Strong-coupling expansion for ultracold bosons in an optical lattice at finite temperatures in the presence of superfluidity

Abstract

We develop a strong-coupling ($t\ll U$) expansion technique for calculating the density profile for bosonic atoms trapped in an optical lattice with an overall harmonic trap at finite temperature and finite on site interaction in the presence of superfluid regions. Our results match well with quantum Monte Carlo simulations at finite temperature. We also show that the superfluid order parameter never vanishes in the trap due to proximity effect. Our calculations for the scaled density in the vacuum to superfluid transition agree well with the experimental data for appropriate temperatures. We present calculations for the entropy per particle as a function of temperature which can be used to calibrate the temperature in experiments. We also discuss issues connected with the demonstration of universal quantum critical scaling in the experiments.

11 pages, 9 figures

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• Non-local correlation and entanglement of ultracold bosons in the two-dimensional Bose-Hubbard lattice at finite temperature
• Staggered quantum phases of dipolar bosons at finite temperatures
• Theoretical description of atomtronic Josephson junctions in an optical lattice
• Phase diagram of disordered Bose-Hubbard model based on mean-field and percolation analysis in two dimensions and at fixed $n=1$ filling