Abstract
In this paper, the critical parameters of quantum phase transition from the superfluid to the Mott insulator phase are studied for three-dimensional traps in 2D optical lattices and permanent magnetic lattices for trapping the 87Rb atoms. Using the harmonic oscillator wave function approximation, the on-site interaction U, the hopping matrix element J and the ratio J/U are calculated to determine the quantum phase transition point analytically. In a magnetic lattice two components of the external magnetic field B 1x and B 1y had been considered for studying quantum phase transition. Here, B 1z as the z- direction component of the bias magnetic field is also considered for further control of the magnetic lattice parameters. In addition, an optical lattice constructed from the interference of two pairs of orthogonal counter-propagating laser beams is investigated. In both optical and magnetic lattices, the ratio J/U and the critical point of the quantum phase transition can be calculated by variation of the potential barrier height between traps. Comparison of optical lattices with permanent magnetic lattices shows that in the critical point of quantum phase transition the potential barrier height of the magnetic potential is higher than that of the optical trap which suggests that the magnetic microtraps are deeper and more stable than the optical traps in similar structures.
Published Version
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