Abstract
One of the most remarkable recent developments in the study of ultracold Bose gases is the observation of a reversible transition from a Bose Einstein condensate to a state composed of localized atoms as the strength of a periodic, optical trapping potential is varied. In [1] a model of this phenomenon has been analyzed rigorously. The gas is a hard core lattice gas and the optical lattice is modeled by a periodic potential of strength ⋋. For small ⋋ and temperature Bose- Einstein condensation (BEC) is proved to occur, while at large ⋋ BEC disappears, even in the ground state, which is a Mott-insulator state with a characteristic gap. The inter-particle interaction is essential for this effect. This contribution gives a pedagogical survey of these results.
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Aizenman, M., Lieb, E., Seiringer, R., Solovej, J., Yngvason, J. (2006). Bose-Einstein Condensation as a Quantum Phase Transition in an Optical Lattice. In: Asch, J., Joye, A. (eds) Mathematical Physics of Quantum Mechanics. Lecture Notes in Physics, vol 690. Springer, Berlin, Heidelberg . https://doi.org/10.1007/3-540-34273-7_16
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