Distillation of Bose-Einstein Condensates in a Double-Well Potential

Bose-Einstein condensates of sodium atoms, prepared in an optical dipole trap, were distilled into a second empty dipole trap adjacent to the first one. The distillation was driven by thermal atoms spilling over the potential barrier separating the two wells and then forming a new condensate. This process serves as a model system for metastability in condensates, provides a test for quantum kinetic theories of condensate formation, and also represents a novel technique for creating or replenishing condensates in new locations.

Figure 1

Scheme for distillation of condensates in a double-well potential. (a) Condensates are loaded into the left well. (b) A new ground state is created by linearly ramping the trap depth of the right well from zero to the final value. (c) Atoms transfer into the right well via high-energy thermal atoms, and a new condensate starts to form in the right well. (d) The whole system has equilibrated. $V$ denotes the height of the potential barrier between the two wells, which is measured with respect to the bottom of the left well, and $\Delta U$ the trap depth difference between the two wells.

Figure 2

Time evolution of atom clouds in a double-well potential. The left (right) well appears as the top (bottom) atom cloud in the images. A condensate was distilled from the left to the right well. The absorption images were taken for various hold times after creating the right well. The field of view of each absorption image is $130\mu \mathrm{m}\times 1160\mu \mathrm{m}$. The trap depths were $U_L=k_B\times 2.4\mu \mathrm{K}$ (left well) and $U_R=k_B\times 2.9\mu \mathrm{K}$ (right well) with a potential barrier of $V=k_B\times 510\mathrm{nK}$ between them. During the hold time, the radial separation between the potential wells was $d=15.9\mu \mathrm{m}$.

Figure 3

Approach to thermal equilibrium in a double-well potential. The temperature and the number of condensed atoms in each well are shown as a function of hold time after creating the right well. Open and solid circles represent atoms in the left and the right well, respectively. Every data point is averaged over three measurements, and the error bar shows $\pm$ one standard deviation. The experimental parameters are the same as for the results shown in Fig. 2.

Figure 4

Onset time of condensation. The onset time in the right well was measured by observing the appearance of a matter wave interference pattern when the condensates were released from the double-well potential. The trap depth difference is defined as $\Delta U=U_R-U_L$. $U_L$ was kept at $k_B\times 2.4\mu \mathrm{K}$ for all experiments. The separations of the two wells, $d$, were $14.3\mu \mathrm{m}$ (open circle), $15.1\mu \mathrm{m}$ (solid circle), and $15.9\mu \mathrm{m}$ (open square). Interference fringes were not observed at $\Delta U=-k_B\times 240\mathrm{nK}$ even after 20 s hold time. The inset shows the same data plotted vs $V-\Delta U/2$, where $V$ is the height of the potential barrier.