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arXiv:1004.2121 · Physical Review A

Excitation dynamics in a lattice Bose gas within the time-dependent Gutzwiller mean-field approach

Konstantin V. Krutitsky, Patrick Navez

Published Sep 2, 2011• 49 citations
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Abstract

The dynamics of the collective excitations of a lattice Bose gas at zero temperature is systematically investigated using the time-dependent Gutzwiller mean-field approach. The excitation modes are determined within the framework of the linear-response theory as solutions of the generalized Bogoliubov--de Gennes equations valid in the superfluid and Mott-insulator phases at arbitrary values of parameters. The expression for the sound velocity derived in this approach coincides with the hydrodynamic relation. We calculate the transition amplitudes for the excitations in the Bragg scattering process and show that the higher excitation modes make significant contributions. We simulate the dynamics of the density perturbations and show that their propagation velocity in the limit of week perturbation is satisfactorily described by the predictions of the linear-response analysis.

DOI
10.1103/physreva.84.033602

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The dynamics of the collective excitations of a lattice Bose gas at zero temperature is systematically investigated using the time-dependent Gutzwiller mean-field approach. The excitation modes are determined within the framework of the linear-response theory as solutions of the generalized Bogoliubov--de Gennes equations valid in the superfluid and Mott-insulator phases at arbitrary values of parameters. The expression for the sound velocity derived in this approach coincides with the hydrodynamic relation. We calculate the transition amplitudes for the excitations in the Bragg scattering process and show that the higher excitation modes make significant contributions. We simulate the dynamics of the density perturbations and show that their propagation velocity in the limit of week perturbation is satisfactorily described by the predictions of the linear-response analysis.
We analyze the collective modes of a harmonically trapped, strongly interacting Bose gas in an optical lattice in the vicinity of the Mott-insulator transition. For that aim we employ the dynamical Gutzwiller mean-field method, by performing real-time evolution and by solving the equations in linear response. We find a strong dependence on the spatial dimension of the system: while in one dimension the frequency of the dipole mode vanishes at the Mott transition, in higher dimensions the dominant dipole mode is featureless and we find a signature only in the breathing mode. We discuss implications for experiments with bosonic and fermionic atoms.
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.
The dynamic response of ultracold Bose gases in one-dimensional optical lattices and superlattices is investigated based on exact numerical time evolutions in the framework of the Bose–Hubbard model. The system is excited by a temporal amplitude modulation of the lattice potential, as it was done in recent experiments. For regular lattice potentials, the dynamic signatures of the superfluid to Mott-insulator transition are studied and the position and the fine-structure of the resonances is explained by a linear response analysis. Using direct simulations and the perturbative analysis it is shown that in the presence of a two-colour superlattice the excitation spectrum changes significantly when going from the homogeneous Mott-insulator to the quasi-Bose-glass phase. A characteristic and experimentally accessible signature for the quasi-Bose-glass is the appearance of low-lying resonances and a suppression of the dominant resonance of the Mott-insulator phase.
Abstract Using the time-dependent Hartree–Fock–Bogoliubov approach, where the condensate is coupled with the thermal cloud and the anomalous density, we study the equilibrium and the dynamical properties of three-dimensional quantum-degenerate Bose gas at finite temperature. Effects of the anomalous correlations on the condensed fraction and the critical temperature are discussed. In uniform Bose gas, useful expressions for the Bogoliubov excitations spectrum, the first and second sound, the condensate depletion and the superfluid fraction are derived. Our results are tested by comparing the findings computed by quantum Monte Carlo simulations. We present also a systematic investigation of the collective modes of a Bose condensate confined in an external trap. Our predictions are in qualitative agreement with previous experimental and theoretical results. We show in particular that our theory is capable of explaining the so-called anomalous behavior of the m = 0 mode.
Taking inspiration from the state-of-the art knowledge of the Bose-Hubbard (BH) model and recent methodological developments in its fermionic counterpart, this work deals with the study of the collective dynamics of a lattice Bose gas beyond the mean-field picture through a quantum description of its elementary excitations. The Hamiltonian quantization, performed via a Bogoliubov quadratization of the BH action within the Gutzwiller approach, allows to expand the effective action of the theory up to second order in the fluctuations around the mean-field solution, as well as to prefigure the possibility of identifying the main decay vertices of the collective modes and other effects that are not evident at the second-order level. This quantum description extends the standard Bogoliubov approach to the study of superfluid Bose systems for comprising higher excitation branches, including the Higgs mode in the superfluid phase, and identifies their physical meaning together with appropriate observables which could be taken into consideration for their experimental characterization. The ultimate aim of the quantization procedure is the determination of fundamental quantities as the depletion of the condensate and the effective superfluid fraction, which are not accessible by a mean-field description or not completely characterized in the regime of strong interactions.
Abstract We study the propagation of the two sound modes in two-dimensional Bose gases across the Berezinksii–Kosterlitz–Thouless transition using classical-field dynamics, which is motivated by recent measurements of Christodoulou et al (2021 Nature 594 191). Based on the dynamic structure factor (DSF), we identify the two sound modes as the Bogoliubov (B) and the non-Bogoliubov (NB) sound mode below the transition, and as the diffusive and the normal sound mode above the transition. The NB sound mode velocity is higher than the B sound mode velocity, which we refer to as the weak-coupling regime of the sound modes. We excite the sound modes by driving the system as in the experiment and by perturbing the density with a step-pulse perturbation, as a secondary comparison. The driven response depends on the driving strength and results in higher velocities for the B sound mode at high temperatures near the transition, compared to the sound results of the DSF and step-pulse excitation. We show that the higher mode velocity has a weak temperature dependence across the transition, which is consistent with the experimental observation.