Bragg spectroscopy of a superfluid Bose–Hubbard gas

Abstract

Bragg spectroscopy is used to measure excitations of a trapped, quantum-degenerate gas of 87 Rb atoms in a 3-dimensional optical lattice. The measurements are carried out over a range of optical lattice depths in the superfluid phase of the Bose-Hubbard model. For fixed wavevector, the resonant frequency of the excitation is found to decrease with increasing lattice depth. A numerical calculation of the resonant frequencies based on Bogoliubov theory shows a less steep rate of decrease than the measurements.PACS numbers: 03.75.Kk, 03.75.Lm, 05.30.Jp, 32.80.Pj Quantum-degenerate atoms in optical lattices form a strongly interacting many-body system whose parameters can be readily controlled. As first pointed out by Jaksch et al., [1] bosonic atoms in an optical lattice constitute a nearly ideal realization of the Bose-Hubbard model [2].This model predicts a superfluid to Mott insulator quantum phase transition that has been observed by Greiner et al. [3]. Since then, this field has attracted great interest due to its potential for the realization of quantum computation and quantum simulation of strongly-correlated manybody systems [4].A key property of a quantum gas is its excitation spectrum. Excitations of a Bose-Hubbard gas by a gradient of magnetic field [3] or a modulated optical lattice depth [5,6] have been previously observed. However, neither of these techniques directly probes the linear excitation spectrum of the gas, since a tilted lattice perturbs the gas only at zero frequency, and a modulated optical lattice only at zero quasi-momentum. The latter case results in a nonlinear excitation spectrum that has been analyzed only very recently [7]. Bragg spectroscopy has been demonstrated as a probe of the linear excitation spectrum of a Bose-Einstein condensate [8][9][10][11], and has also been proposed as a method to study the Mott insulator phase of the Bose-Hubbard

Ultracold bosons with short-range interaction in regular optical lattices

“…18. In the absence of interactions (U = 0), b K = ±1 and the normalization condition (191) cannot be fulfilled which means that the bound state does not exist in this case. As soon as the interactions are present (U = 0), |b K | < 1 which guarantees the normalization.…”

Properties of spin–orbit-coupled Bose–Einstein condensates

“…This experimental technique has become a standard method for measuring the collective excitations of a BEC [128]. Since its first employment in BEC systems [129], Bragg spectroscopy has been used to reveal excitations in diverse situations, such as homogeneous BECs [131][132][133], BECs in optical lattices [134][135][136][137], and dipolar BECs [138].…”

Excitations of Bose-Einstein condensates in a one-dimensional periodic potential

“…It has allowed to measure the dispersion relation of interacting BECs in the mean-field regime [11,12,13] In this work we use Bragg spectroscopy to probe the excitation spectrum of a 3D BEC loaded in a 1D optical lattice. Previous experimental studies have so far investigated the excitations of superfluid BECs within the lowest energy band of a 3D optical lattice by means of lattice modulation [19] and Bragg spectroscopy [18,20]. This paper presents a detailed experimental study of the different bands in the excitation spectrum of an interacting 3D BEC in the presence of a 1D optical lattice.…”

“…Previous experimental studies have so far investigated the excitations of superfluid BECs within the lowest energy band of a 3D optical lattice by means of lattice modulation [19] and Bragg spectroscopy [18,20]. This paper presents a detailed experimental study of the different bands in the excitation spectrum of an interacting 3D BEC in the presence of a 1D optical lattice.…”