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arXiv:cond-mat/0307412 · Physical Review Letters

Reentrant Phenomenon in the Quantum Phase Transitions of a Gas of Bosons Trapped in an Optical Lattice

Hagen M. Kleinert, Sebastian Schmidt, Axel Pelster

Published Oct 12, 2004• 35 citations
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Abstract

We calculate the location of the quantum phase transitions of a Bose gas trapped in an optical lattice as a function of effective scattering length a(eff) and temperature T. Knowledge of recent high-loop results on the shift of the critical temperature at weak couplings is used to locate a nose in the phase diagram above the free Bose-Einstein critical temperature T((0))(c), thus predicting the existence of a reentrant transition above T((0))(c), where a condensate should form when increasing a(eff). At zero temperature, the transition to the normal phase produces the experimentally observed Mott insulator.

DOI
10.1103/physrevlett.93.160402

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We study the quantum phases of bosons confined in a combined potential of a one-dimensional double-well optical lattice and a parabolic trap. We apply the time-evolving block decimation method to the corresponding two-legged Bose-Hubbard model. In the absence of a parabolic trap, the system of bosons in the double-well optical lattice exhibits a reentrant quantum phase transition between Mott insulator and superfluid phases at unit filling as the tilt of the double-wells is increased. We show that the reentrant phase transition occurs also in the presence of a parabolic trap and suggest that it can be detected in experiments by measuring the matter-wave interference pattern.
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Abstract We calculate the quantum phase transition for a homogeneous Bose gas in the plane of s‐wave scattering length as and temperature T. This is done by improving a one‐loop result near the interaction‐free Bose‐Einstein critical temperature Tc(0) with the help of recent high‐loop results on the shift of the critical temperature due to a weak atomic repulsion based on variational perturbation theory. The quantum phase diagram shows a nose above Tc(0), so that we predict the existence of a reentrant transition above Tc(0), where an increasing repulsion leads to the formation of a condensate.