Bose-Einstein Condensation in a Circular Waveguide

We have produced Bose-Einstein condensates in a ring-shaped magnetic waveguide. The few-millimeter diameter, nonzero-bias ring is formed from a time-averaged quadrupole ring. Condensates that propagate around the ring make several revolutions within the time it takes for them to expand to fill the ring. The ring shape is ideally suited for studies of vorticity in a multiply connected geometry and is promising as a rotation sensor.

Figure 1

Forming a circular magnetic waveguide. (a) Four coaxial circular electromagnets (see 21 for details) are used to generate both the static (currents as shown) and rotating fields needed for the waveguide. Axes are indicated; gravity points along $-\widehat{z}$. (b) As shown schematically, the field (arrows) from just the two outer coils (curvature coils, outer pair) points axially in the midplane between the coils, with largest fields at the axis. (c) Adding a uniform opposing bias field (using antibias coils, inner pair) produces a ring of field zeros (×) in the $\widehat{x}\mathrm{\text{−}}\widehat{y}$ plane around which weak-field seeking atoms (shaded region) are trapped. (d) Rapidly rotating the field zeros around the trapped atoms produces the TORT.

Figure 2

Atoms in a ring-shaped magnetic trap. Shown are top (a)–(f) and side (g)–(i) absorption images of ultracold ${}^{87}\mathrm{Rb}$ clouds in either a $Q$ ring (a)–(c) or TORT (d)–(i) with applied side field $B_s=9.2$ (left), 0 (middle), and $-2.5\mathrm{G}$ (right column), respectively, in the $\widehat{x}$ direction. Images were taken 2 ms after turning off the traps. The applied field tilts the $Q$ ring or TORT and favors atomic population in one side or another of the trap. For $B_s\sim 0$, the trap lies nearly in the horizontal plane and its azimuthal potential variation is minimized. For the $Q$ ring, $B_0=22\mathrm{G}$; for the TORT, $B_0=20\mathrm{G}$ and $B_{\mathrm{rot}}=17\mathrm{G}$; and $B_z^{\prime \prime }=5300\mathrm{G}/{\mathrm{cm}}^2$ for both. The temperature of trapped atoms is $90\mu \mathrm{K}$ in the $Q$ ring, and $10\mu \mathrm{K}$ in the TORT. Resonant absorption ranges from 0 (blue) to $>80\%$ (red).

Figure 3

Elimination of Majorana losses in the TORT. The measured number of trapped atoms in a $Q$ ring (open circles) or TORT (solid circles) trap is shown vs residence time in the trap. Exponential fits indicate a 3 s Majorana-loss-limited lifetime in the $Q$ ring. In the TORT, following an initial (30 s) loss of atoms due to evaporation, a vacuum limited lifetime of 90 s was observed. Settings for $B_0$, $B_z^{\prime \prime }$, and $B_{\mathrm{rot}}$ are as in Fig. 2, $B_s\sim 0$, and the initial temperature is $60\mu \mathrm{K}$.

Figure 4

Circular motion of a quantum degenerate atomic beam in a waveguide. A Bose-Einstein condensate was launched into a balanced TORT and allowed to propagate. (a) Top view in-trap absorption image during the propagation. The mean azimuthal position of the BEC measured from such images is shown in (b). Annular portions (indicated by dashed circles) of top-view images taken at different guiding times are shown in (c) displayed in polar coordinates (radius vs azimuthal angle). The beam advances at an angular velocity of $40.5\mathrm{rad}/\mathrm{s}$ while expanding due to an rms azimuthal velocity spread of $1.4\mathrm{mm}/\mathrm{s}$. After 1 s, the beam fills the entire guide.