Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2004-03-09
Phys. Rev. A 70, 023612 (2004)
Physics
Condensed Matter
Statistical Mechanics
RevTeX4, 13 pages, 2 figures
Scientific paper
10.1103/PhysRevA.70.023612
Bose-Einstein condensation (BEC) in cold gases can be turned on and off by an external potential, such as that presented by an optical lattice. We present a model of this phenomenon which we are able to analyze rigorously. The system is a hard core lattice gas at half-filling and the optical lattice is modeled by a periodic potential of strength $\lambda$. For small $\lambda$ and temperature, BEC is proved to occur, while at large $\lambda$ or temperature there is no BEC. At large $\lambda$ the low-temperature states are in a Mott insulator phase with a characteristic gap that is absent in the BEC phase. The interparticle interaction is essential for this transition, which occurs even in the ground state. Surprisingly, the condensation is always into the $p=0$ mode in this model, although the density itself has the periodicity of the imposed potential.
Aizenman Michael
Lieb Elliott H.
Seiringer Robert
Solovej Jan Philip
Yngvason Jakob
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