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arXiv:cond-mat/0507256 · Physical Review A

Bose-Einstein-condensate superfluid–Mott-insulator transition in an optical lattice

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

Published Feb 14, 2006• 17 citations
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Abstract

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.

DOI
10.1103/physreva.73.023610

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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.
The objective of this paper is the theoretical description of the Mott insulator to superfluid quantum phase transition of a Bose gas in an optical lattice. In former works the Rayleigh-Schr\"odinger perturbation theory was used within a mean-field approach, which yields partially nonphysical results since the degeneracy between two adjacent Mott lobes is not taken into account. In order to correct such nonphysical results we apply the Brillouin-Wigner perturbation theory to the mean-field approximation of the Bose-Hubbard model. Detailed explanations of how to use the Brillouin-Wigner theory are presented, including a graphical approach that allows one to efficiently keep track of the respective analytic terms. To prove the validity of this computation, the results are compared with other works. Besides the analytic calculation of the phase boundary from Mott insulator to superfluid phase, the condensate density is also determined by simultaneously solving two algebraic equations. The analytical and numerical results turn out to be physically meaningful and can cover a region of system parameters inaccessible until now. Our results are of particular interest provided a harmonic trap is added to the former calculations in a homogeneous system, in view of describing an experiment within the local-density approximation. Thus, the paper represents an essential preparatory work for determining the experimentally observed wedding cake structure of particle-density profile at both finite temperature and finite hopping.
We present a strong-coupling expansion of the Bose-Hubbard model which describes both the superfluid and the Mott phases of ultracold bosonic atoms in an optical lattice. By performing two successive Hubbard-Stratonovich transformations of the intersite hopping term, we derive an effective action which provides a suitable starting point to study the strong-coupling limit of the Bose-Hubbard model. This action can be analyzed by taking into account Gaussian fluctuations about the mean-field approximation as in the Bogoliubov theory of the weakly interacting Bose gas. In the Mott phase, we reproduce results of previous mean-field theories and also calculate the momentum distribution function. In the superfluid phase, we find a gapless spectrum and compare our results with the Bogoliubov theory.
We study the Bose-Hubbard model using the finite size density matrix renormalization group method. We obtain a complete phase diagram for a system in the presence of a harmonic trap and compare it with that of the homogeneous system. The superfluid to the Mott-insulator phase transition is investigated using different experimental signatures of these phases in quantities such as momentum distribution, visibility, condensate fraction, and the total number of bosons at a particular density. The relationships between the various experimental signatures and the phase diagram are highlighted.
87Rb Bose Einstein Condensate in 3D optical lattice was studied in the regime of weak interaction(the superfluid phase) and strong interaction(the Mott insulating phase). The stability of superfluid currents was studied using a moving optical lattice. The critical momentum for stable superfluid current varies from 0.5 recoil momentum (shallow lattice) to 0 (the Mott insulator) as the system reaches the Mott insulator transition. The phase diagram for the disappearance of superfluidity was studied as a function of momentum and lattice depth. Our phase diagram boundary ex-trapolates to the critical lattice depth for the superfluid-to-MI transition. When a one-dimensional gas was loaded into a moving optical lattice a sudden broadening of the transition between stable and unstable phases was observed. A new auxiliary vacuum chamber, which is called the science chamber, was de-signed and installed to improve optical lattice experimental performance and imaging resolution power. Atoms are transported from the main chamber to the science cham-ber. By further evaporation cooling, BECs with N- 2-3 x 104 atoms are produced