Smooth inductively coupled ring trap for atoms

We propose and numerically investigate a scalable ring trap for cold atoms that surmounts problems of roughness of the potential and end effects of trap wires. A stable trapping potential is formed about an electrically isolated, conducting loop in an ac magnetic field by time averaging the superposition of the external and induced magnetic fields. We investigate the use of additional fields to eliminate Majorana spin-flip losses and to create a stable trapping geometry. The possibility of microfabrication of these ring traps offers the prospect of developing Sagnac atom interferometry in atom-chip devices.

Figure 1

(Color online) Schematic of the instantaneous vector fields for the system described in the text. The external bias field, increasing in magnitude, points upwards, while the induced current in the loop, indicated by the arrow, creates a field about the loop. The fields cancel at a radius inside the loop, indicated by the red, dashed circle. The gray scale in the field slice indicates field magnitude and arrows show the field direction.

Figure 2

The phase between current in the conducting loop and the driving field (left) and the induced current (right) as a function of the frequency of the driving field. Note that at low frequencies, the phase-induced current lags $\pi ∕2$ behind the driving field. For the simulations in Fig. 3, $\Omega =4$.

Figure 3

(Color online) The magnetic potential about the conducting loop showing the effect of the control parameters. The positions of the time-averaged trap minima are marked by the gray crosses, and the instantaneous zeros of the $B$ field are denoted by the black dots. The trajectory that the minima follow is indicated by the numbered, black arrows. For these results, $\omega =\left(2\pi \right)30\mathrm{kHz}$, $B_0=100\mathrm{G}$. (a) No additional fields. (b) A dc quadrupole field, $B_{\mathrm{dcq}}=25\mathrm{G}{\mathrm{cm}}^{-1}$, is added.

Figure 4

(Color online) The transfer from the single quadrupole potential to a ring trap. The quadrupole field is reduced while a transverse bias field is applied to shift the zero of the quadrupole toward the ring radius. The top figure shows the potential along a radius parallel to the bias field as the applied fields vary in time, shown in the lower figure.

Figure 5

(Color online) The scaling of drive frequency, ${\omega }_{\mathrm{drive}}\sim \omega =R∕L$, as a function of $r_{\mathrm{ring}}$ and $r_{\mathrm{wire}}$. The $y$ axis is presented as the ratio of the length scales in the range of experimental interest.