Time-averaged adiabatic ring potential for ultracold atoms

We report the experimental realization of a versatile ring trap for ultracold atoms. The ring geometry is created by the time-averaged adiabatic potential resulting from the application of an oscillating magnetic bias field to a rf-dressed quadrupole trap. Lifetimes for a Bose-Einstein condensate in the ring exceed $11\mathrm{s}$ and the ring radius was continuously varied from $50\hspace{0.5em}\mu \text{m}$ to $262\hspace{0.5em}\mu \text{m}$. An efficient method of loading the ring from a conventional time-averaged orbiting potential trap is presented together with a rotation scheme which introduces angular momentum into the system. The ring presents an opportunity to study the superfluid properties of a condensate in a multiply connected geometry and also has applications for matter-wave interferometry.

Figure 1

Absorption image of atoms confined in the TAAP ring trap. In (a) the cloud of atoms has a radius of $262\hspace{0.5em}\mu \text{m}$ and in (b) the radius is $71\hspace{0.5em}\mu \text{m}$. This change is achieved by increasing the gradient of the quadrupole field from (a) $65.3\hspace{0.5em}$G/cm to (b) $277.1\hspace{0.5em}$G/cm. In both cases ${\omega }_{\mathrm{rf}}=2\pi \times 1.4\hspace{0.5em}\text{MHz}$, $B_{\mathrm{rf}}=0.8\hspace{0.5em}\text{G}$, and $B_T^z=0.9\hspace{0.5em}\text{G}$.

Figure 2

The isosurface of constant $|\mathbf{B}(\mathbf{r})|$ for an rf-dressed quadrupole on which the atoms are trapped. The atoms’ position around the ellipsoid is determined by the balance between gravity and the variation of the Rabi frequency ${\Omega }_R(\mathbf{r})$. A cross section of the potential (with gravity included) in the $x=0$ plane for circularly polarized rf is projected on the left side of the figure. For this polarization ${\Omega }_R(\mathbf{r})$ varies smoothly from zero at A to its maximum value at B where the ellipse is the projection of the isosurface.

Figure 3

The ring-trap loading scheme. The bold line shows the locus of the center of the quadrupole field. Cross sections of the potential the plane $x=0$ are projected at the rear of each plot. (a) A conventional TOP trap. Switching on the rf does not significantly modify the potential experienced by the atoms (represented by the central darkened region) as the resonant ellipsoid orbits exterior to their position. (b) A double-well TAAP trap [18]. Lowering $B_T$ causes the resonant ellipsoid to spiral inwards, trapping the atoms at the two positions where it intersects with the rotation axis. Note due to gravity, in this case only the lower well is loaded. (c) The shell trap. In the absence of a time-averaging field, the atoms are trapped on the resonant ellipsoid, their final position being determined by the balance between gravity and the variation in ${\Omega }_R(\text{r})$. (d) The ring trap. Ramping on $B_T^z$ time averages the shell potential along its (vertical) symmetry axis. Atoms congregate at the equator of the ellipse (or just below because of gravity).

Figure 4

Variation of ring radius $r_0$ with $B_q^{\text{'}}$, for $B_{\mathrm{rf}}=0.8\hspace{0.5em}\text{G}$ and $B_T^z=0.9\hspace{0.5em}\text{G}$. The dashed line represents the theoretical value for semimajor axis of the resonant ellipsoid $r_e$ using ${\omega }_{\mathrm{rf}}=1.4\hspace{0.5em}\text{MHz}$.

Figure 5

Ring-trap frequency measurements as a function of $B_T^z$ with $B_q^{\text{'}}=83.5\hspace{0.5em}$G/cm and $B_{\mathrm{rf}}=0.8\hspace{0.5em}\text{G}$. The dashed and dot-dashed lines represent numerical results plotted for the same experimental parameters.

Figure 6

Images of a BEC in a tilted ring trap. The direction of the tilt is controlled by the relative phase ${\Delta }_z$ of the axial dressing radiation $B_{\mathrm{rf}}^z$. Here (a) ${\Delta }_z=0^{°}$, (b) ${\Delta }_z={90}^{°}$, (c) ${\Delta }_z={180}^{°}$, and (d) ${\Delta }_z={270}^{°}$. A gravitational tilt in the ring trap prevents the atoms from responding linearly to changes in the rf polarization. It is apparent that the adjustment is sufficient to offset the intrinsic tilt caused by imperfect alignment of the coils with respect to the vertical axis defined by gravity.

Figure 7

(Top) Contour plot of the rotation scheme in the $z=0$ plane. Circular symmetry around the ring is broken by transforming to elliptically polarized rf. Rotating the deformations acts to spin up the cloud. (Bottom) Evidence for rotation. (a) In the absence of rotation, when $B_T^z$ is ramped to zero the atoms return to the rf-dressed shell potential where they are approximately uniformly distributed around the lower half of the ellipsoid (for the parameters listed below). (b) For a rotating cloud (potential rotated at $25\hspace{0.5em}\mathrm{Hz}$ for $800\hspace{0.5em}\mathrm{ms})$, the ring shape persists after the removal of the time-averaging field, because the atoms’ angular momentum holds them at the equatorial regions of the ellipsoid. Both images are of a thermal cloud in a trap where $B_q^{\text{'}}=71\hspace{0.5em}$G/cm and $B_{\mathrm{rf}}=0.8\hspace{0.5em}\text{G}$.