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arXiv:cond-mat/0510725 · Physical Review A

Itinerant-localized dual character of a strongly correlated superfluid Bose gas in an optical lattice

Yoji Ohashi, M Kitaura, H. Matsumoto

Published Mar 20, 2006• 42 citations
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Abstract

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 $T=0$. 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.

DOI
10.1103/physreva.73.033617

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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.
The strongly correlated bosons in flat-band systems are an excellent platform to study a wide range of quantum phenomena. Such systems can be realized in optical lattices filled with ultracold atomic gases. In this paper we study the Bose-Hubbard model in the Lieb lattice by means of the time-dependent Gutzwiller mean-field approach. We find that in the Mott insulator phase the excitation modes are gapped and display purely particle or purely hole character, while in the superfluid phase the excitation spectrum is gapless. The geometry of the Lieb lattice leads to a nonuniform order parameter and nonuniform oscillation energy in the ground state. This results in additional anticrossings between dispersive bands in the excitation spectra, while the flat bands remain insensitive to this effect. We analyze the oscillations of the order parameter on the sublattices as well as the particle-hole character of the excitations. For certain model parameters we find simultaneous pure phase and pure amplitude oscillations within the same mode, separated between the sublattices. Also, we propose a simple method to differentiate between the hole and particle superfluid regions in the Lieb lattice by in situ measurement of the atom population on the sublattices.
We study ground-state phase diagrams and excitation spectra of Bose-Bose mixtures in an optical lattice by applying the Gutzwiller approximation to the two-component Bose-Hubbard model. A case of equal hoppings and equal intra-component interactions for both components is considered. Due to the existence of inter-component interaction, there appear several quantum phases, such as the superfluid, paired superfluid, and counterflow superfluid phases. We find that the transition from superfluid (SF) to Mott insulator (MI) with even filling factors can be of the first order for a wide range of the chemical potential. We calculate the excitation spectra as a useful probe to identify the quantum phases and the SF-to-MI transitions. In the excitation spectra of the SF phase, there are two gapless modes and a few gapful modes, which respectively correspond to phase and amplitude fluctuations of the order parameters. At the SF-to-MI transition point, we show that the energy gaps of certain amplitude modes reach zero for the second-order transition while they remain finite for the first-order one. Since the excitation spectrum can be measured by the Bragg scattering, we calculate the dynamical structure factor by using the linear response theory. We consider three types of density fluctuations, and show that the density fluctuations are coupled to different excitation branches in different quantum phases.
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.
The Bose Hubbard model describing interacting bosons in an optical lattice is reduced to a simple spin-1 XY model with single-ion anisotropy in the vicinity of the Mott phase. In the strong coupling Mott insulating regime, we propose a mean field theory based on a constraint SU (3) pseudo-boson representation on the effective model and discuss the excitation spectra and the phase transition to the superfluid state. Further to the superfluid phase, we use the coherent-state approach to derive the collective excitation modes. It is found that the Mott phase has two degenerate gapped quadratic excitation spectra which graduate into two degenerate gapless linear ones at the transition point, and one gapless linear mode with one gapped quadratic mode in the superfluid phase.
We study single-particle excitations of a Bose gas in an optical lattice in the Mott-insulator phase. The characteristic feature of the single-particle spectrum in the Mott-insulator phase is the existence of an energy gap between the particle and hole excitations. We show that the single-particle excitation energies and associated energy gap in the Mott-insulator phase can be directly probed by an output-coupling experiment. We apply the general expression for the output current derived by Luxat and Griffin, which is given in terms of the single-particle Green's functions of a trapped Bose gas, to the Mott-insulator phase using the Bose-Hubbard model. The energy spectrum of the momentum-resolved output current exhibits two characteristic peaks corresponding to the particle and hole excitations, and thus it can be used to detect the transition point from the Mott insulator to superfluid phase where the energy gap disappears.
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.