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 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.

RevTeX4, 13 pages, 2 figures

References in corpus (14)

• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Cold bosonic atoms in optical lattices
• Collapse and Revival of the Matter Wave Field of a Bose-Einstein Condensate
• Oscillating Superfluidity of Bosons in Optical Lattices
• Geometric Aspects of Quantum Spin States
• Ultracold atoms in optical lattices
• Bogoliubov approach to superfluidity of atoms in an optical lattice
• Ground state properties of a fully frustrated quantum spin system
• Variational ansatz for the superfluid Mott-insulator transition in optical lattices
• Two-component Bose gas in an optical lattice at single-particle filling
• Singlets and reflection symmetric spin systems
• Quantum States of Matter of Simple Bosonic Systems: BEC's, Superfluids and Quantum Solids
• Manipulating the superfluid - Mott insulator transition of a Bose - Einstein condensate in an amplitude - modulated optical lattice
• On Quantum Bosonic Solids and Bosonic Superfluids

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