Routes Towards Anderson-Like Localization of Bose-Einstein Condensates in Disordered Optical Lattices

We investigate, both experimentally and theoretically, possible routes towards Anderson-like localization of Bose-Einstein condensates in disordered potentials. The dependence of this quantum interference effect on the nonlinear interactions and the shape of the disorder potential is investigated. Experiments with an optical lattice and a superimposed disordered potential reveal the lack of Anderson localization. A theoretical analysis shows that this absence is due to the large length scale of the disorder potential as well as its screening by the nonlinear interactions. Further analysis shows that incommensurable superlattices should allow for the observation of the crossover from the nonlinear screening regime to the Anderson localized case within realistic experimental parameters.

Figure 1

Typical absorption images of a BEC with $N=7\times {10}^4$ released from the combined MT plus DP (left column) and MT plus OL plus DP (right column). The second row shows the column density and the third row shows the result of a 1D simulation. The lattice depth was $6.5E_r$ and the DP had a depth of $0.2E_r$.

Figure 2

Size of the central peak after 20 ms of ballistic expansion versus the number of atoms. The clouds were released from the following potentials MT (○) (red online), MT plus DP (□) (black online), MT plus OL (◃) (blue online), MT plus DP plus OL (▹) (green online). The lines correspond to a theoretical prediction (see text). The lattice depth was $6.5E_r$ and the DP had a depth of $0.1E_r$.

Figure 3

Superfluid fraction as a function of the coupling constant $g$ obtained from a 1D GPE simulation for a pseudorandom potential. Full (open) symbols correspond to a trap frequency of $2\pi \times 14\mathrm{Hz}$ ($2\pi \times 4\mathrm{Hz}$).

Figure 4

Ground states of the GPE (note the varying logarithmic scales) for a condensate in the combined potential of the MT, OL, and pseudorandom potential. The depth of the OL is $6.5E_r$ while the depths of the additional lattices forming the pseudorandom potential are $0.2E_r$. The coupling constants $g$ for the panels are 0.5 (a), 8 (b), 256 (c). Oscillator units corresponding to a trap frequency of $2\pi \times 4\mathrm{Hz}$ are used.

Figure 5

Atomic density after 20 ms of ballistic expansion for a condensate prepared initially in the states shown in Fig. 4 (left column) and without DP (right column). Oscillator units corresponding to a trap frequency of $2\pi \times 4\mathrm{Hz}$ are used.