Abstract
AbstractThis chapter discusses some features exhibited by quantum gases in the presence of periodic optical potentials (optical lattices). The behaviour of the single-particle excitation spectrum exhibiting the typical Bloch band structure is briefly summarized. The equilibrium properties of a Bose–Einstein condensate and of the ideal Fermi gas are discussed, with special focus on the behaviour of the momentum distribution. It also considers the effects of localization in one-dimensional quasiperiodic potentials and the nature of Bloch oscillations. The chapter discusses the structure of the elementary excitations in an optical potential, including the motion of the centre of mass in the presence of an additional harmonic potential. Finally, the chapter mentions the problem of quantum fluctuations, and it introduces the physics of the Bose–Hubbard and Fermi–Hubbard models, whose systematic investigation lies outside the scope of this book.
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