Density modulations in an elongated Bose-Einstein condensate released from a disordered potential

Abstract

We observe large density modulations in time-of-flight images of elongated Bose-Einstein condensates, initially confined in a harmonic trap and in the presence of weak disorder. The development of these modulations during the time-of-flight and their dependence with the disorder are investigated. We render an account of this effect using numerical and analytical calculations. We conclude that the observed large density modulations originate from the weak initial density modulations induced by the disorder, and not from initial phase fluctuations (thermal or quantum).

Cold bosons in optical lattices

“…There permanently appear new interesting results. For instance, density modulations in an elongated BEC with a disorder potential were observed [478]. The direct observation of the Anderson localization [358] of boson matter waves in a one-dimensional non-interacting BEC with disorder was announced [479,480].…”

Bose systems in spatially random or time-varying potentials

“…Experimentally, such random potentials are realized by means of optical speckles [14][15][16][17]. Physical properties of these Bose systems in an external random potential have been theoretically studied for the case of weak disorder [18][19][20][21] and for arbitrarily strong disorder [22,23].…”

Experimental studies of Bose–Einstein condensates in disorder

“…We find the positions of these irregularly spaced fringes are reproducible in repeated measurements, even with different holding times of the BEC in the disordered potential. Another recent experiment [22] has reported reproducible fringes in TOF images of a disordered 87 Rb BEC. The reproducibility suggests that these fringes are unlikely due to some initial (before release) phase fluctuations [34] in the disordered BEC, or due to interference of a few BECs separated by high potential barriers with no well defined relative phase between them, as in either of these scenarios the fringe positions are not expected to be reproducible.…”

“…Numerical simulations based on the Gross-Pitaevskii equation [19,22] have shown that such interference can occur when moderate disorder-induced density fluctuations cause different parts of a phase coherent BEC to expand with different velocities and overlap. As V D is increased from 0, the contrast of the interference is expected to increase at small V D .…”

“…Studying disordered BECs may also provide valuable insights to understand the behaviors of nonlinear systems in the presence of randomness. Since 2005, there have been a flurry of experimental activities [16][17][18][19][20][21][22][23][24][25][26][27] to study BECs in disordered potentials. The physics investigated have included disorder induced inhibition of transport [16][17][18][19]21], effects of disorder on collective modes [16,21,24], Bose glass [20], granular BEC and phase coherence [21], density modulations [21,22], disordered Bose-Hubbard model [23], Anderson localization [25,26] and solitons in disorder [27].…”