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arXiv:1106.0575 · Physical Review A

Collective modes of a strongly interacting Bose gas: Probing the Mott transition

Michiel Snoek

Published Jan 25, 2012• 8 citations
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Abstract

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.

DOI
10.1103/physreva.85.013635

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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.
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.
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.
Ultracold bosonic gases in optical lattices are strongly correlated quantum systems similar to solids. The strong correlation between the electrons in a solid on the one hand, and the bosonic atoms in optical lattice on the other, exhibit various quantum phenomena like insulation, conductivity, localization of electrons and atoms, respectively. Controlled by the intensity of the lattice laser, the ultracold bosonic gas can be transferred from a regime with superfluid character for shallow lattices into a regime of strong correlations, the Mott insulator. As an additional external parameter besides the lattice depth, one can generate spatial inhomogeneities by superimposing an additional standing wave (so-called two-color superlattices), which gives rise to localization effects or the formation of a Bose-glass phase. In the present work, numerical simulations are employed in order to investigate characteristic signatures of the quantum phases in the low-energy excitation spectrum of one-dimensional systems. We simulate temporal small amplitude modulations of the optical lattice in analogy to experiments, and evaluate the response of the system from the time-evolved initial state. The lattice systems are described in the framework of the Bose-Hubbard model. For the evaluation of the time-evolved state, we employ several numerical methods. We analyze systems of small size (6 particles on 6 sites) using an exact time-evolution by integration of the time-dependent Schrödinger equation. The formulation of an importance truncation scheme enables us to retain only the relevant components of the model space in the strongly correlated regime and, thus, allows for the investigation of systems with 10 particles on 10 sites using exact time-evolution. Based on this method, we present results of the Mott-insulating regime as well as for the Bose-glass phase. Furthermore, we employ particle-hole methods, which allow for the treatment of systems with experimental lattice sizes and particle numbers. Starting from the equation of motion method we adapt the Tamm-Dancoff approximation as well as the random-phase approximation for the occupation number representation of the Bose-Hubbard model. We present results of simulations of up to 50 particles on 50 sites and discuss the impact of the lattice depth on the low-energy excitations (U-resonance). Moreover, the impact of a two-color superlattice and the variation of its amplitude is investigated.
We report on the realization of a trapped one-dimensional Bose gas and its characterization by means of measuring its lowest lying collective excitations. The quantum degenerate Bose gas is prepared in a 2D optical lattice, and we find the ratio of the frequencies of the lowest compressional (breathing) mode and the dipole mode to be (omega(B)/omega(D))(2) approximately 3.1, in accordance with the Lieb-Liniger and mean-field theory. For a thermal gas we measure (omega(B)/omega(D))(2) approximately 4. By heating the quantum degenerate gas, we have studied the transition between the two regimes. For the lowest number of particles attainable in the experiment the kinetic energy of the system is similar to the interaction energy, and we enter the strongly interacting regime.
Abstract. 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 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.