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arXiv:0712.0428

Experimentally accessible reentrant phase transitions in double-well optical lattices

Ippei Danshita, Carlos A. R. Sá de Melo, Charles W. Clark

Published Dec 4, 2007• 0 citations
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Abstract

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.

DOI
10.48550/arxiv.0712.0428

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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.
We study the quantum phases of bosons confined to a combined potential of a one-dimensional double-well optical lattice and a parabolic trap (two-legged ladders). We apply the time-evolving block decimation method to the corresponding ladders described by a 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 this reentrant phase transition still occurs in the presence of a parabolic trap, and we suggest that it can be detected experimentally by measuring matter-wave interference patterns.
We study the superfluid and insulating phases of bosons in double-well optical lattices, and focus on the specific example of a two-legged ladder, which is currently accessible in experiments. We obtain the zero-temperature phase diagram using both mean-field and time-evolving block decimation techniques. We find that the mean-field approach describes the correct phase boundaries only when the intrachain hopping is sufficiently small in comparison to the on-site repulsion. We show the dependence of the phase diagram on the interchain hopping or tilt between double wells. We find that the Mott-insulator phase at unit filling exhibits a nonmonotonic behavior as a function of the tilt parameter, producing a reentrant phase transition between Mott insulator and superfluid phases. Finally, we determine the critical point separating the insulating and superfluid phases at commensurate fillings, where the Berezinskii-Kosterlitz-Thouless transition occurs.
We study the superfluid-to-Mott insulator transition of bosons in a two-legged ladder optical lattice of a type accessible in current experiments on double-well optical lattices. The zero-temperature phase diagram is mapped out, with a focus on its dependence upon interchain hopping and the tilt between double wells. We find that the unit-filling Mott phase exhibits a nonmonotonic behavior as a function of the tilt parameter, producing a reentrant phase transition between the Mott insulator and superfluid phases.
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In the absence of a confining potential, the boson-Hubbard model exhibits a superfluid to Mott insulator quantum phase transition at commensurate fillings and strong coupling. We use quantum Monte Carlo simulations to study the ground state of the one-dimensional bosonic Hubbard model in a trap. Some, but not all, aspects of the Mott insulating phase persist. Mott behavior occurs for a continuous range of incommensurate fillings, very different from the unconfined case, and the establishment of the Mott phase does not proceed via a traditional quantum phase transition. These results have important implications for interpreting experiments on ultracold atoms on optical lattices.
We study the quantum phases of mixtures of ultracold bosonic atoms held in an optical lattice that confines motion or hopping to one spatial dimension. The phases are found by using the Tomonaga-Luttinger liquid theory as well as the numerical method of time-evolving block decimation (TEBD). We consider a binary mixture of equal density with repulsive intraspecies interactions and either repulsive or attractive interspecies interaction. For a homogeneous system, we find paired and counterflow superfluid phases at different filling and hopping energies. We also predict parameter regions in which these types of superfluid order coexist with charge-density wave order. We show that the Tomonaga-Luttinger liquid theory and the TEBD qualitatively agree on the location of the phase boundary to superfluidity. We then describe how these phases are modified and can be detected when an additional harmonic trap is present. In particular, we show how experimentally measurable quantities, such as time-of-flight images and the structure factor, can be used to distinguish the quantum phases. Finally, we suggest applying a Feshbach ramp to detect the paired superfluid state and a $\ensuremath{\pi}/2$ pulse followed by Bragg spectroscopy to detect the counterflow superfluid phase.