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International Journal of Modern Physics B

BOSE - EINSTEIN CONDENSATE SUPERFLUID - MOTT INSULATOR TRANSITION IN AN OPTICAL LATTICE

Ana María Rey, Esteban Calzetta, B. L. Hu

Published Dec 15, 2006• 0 citations
Publisher

Abstract

We present in this paper an analytical model for a cold bosonic gas on an optical lattice (with densities of the order of 1 particle per site) targeting the critical regime of the Bose - Einstein Condensate superfluid - Mott insulator transition.
DOI
10.1142/s0217979206036284

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We present an analytical model for a cold bosonic gas on an optical lattice (with densities of the order of 1 particle per site), targeting the critical regime of the Bose-Einstein-condensate superfluid--Mott-insulator transition. We focus on the computation of the one-body density matrix and its Fourier transform, the momentum distribution which is directly obtainable from ``time-of-flight'' measurements. The expected number of particles with zero momentum may be identified with the condensate population if it is close to the total number of particles. Our main result is an analytic expression for this observable, interpolating between the known results valid for the two regimes separately: the standard Bogoliubov approximation valid in the superfluid regime and the strong-coupling perturbation theory valid in the Mott regime.
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We derive the equation of state of bosons in an optical lattice in the framework of the Bose-Hubbard model. Near the density-driven Mott transition, the expression of the pressure $P(\ensuremath{\mu},T)$ versus chemical potential and temperature is similar to that of a dilute Bose gas but with renormalized mass m∗{m}^{*}m∗ and scattering length a∗{a}^{*}a∗. Here m∗{m}^{*}m∗ is the mass of the elementary excitations at the quantum critical point governing the transition from the superfluid phase to the Mott-insulating phase, while a∗{a}^{*}a∗ is related to their effective interaction at low energy. We use a nonperturbative renormalization-group approach to compute these parameters as a function of the ratio t/Ut/Ut/U between hopping amplitude and on-site repulsion.