Vortex Formation by Merging of Multiple Trapped Bose-Einstein Condensates

We report observations of vortex formation by merging and interfering multiple ${}^{87}\mathrm{Rb}$ Bose-Einstein condensates (BECs) in a confining potential. In this experiment, a single harmonic potential well is partitioned into three sections by a barrier, enabling the simultaneous formation of three independent, uncorrelated BECs. The BECs may either automatically merge together during their growth, or for high-energy barriers, the BECs can be merged together by barrier removal after their formation. Either process may instigate vortex formation in the resulting BEC, depending on the initially indeterminate relative phases of the condensates and the merging rate.

Figure 1

(a) Potential-energy contours of a horizontal slice through the center of our triple-well trap, representing the addition of the potential-energy profiles of our TOP trap and barrier beam. (b) The binary transmission mask used to create the optical barrier. (c) An image of the optical barrier. (d),(e) Phase-contrast images of trapped condensates as viewed along the trap axis. Each shows an area of $85\mu \mathrm{m}$ per side, as do (a) and (c). In (d), three condensates are created in the presence of a strong barrier beam with $170\mu \mathrm{W}$. (e) With $45\mu \mathrm{W}$ in the beam, the initial three condensates merge together during evaporative cooling. A hole in the BEC is formed by the barrier beam displacing atoms from the trap center.

Figure 2

(a)–(d) $170\mathrm{\text{−}}\mu \mathrm{m}$ wide images showing vortices in condensates created as a strong ($k_B\times 26\mathrm{nK}$) barrier was ramped off over the time $\tau$ indicated. (e) Vortex observation fraction $F_v$ vs $\tau$. The data for $\tau$ values of 50 ms, 200 ms, 500 ms, 1 sec, 3 sec, and 5 sec, consisted of 5, 11, 10, 10, 5, and 5 images, respectively. For clarity, statistical uncertainties due to finite sample sizes are not shown, but they generally exceed our counting uncertainties. The expected lower limit of $F_v\sim P_v=0.25$ is represented by a dashed line.

Figure 3

(a),(b) $170\mathrm{\text{−}}\mu \mathrm{m}$ wide images showing vortices naturally occurring in condensates created in a trap with a $k_B\times 7\mathrm{nK}$ barrier. (c)–(h) Images obtained using various barrier energies. (i),(j) BECs created without an optical barrier.