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Laser Physics

Quantum phase transition of ultracold bosons in double-well optical lattices

Ippei Danshita, Jamie Williams, C. A. R. Sá de Melo, Charles W. Clark

Published Mar 1, 2008• 4 citations
Publisher

Abstract

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.

DOI
10.1134/s1054660x08030213

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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.
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 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 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 superfluid-Mott-insulator transition of ultracold bosonic atoms in a one-dimensional optical lattice with a double-well confining trap using the density-matrix renormalization group method. At low density, the system behaves similarly as two separated ones inside each well. At high density, however, interesting features appear resulting from the quantum tunnelling between the two wells and the competition between the ``superfluid'' and Mott regions. These interesting features are characterized by a rich step-plateau structure in the visibility and the satellite peaks in the momentum distribution function, with an oscillating pattern as a function of the on-site repulsion. These properties shed light on the understanding of the quantum phase coherence between two coupled condensates.
We study the Mott phases and the superfluid-insulator transition of two-component ultracold bosons on a square optical lattice in the presence of a non-Abelian synthetic gauge field, which renders a SU(2)-hopping matrix for the bosons. Using a resummed hopping expansion, we calculate the excitation spectra in the Mott insulating phases and demonstrate that the superfluid-insulator phase boundary displays a nonmonotonic dependence on the gauge-field strength. We also compute the momentum distribution of the bosons in the presence of the non-Abelian field and show that they develop peaks at nonzero momenta as the superfluid-insulator transition point is approached from the Mott side. Finally, we study the superfluid phases near the transition and discuss the induced spatial pattern of the superfluid density due to the presence of the non-Abelian gauge potential.
We study Mott phases and superfluid-insulator (SI) transitions of ultracold bosonic atoms in a two-dimensional square optical lattice at commensurate filling and in the presence of a synthetic periodic vector potential characterized by a strength ppp and a period l=qal=qal=qa, where qqq is an integer and aaa is the lattice spacing. We show that the Schr\"odinger equation for the noninteracting bosons in the presence of such a periodic vector potential can be reduced to an one-dimensional Harper-like equation which yields qqq energy bands. The lowest of these bands have either single or double minima whose position within the magnetic Brillouin zone can be tuned by varying ppp for a given qqq. Using these energies and a strong-coupling expansion technique, we compute the phase diagram of these bosons in the presence of a deep optical lattice. We chart out the ppp and qqq dependence of the momentum distribution of the bosons in the Mott phases near the SI transitions and demonstrate that the bosons exhibit several reentrant field-induced SI transitions for any fixed period qqq. We also predict that the superfluid density of the resultant superfluid state near such a SI transition has a periodicity qqq (q/2)(q/2)(q/2) in real space for odd (even) qqq and suggest experiments to test our theory.