Measurement of Spectral Functions of Ultracold Atoms in Disordered Potentials

Abstract : We report on the measurement of the spectral functions of non-interacting ultra-cold atoms in a three-dimensional disordered potential resulting from an optical speckle field. Varying the disorder strength by two 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. Introduction.— The spectral function provides essential information on the energy-momentum relation of one-particle excitations in complex systems. This relation takes a non-trivial form in the presence of random scatterers or inter-particle interactions [1]. The direct measurement of the spectral function via angle-resolved photoemission spectroscopy (ARPES) [2] in strongly correlated electronic systems has led to significant progress in the understanding of high-T c superconductivity [3]. More recently, the ability to measure and exploit spectral functions in ultracold atomic systems has also been widely demonstrated, for instance using radio-frequency spectroscopy [4, 5] to reveal the presence of a pseudo-gap in strongly interacting Fermi gases [6, 7], or to probe the Mott insulator and superfluid regimes of interacting Bose gases in periodic lattices using Bragg spectroscopy [8–10].