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Journal of Physics B Atomic Molecular and Optical Physics

Mott insulator–superfluid phase transition in two-band Bose–Hubbard models with gapless nodal lines

Beibing Huang, Xiaosen Yang

Published Nov 1, 2017• 1 citation
Publisher

Abstract

Abstract Recent studies on ultracold atoms have reported the implementation of laser-assisted tunneling in lattice systems, facilitating the realization of topological phases. Motivated by such advances, we investigate a two-band Bose–Hubbard model with its single-particle energy bands showing gapless nodal lines, which can be realized for ultracold atoms in the cubic optical lattices using laser-assisted tunneling. We analyze the superfluid–Mott insulator (MI) phase transition in this model and obtain a global phase diagram by using the strong-coupling expansion method. The excitation spectra in strong and weak coupling limits inherit the topological properties of single-particle energy bands to show the structures of nodal lines. The topological invariants, the flat surface states and the critical properties are analyzed theoretically in detail. The excitation spectra in the MI and superfluid phases are measurable in ultracold atom experiments to prove our results.

DOI
10.1088/1361-6455/aa9787

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Abstract Recent studies on ultracold atoms have reported the implementation of laser-assisted tunneling in lattice systems, facilitating the realization of topological phases. Motivated by such advances, we investigate a two-band Bose–Hubbard model with its single-particle energy bands showing gapless nodal lines, which can be realized for ultracold atoms in the cubic optical lattices using laser-assisted tunneling. We analyze the superfluid–Mott insulator (MI) phase transition in this model and obtain a global phase diagram by using the strong-coupling expansion method. The excitation spectra in strong and weak coupling limits inherit the topological properties of single-particle energy bands to show the structures of nodal lines. The topological invariants, the flat surface states and the critical properties are analyzed theoretically in detail. The excitation spectra in the MI and superfluid phases are measurable in ultracold atom experiments to prove our results.
In this paper, a Bose-Hubbard extension of a Weyl semimetal is proposed that can be realized for ultracold atoms using laser-assisted tunneling and Feshbach resonance technique in three-dimensional optical lattices. The global phase diagram is obtained consisting of a superfluid phase and various Mott insulator phases by using Landau theory. The Bogoliubov excitation modes for the weakly interacting case have nontrivial properties (Weyl nodes, bosonic surface arc, etc.), analogs of those in Weyl semimetals of electronic systems, which are smoothly carried over to those of Bloch bands for the noninteracting case. The properties of the insulating phases for the strongly interacting case are explored by calculating both the quasiparticle and quasihole dispersion relation, which shows that two quasiparticle spectra touch at Weyl nodes.
We present a strong-coupling expansion of the Bose-Hubbard model which describes both the superfluid and the Mott phases of ultracold bosonic atoms in an optical lattice. By performing two successive Hubbard-Stratonovich transformations of the intersite hopping term, we derive an effective action which provides a suitable starting point to study the strong-coupling limit of the Bose-Hubbard model. This action can be analyzed by taking into account Gaussian fluctuations about the mean-field approximation as in the Bogoliubov theory of the weakly interacting Bose gas. In the Mott phase, we reproduce results of previous mean-field theories and also calculate the momentum distribution function. In the superfluid phase, we find a gapless spectrum and compare our results with the Bogoliubov theory.
Abstract The gapless Weyl superfluid has been widely studied in the three-dimensional ultracold fermionic superfluid. In contrast to Weyl superfluid, there exists another kind of gapless superfluid with topologically protected nodal lines, which can be regarded as the superfluid counterpart of nodal line semimetal in the condensed matter physics, just as Weyl superfluid with Weyl semimetal. In this paper we study the ground states of the cold fermionic gases in cubic optical lattices with one-dimensional spin-orbit coupling and transverse Zeeman field and map out the topological phase diagram of the system. We demonstrate that in addition to a fully gapped topologically trivial phase, some different nodal line superfluid phases appear when the Zeeman field is adjusted. The presence of topologically stable nodal lines implies the dispersionless zero-energy flat band in a finite region of the surface Brillouin zone. Experimentally these nodal line superfluid states can be detected via the momentum-resolved radio-frequency spectroscopy. The nodal line topological superfluid provide fertile grounds for exploring exotic quantum matters in the context of ultracold atoms.
We study the ground-state properties of ultracold bosons in an optical lattice in the regime of strong interactions. The system is described by a non-standard Bose–Hubbard model with both occupation-dependent tunneling and on-site interaction. We find that for sufficiently strong coupling, the system features a phase transition from a Mott insulator with one particle per site to a superfluid of spatially extended particle pairs living on top of the Mott background—instead of the usual transition to a superfluid of single particles/holes. Increasing the interaction further, a superfluid of particle pairs localized on a single site (rather than being extended) on top of the Mott background appears. This happens at the same interaction strength where the Mott-insulator phase with two particles per site is destroyed completely by particle–hole fluctuations for arbitrarily small tunneling. In another regime, characterized by weak interaction but high occupation numbers, we observe a dynamical instability in the superfluid excitation spectrum. The new ground state is a superfluid, forming a two-dimensional (2D) slab, localized along one spatial direction that is chosen spontaneously.
We investigate a strongly correlated Bose gas in an optical lattice. Extending the standard-basis operator method developed by Haley and Erd\"os to a boson Hubbard model, we calculate excitation spectra in the superfluid phase, as well as in the Mott insulating phase, at T=0T=0T=0. In the Mott phase, the excitation spectrum has a finite energy gap, reflecting the localized character of atoms. In the superfluid phase, the excitation spectrum is shown to have an itinerant-localized dual structure, where the gapless Bogoliubov mode (which describes the itinerant character of superfluid atoms) and a band with a finite energy gap coexist. We also show that the rf-tunneling current measurement would give useful information about the duality of a strongly correlated superfluid Bose gas near the superfluid-insulator transition.