Bose-Einstein quantum phase transition in an optical lattice model

Abstract

Bose-Einstein condensation (BEC) in cold gases can be turned on and off by an\nexternal potential, such as that presented by an optical lattice. We present a\nmodel of this phenomenon which we are able to analyze rigorously. The system is\na hard core lattice gas at half-filling and the optical lattice is modeled by a\nperiodic potential of strength $\\lambda$. For small $\\lambda$ and temperature,\nBEC is proved to occur, while at large $\\lambda$ or temperature there is no\nBEC. At large $\\lambda$ the low-temperature states are in a Mott insulator\nphase with a characteristic gap that is absent in the BEC phase. The\ninterparticle interaction is essential for this transition, which occurs even\nin the ground state. Surprisingly, the condensation is always into the $p=0$\nmode in this model, although the density itself has the periodicity of the\nimposed potential.\n

Keywords

Affiliated Institutions

• Schrodinger (United States) US
• University of Copenhagen DK
• Princeton University US
• University of Vienna AT

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