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arXiv:1108.2672 · Physical Review A

Quantum phase transition of ultracold bosons in the presence of a non-Abelian synthetic gauge field

Tobias Graß, Kush Saha, K. Sengupta, Maciej Lewenstein

Published Nov 28, 2011• 57 citations
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Abstract

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.

DOI
10.1103/physreva.84.053632

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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 the Mott-insulator–superfluid transition of ultracold bosonic atoms in a two-dimensional square optical lattice in the presence of a synthetic magnetic field with p / q ( p and q being co-prime integers) flux quanta passing through each lattice plaquette. We show that on approach to the transition from the Mott side, the momentum distribution of the bosons exhibits q precursor peaks within the first magnetic Brillouin zone. We also provide an effective theory for the transition and show that it involves q interacting boson fields. We construct, from a mean-field analysis of this effective theory, the superfluid ground states near the transition and compute, for q =2, 3, both the gapped and the gapless collective modes of these states. We suggest experiments to test our theory.
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.
We study the phase diagram of ultracold bosons in an optical lattice near a Feshbach resonance. Depending on the boson density, the strength of the optical-lattice potential and the detuning from resonance, the ground state can be a Mott insulator, a superfluid phase with both an atomic and a molecular condensate, or a superfluid phase with only a molecular condensate. Mott insulator to superfluid transitions can be induced either by decreasing the strength of the optical-lattice potential or by varying the detuning from the Feshbach resonance. Quite generally, we find that for a commensurate density the ground state may undergo several insulator-superfluid or superfluid-insulator transitions as the magnetic field is varied through the resonance.
We discuss the possibility of realizing metal-insulator transitions with ultracold atoms in two-dimensional optical lattices in the presence of artificial gauge potentials. For Abelian gauges, such transitions occur when the magnetic flux penetrating the lattice plaquette is an irrational multiple of the magnetic flux quantum. Here we present the first study of these transitions for non-Abelian U(2) gauge fields. In contrast to the Abelian case, the spectrum and localization transition in the non-Abelian case is strongly influenced by atomic momenta. In addition to determining the localization boundary, the momentum fragments the spectrum. Other key characteristics of the non-Abelian case include the absence of localization for certain states and satellite fringes around the Bragg peaks in the momentum distribution and an interesting possibility that the transition can be tuned by the atomic momenta.
We study the effect of an artificial gauge field on the zero-temperature phase diagram of an extended Bose-Hubbard model that describes ultracold atoms in optical lattices with long-range interactions by using strong-coupling perturbation theory. We determine analytically the effect of the artificial gauge field on the density-wave--supersolid (DW-SS) and the Mott-insulator--superfluid (MI-SF) transition boundary. The momentum distribution at these two transition boundaries is also calculated in this approach. It is shown that such a momentum distribution, which can be observed in time-of-flight measurements, reveals the symmetry of the gauge potential through the formation of a magnetic Brillouin zone and clearly distinguishes between the DW-SS and MI-SF boundary. We also point out that, in a symmetric gauge, the momentum distribution structure at these transition boundaries bears distinctive signatures of vortices in supersolid and superfluid phases.
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.