Phase coherence and superfluid-insulator transition in a disordered Bose-Einstein condensate

Abstract

We have studied the effects of a disordered optical potential on the transport and phase coherence of a Bose-Einstein condensate ͑BEC͒ of 7 Li atoms. At moderate disorder strengths ͑V D ͒, we observe inhibited transport and damping of dipole excitations, while in time-of-flight images, random but reproducible interference patterns are observed. In situ images reveal that the appearance of interference is correlated with density modulation, without complete fragmentation. At higher V D , the interference contrast diminishes as the BEC fragments into multiple pieces with little phase coherence. The behavior of a superfluid or a superconductor in the presence of disorder is of fundamental interest. A superfluid can flow without friction around obstacles, and a superconductor can have zero resistance despite material defects. On the other hand, disorder is able to localize particles, resulting in an insulating state ͓1͔. Experimentally, disorder-induced superfluid/superconductor to insulator transitions ͑SIT͒ have been probed in many systems, including superfluid helium in porous media ͓2͔, thin-film and granular superconductors ͓3,4͔, and random Josephson junction arrays ͓5͔. While many believe that such a SIT is a quantum phase transition driven by quantum fluctuations, it remains a central task to understand exactly how the superfluid/superconducting order parameter, which consists both an amplitude and a phase, may be destroyed with increasing disorder. Numerous fundamental questions remain, such as the nature of the insulator, the fate of phase coherence throughout the transition, and the possibility of intermediate metallic phases ͓3,6,7͔.Cold atoms, with their intrinsic cleanliness coupled with remarkable controllability of physical parameters, have emerged as exceptional systems to study various condensed matter problems. Recently, several experiments ͓8-11͔ have studied 87 Rb condensates in random optical potentials and observed, for example, damping of collective excitations ͓8͔ and inhibition of expansion ͓9-11͔ due to disorder. Another experiment ͓12͔ has examined a Bose-Einstein condensate ͑BEC͒ in an incommensurate ͑quasirandom͒ optical lattice in order to investigate a possible "Bose-glass" phase ͓13͔. Experiments with disordered atomic quantum gases may provide unique insights into disordered quantum systems and may uncover a rich variety of quantum phases ͓14͔.Here we report experiments on a BEC of interacting 7 Li atoms subject to a well-controlled disordered potential. While we corroborate previous transport measurements ͓8-11͔, we have also probed the ground-state density distribution and phase coherence of the disordered BEC by performing both in situ and time-of-flight ͑TOF͒ imaging. While disorder inhibits transport of the BEC, reproducible TOF interference patterns are observed for intermediate disorder strengths V D , reflecting an underlying phase coherence in the disordered BEC. At stronger V D , the interference contrast diminishes as the BEC fragments into a "granular" condensate, which...

Mean-field phase diagram of the one-dimensional Bose gas in a disorder potential

“…Anderson localization has been experimentally observed recently in one-dimensional bosonic systems with vanishing interaction [2,3]. More recent experiments have moved away from the limit of vanishing interactions to study the insulator to superfluid phase transition [4,5].…”

“…We make the general choice of Gaussdistributed disorder. We are aware that many experiments aimed at the characterization of the phase transition deal with speckle potentials [2,5]. These potentials have a lower bound and their statistical distribution does not show a lower Gaussian tail.…”

“…More recently, several experimental works have addressed the quite different regime where the gas is in the weakly interacting limit and with many particles in each potential minimum. Above a critical strength of the disorder, fragmentation of the condensate density and loss of spatial coherence were identified [4,5]. All these experiments have considered the one-dimensional geometry.…”

Collective excitation of a Bose-Einstein condensate by modulation of the atomic scattering length

“…Fundamental information about condensate dynamics can be determined from observations of collective modes [1][2][3], including the effects of temperature [4][5][6], and the dimensionality of the system [7]. In addition, the interplay between these modes and external agents, such as random potentials [8,9], lattices [10,11], as well as other atoms [12][13][14][15][16], can be investigated. Examining the excitation spectrum of the BEC allows for a detailed comparison with theoretical models [17][18][19][20] and related quantum systems such as superfluid helium [21,22] and superconductors [23,24].…”

Disorder-induced vortex lattice melting in a Bose-Einstein condensate

“…Random potential in BEC can be created by optical speckles [2][3][4]. Bose-Einstein condensates in random potential has emerged as an ideal ground for studying several problems such as Anderson localization [5], superfluid behavior [6], superfluid-Mottinsulator transition [7,8], Bose glass and their microscopic properties [9,10], superconductivity and quantum magnetism etc [11].…”