Effect of Optical Disorder and Single Defects on the Expansion of a Bose-Einstein Condensate in a One-Dimensional Waveguide

We investigate the one-dimensional expansion of a Bose-Einstein condensate in an optical guide in the presence of a random potential created with optical speckles. With the speckle the expansion of the condensate is strongly inhibited. A detailed investigation has been carried out varying the experimental conditions and checking the expansion when a single optical defect is present. The experimental results are in good agreement with numerical calculations based on the Gross-Pitaevskii equation.

Figure 1

(a) rms radius of the condensate expanding in the $\mathrm{\text{optical linear guide}}+\mathrm{\text{speckle potential}}$ as a function of time for three different values of the speckle height with $V_S/\mu <1$. (b) Corresponding center of mass motion. The lines are guides for the eyes.

Figure 2

(a) left: picture of the speckle potential and in situ density profiles of the condensate after 118 ms of expansion in the linear guide for $0<V_S<1.7\mathrm{kHz}$. right: density profile of the condensate released from the $\mathrm{\text{crossed dipole trap}}+\mathrm{\text{speckle potential}}$ after 18 ms of free expansion. (b) For two different positions of the speckle field we show the density distribution of the atomic cloud after 300 ms of expansion in the linear optical guide with the speckle switched on abruptly and $V_S=2\mathrm{kHz}$.

Figure 3

(a) Intensity profile of the laser beam creating the single defect and density profiles of the condensate after 300 ms of expansion for $500\mathrm{Hz}<V_w<9.0\mathrm{kHz}$ either adiabatically or abruptly adding the defect. (b) Number of atoms trapped in the single defect as a function of $V_w$ when the potential well is switched on adiabatically.

Figure 4

Calculated density profiles after 75 ms of expansion for random potential (a), single Gaussian well (b), and periodic potential (c), compared with the free expansion case (dashed line). In all three cases the potential height is $0.4\mu$.

Figure 5

Top: Schematic of the experiment. Bottom: Density profiles of the condensate performing dipole oscillations in the magnetic trap and interacting with a single well.