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arXiv:0707.2937

Excitation Spectra of Correlated Lattice Bosons in a Confining Trap

Dmitry L. Kovrizhin, G. Venketeswara Pai, Subhasis Sinha

Published Jul 19, 2007• 0 citations
arXivHTMLPDF

Abstract

We consider ultracold bosonic atoms in an optical lattice with an external trapping potential. To study the excitation energies of the resulting Bose-Hubbard model, we develop a method based on a time-dependent generalization of the Gutzwiller ansatz. We calculate the excitations of the homogeneous system both in insulating and superfluid regime, concentrating particularly on those near the superfluid-Mott insulator boundary. Low-lying excitation energies in presence of a static harmonic trap are obtained using this method and compared with the homogeneous case. Further, we explore the dynamics of the center of mass and the breathing mode in response to time-dependent perturbations of the trap.

DOI
10.48550/arxiv.0707.2937

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We consider ultracold bosonic atoms in an optical lattice with an external trapping potential. To study the excitation energies of the resulting Bose-Hubbard model, we develop a method based on a time-dependent generalization of the Gutzwiller ansatz. We calculate the excitations of the homogeneous system both in insulating and superfluid regime, concentrating particularly on those near the superfluid-Mott insulator boundary. Low-lying excitation energies in presence of a static harmonic trap are obtained using this method and compared with the homogeneous case. Further, we explore the dynamics of the center of mass and the breathing mode in response to time-dependent perturbations of the trap.
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.
We investigate the breathing mode of harmonically trapped bosons in an optical lattice at small site occupancies. The Bose-Hubbard model with a trapping potential is used to describe the breathing-mode dynamics initiated through weak quenches of the trap strength. We connect to results for continuum bosons (Lieb-Liniger and Gross-Pitaevskii results) and also present deviations from continuum physics. We take a spectral perspective, identifying the breathing-mode frequency with a particular energy gap in the spectrum of the trapped Bose-Hubbard Hamiltonian. We present the low-energy eigenspectrum of the trapped many-boson system and study overlaps of the initial state with eigenstates of the quenched Hamiltonian. There is an intermediate interaction regime, between a ``free-boson'' limit and a ``free-fermion'' limit, in which the Bose-Hubbard breathing-mode frequency approaches the Gross-Pitaevskii prediction. In addition, we present a striking failure of the time-dependent Gutzwiller approximation for describing breathing modes.
Motivated by recent developments in experimental studies of Bose–Fermi mixtures, we investigate monopole oscillation dynamics of Bose–Fermi mixtures in a three-dimensional (3D) optical lattice and an external isotropic harmonic trap potential. We use dynamical Gutzwiller approximation and calculate time dependence of the average spatial extent of particles in a coexisting phase where superfluid bosons and metal fermions coexist. With the trap potential, the bosons concentrate at and around the center of the potential and the fermions surround the bosons. They begin to demonstrate monopole oscillations when the trap potentials are suddenly changed to the ones with smaller curvature. In particular, the correlation between the oscillations of the bosons and fermions is different depending on the condition of the initial confinement. We also show the case where only one of the two trap potentials is changed.
We study the dynamic response of ultracold bosons trapped in one-dimensional optical lattices using Quantum Monte Carlo simulations of the boson Hubbard model with a confining potential. The dynamic structure factor reveals the inhomogeneous nature of the low temperature state, which contains coexisting Mott insulator and superfluid regions. We present new evidence for local quantum criticality and discuss implications for the experimental excitation spectrum of 87Rb^{87}\mathrm{Rb}87Rb atoms confined in one dimension.
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.
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.