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

Abstract

We report on the experimental investigation of the response of a three-dimensional Bose-Einstein condensate (BEC) in the presence of a one-dimensional (1D) optical lattice. By means of Bragg spectroscopy we probe the band structure of the excitation spectrum in the presence of the periodic potential. We selectively induce elementary excitations of the BEC choosing the transferred momentum and we observe different resonances in the energy transfer, corresponding to the transitions to different bands. The frequency, the width and the strength of these resonances are investigated as a function of the amplitude of the 1D optical lattice.PACS numbers: 67.85. Hj, 67.85.De The knowledge of the linear response of a complex system gives crucial information about its many-body behavior. For example, the superfluid properties of a three-dimensional (3D) Bose-Einstein condensate (BEC) are related to the linear part of the phononic dispersion relation at low momenta [1]. The presence of optical lattices enriches the excitation spectrum of a BEC in a remarkable way. For deep three-dimensional lattices, the gas enters the strongly correlated Mott insulator phase and the spectrum exhibits a gap at low energies [2]. The response of a BEC in the superfluid phase is also drastically modified by the presence of a one-dimensional (1D) optical lattice [3,4,5,6,7]. Indeed, as in any periodic system, energy gaps open in the spectrum at the multiples of the lattice momentum and it is possible to excite several states corresponding to different energy bands at a given value of the momentum transfer [8,9]. In addition, the linear dispersion relation of the superfluid, and thus its sound velocity, is changed. In the mean-field regime of interactions these peculiar features of the excitations of a superfluid BEC in the presence of an optical lattice are captured by the Bogoliubov theory [1].Bragg spectroscopy represents an excellent experimental tool to investigate the linear response of gaseous BECs [10]. 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. We measure the resonance frequencies, the strengths and the widths of the transitions to different bands of the 1D optical lattice. The measurements are quantitatively compared with Bogoliubov mean-field calculations for our experimental system [7]. We produce a 3D cigar-shaped BEC of N≃ 3 × 10 5 87 Rb atoms in a Ioffe-Pritchard magnetic trap whose

Multi-band spectroscopy of inhomogeneous Mott-insulator states of ultracold bosons

“…Our experimental resolution is good enough to observe that this spread in energy is a small fraction of the energy bandwidth. As it is shown on figure 5(b), the experimental spectrum of this phase-coherent system (s y = 9, s ⊥ = 0) exhibits several well-defined resonances corresponding to excitations created in the different lattice bands [48].…”

“…As demonstrated for example in [48], the presence of a periodic potential implies the existence of different energy bands in the excitation spectrum, the so-called Bloch bands (see figure 5(a)). The typical tunneling time of atoms in a lattice is ∼h/J .…”

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].…”

Anisotropic superfluidity of two-dimensional excitons in a periodic potential

“…Considerable success in this field has been attained with atomic systems in laser traps 81 : excitation spectrum measurements by Bragg spectroscopy were performed 82 , a roton-maxon form of the excitation spectrum has been demonstrtated 83 , processes similar to Bloch oscillations in crystals have been observed 84 . From the theory side ground state and excitation spectrum have been calculated for models with a one-dimensional periodic potential 85 and effects similar to the ones for electrons in a crystal have been predicted, such as Bloch oscillations 86 .…”