆t [16,17]. As it appears in the master equation (11) in a similar form to the − i [H, ρ] of a Hamiltonian, but describes only evolution under the condition of no photon loss, this term is called the conditional Hamiltonian. Unlike a normal Hamiltonian, it is not Hermitian, but norm decreasing; this represents the decreasing probability that this condition will continue to hold, and in the master equation is balanced by R(ρ).…”

“…Under the master equation (11), the density matrix converges to a steady state, and for cooling we would like it to converge within a reasonable time to a state with the lowest possible temperature, or equivalently phonon number. In this section, we calculate this steady state using an open system version of Feynman diagrams.…”

“…The resulting ultracold atoms can be made into a Bose-Einstein condensate [5,6]. They can also be put into an optical lattice (an optical standing wave forming a periodic potential [10][11][12]), where they can be used for quantum simulation of condensed matter systems [12], or potentially for quantum information processing [10]. However, laser cooling does have limitations, which often require it to be followed by the loss of ∼ 99 − 99.9% of the atoms by evaporative cooling [5,6].…”