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New Journal of Physics

Quantum phases for bosons in a magnetic lattice with a harmonic trap

Ya-Fei Song, Shi-Jie Yang

Published Jul 1, 2020• 8 citations
Publisher

Abstract

Abstract The phase diagram of ultracold bosons in a 2D optical lattice subjected to a uniform magnetic flux is studied by the inhomogeneous Gutzwiller variational method. With a harmonic external potential, the density profile exhibits wedding-cake shape and the Mott phase forms a series of circular platforms with integer fillings. There are annular rings of superfluid between these platforms. We identify a lot of phases, including the unicirculation phase, the Meissner phase, the vortex phase, the reversed current phase and the vortex superfluid phase, by examining the super-currents. The circular chiral currents of the reversed current phase are opposite to other phases in annular superfluid and we analyzed the transitions between different phases.

DOI
10.1088/1367-2630/ab95e0

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Abstract The phase diagram of ultracold bosons in a 2D optical lattice subjected to a uniform magnetic flux is studied by the inhomogeneous Gutzwiller variational method. With a harmonic external potential, the density profile exhibits wedding-cake shape and the Mott phase forms a series of circular platforms with integer fillings. There are annular rings of superfluid between these platforms. We identify a lot of phases, including the unicirculation phase, the Meissner phase, the vortex phase, the reversed current phase and the vortex superfluid phase, by examining the super-currents. The circular chiral currents of the reversed current phase are opposite to other phases in annular superfluid and we analyzed the transitions between different phases.
Abstract Ground-state phases of the ultracold bosons in 2D optical lattices subject to artificial magnetic flux are studied by the inhomogeneous Gutzwiller variational method. Results show that the density of a vortex increases linearly with the magnetic flux per plaquette. For a smaller magnetic flux, no supersolid (SS) states are present. The superfluid (SF) states are vortex liquids of either particle-type or hole-type, depending on whether the average filling is greater or less than the integer number. For a larger magnetic flux, regular density-wave states, which also exhibit superfluidity of either particle-type or hole-type, appear at the boundary between the Mott insulator and the SF. Moreover, the uniform SF phases differ to the conventional SF by carrying convection super-current and coreless vorticity. The convection super-current or vorticity in the SS phases assemble in pairs or stripes, as well as checkerboards, according to the flux strength per unit cell.
We study the ground-state properties of spin-1 bosonic atoms trapped in a one-dimensional optical lattice with harmonic confinement. We have developed a highly efficient numerical method based on the Gutzwiller approximation to clarify the inhomogeneous magnetic phases induced by the harmonic confining potential. A quantum phase transition from a superfluid to a Mott insulator is examined for the respective cases with antiferromagnetic and ferromagnetic interactions. It is shown that the profile of local spins over the lattice sites changes as a function of the interaction strength forming the characteristic structures, which closely correlates with the average number of atoms at the sites. For antiferromagnetic cases, we find that there is a crossover from a superfluid polar condensate to Mott-insulator domains consisting of either a spin-singlet pair or a single spin at each site.
We use quantum Monte Carlo (QMC) simulations to study the combined effects of harmonic confinement and temperature for bosons in a two-dimensional(2D) optical lattice. The scale-invariant, finite temperature state diagram is presented for the Bose-Hubbard model in terms of experimental parameters -- the particle number, confining potential and interaction strength. To distinguish the nature of the spatially separated superfluid, Mott insulator, and normal Bose liquid phases, we examine the local density, compressibility, superfluid density, and Green's function. In the annular superfluid rings, as the width of the ring decreases, the long-range superfluid correlations start to deviate from an equivalent homogeneous 2D system. At zero temperature, the correlation decay is intermediate between one-dimension and two-dimensions, while at a finite temperature, the decay is similar to that in one-dimension at a much lower temperature. The calculations reveal shortcomings of the local density approximation in describing superfluid properties of trapped bosons. We also present the finite-temperature phase diagram for the homogeneous two dimensional Bose-Hubbard model. We compare our state diagram with the results of a recent experiment at NIST on a harmonically trapped 2D lattice [Phys. Rev. Lett. 105, 110401 (2010)], and identify a finite-temperature effect in the experiment.
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 use quantum Monte Carlo simulations to obtain zero-temperature state diagrams for strongly correlated lattice bosons in one and two dimensions under the influence of a harmonic confining potential. Since harmonic traps generate a coexistence of superfluid and Mott insulating domains, we use local quantities such as the quantum fluctuations of the and a local compressibility to identify the phases present in the inhomogeneous profiles. We emphasize the use of the characteristic density to produce a state diagram that is relevant to experimental optical lattice systems, regardless of the number of bosons or trap curvature and of the validity of the local-density approximation. We show that the critical value of U/t at which Mott insulating domains appear in the trap depends on the filling in the system, and it is in general greater than the value in the homogeneous system. Recent experimental results by Spielman et al. [Phys. Rev. Lett. 100, 120402 (2008)] are analyzed in the context of our two-dimensional state diagram, and shown to exhibit a value for the critical point in good agreement with simulations. We also study the effects of finite, but low (T<t/2), temperatures. We find that in two dimensions they have little influence on our zero-temperature results, while their effect is more pronounced in one dimension.
Motivated by the recent rapid development of the field of quantum gases in optical lattices, we present a comprehensive study of the spectrum of ultracold atoms in a one-dimensional optical lattice subjected to a periodic lattice modulation. Using the time-dependent density matrix renormalization group method, we study the dynamical response due to lattice modulations in different quantum phases of the system with varying density. For the Mott-insulating state, we identify several excitation processes, which provide important information about the density profile of the gases. For the superfluid, the dynamical response can be well described in a local density approximation. This simplification can be valuable in understanding the strong-correlated superfluid in a slow-varying harmonic potential. All these spectroscopic features of an inhomogeneous system can be used as a test for the validity of the Bose-Hubbard model in a parabolic trapping potential.