Quantum states of ultracold Bose gases in 1D random potentials

Finite temperature correlations in the Bose-Hubbard model: application of the Gauge $P$ representationFinite temperature correlations in the Bose-Hubbard model: application of the Gauge $P$ representation

Saeed Ghanbari, Joel Frederick Corney, Tien D. Kieu

We study ultracold Bose gases in periodic potentials as described by the Bose-Hubbard model. In 1D and at finite temperature, we simulate ultracold Bose gases in imaginary time with the gauge $P$ representation. We study various quantities including the Luttinger parameter $K$ , which is important for locating the boundaries of the Mott insulator lobes, and find a simple relation for the kinetic energy part of the Bose-Hubbard Hamiltonian. We show that for J=0, the stepwise pattern of the average number of particles per lattice site versus the chemical potential vanishes at temperatures above $T \approx 0.1 U$ . Also, at chemical potential $μ=0.5 U$ and temperature $T=0.5 U$ by increasing $J$ , the relative value of the number fluctuation decreases and approaches that of a coherent state.We study ultracold Bose gases in periodic potentials as described by the Bose-Hubbard model. In 1D and at finite temperature, we simulate ultracold Bose gases in imaginary time with the gauge $P$ representation. We study various quantities including the Luttinger parameter $K$, which is important for locating the boundaries of the Mott insulator lobes, and find a simple relation for the kinetic energy part of the Bose-Hubbard Hamiltonian. We show that for J=0, the stepwise pattern of the average number of particles per lattice site versus the chemical potential vanishes at temperatures above $T \approx 0.1 U$. Also, at chemical potential $μ=0.5 U$ and temperature $T=0.5 U$ by increasing $J$, the relative value of the number fluctuation decreases and approaches that of a coherent state.

arXiv:1002.4735Feb 25, 20101 citation

Finite temperature correlations in the Bose-Hubbard model: application of the Gauge

P

representation

We study ultracold Bose gases in periodic potentials as described by the Bose-Hubbard model. In 1D and at finite temperature, we simulate ultracold Bose gases in imaginary time with the gauge

P

representation. We study various quantities including the Luttinger parameter

K

, which is important for locating the boundaries of the Mott insulator lobes, and find a simple relation for the kinetic energy part of the Bose-Hubbard Hamiltonian. We show that for J=0, the stepwise pattern of the average number of particles per lattice site versus the chemical potential vanishes at temperatures above

T \approx 0.1 U

. Also, at chemical potential

μ=0.5 U

and temperature

T=0.5 U

by increasing

J

, the relative value of the number fluctuation decreases and approaches that of a coherent state.