Measurement of Spectral Functions of Ultracold Atoms in Disordered Potentials

Abstract

We report on the measurement of the spectral functions of noninteracting ultracold atoms in a three-dimensional disordered potential resulting from an optical speckle field. Varying the disorder strength by 2 orders of magnitude, we observe the crossover from the "quantum" perturbative regime of low disorder to the "classical" regime at higher disorder strength, and find an excellent agreement with numerical simulations. The method relies on the use of state-dependent disorder and the controlled transfer of atoms to create well-defined energy states. This opens new avenues for experimental investigations of three-dimensional Anderson localization.

Ultracold atoms in disordered potentials: elastic scattering time in the strong scattering regime

“…To get further insight, we show in a second step that these deviations can be traced to the peculiar behavior of the spectral functions for such disordered potentials [46,47]. Indeed, we recover full consistency between our measurements of t s and the width of the spectral functions when considering the real profiles that have been measured independently using an radio-frequency spectroscopic method, see [48].…”

“…The spectral function  ( ) A k , i gives the probability distribution for an excitation of momentum k i to have a certain energy  , thereby generalizing the concept of dispersion relation. It is for instance used to describe quasi-particles in many-body physics [44,[51][52][53][54][55][56] or in disordered systems [14,16,17,[46][47][48]. Of particular .…”

“…A full understanding requires to explore in detail the features of the real spectral functions, which can in those cases exhibit complicated profiles. We perform such an analysis on the basis of the spectral functions measured in [48] in the specific case of k i =0. We show that the differences reported between attractive and repulsive laser speckle disorder are at the root of the distinct behaviors that we observe on the scattering time t s .…”

“…To further investigate the different behaviors of t s , a comparison to the real spectral functions is needed. Experimentally, spectral functions of matter-waves in laser speckle disorder have been measured in the specific case k i =0 and for a large set of disorder strength | | , although deviations due to quantum corrections still persist around ~0 [48]. For those measured spectral functions, we extract the FWHM from a fit and we deduce the elastic scattering time t s sf in the limit k i =0 as a function of | | V R (appendix C).…”

Properties of the superfluid in the disordered Bose-Hubbard model

“…For bosons, where interactions play a crucial role, the disordered Bose-Hubbard model (DBHM) allows one to study the interplay between correlation and disorder. Ever since the seminal work of Fisher et al [1], this model has received a lot of attention and its properties have been explored using renormalization-group (RG) approaches and numerical techniques, as well as experiment [1][2][3][4][5][6][7][8][9][10][11].…”