Ring trap for ultracold atoms

We propose a toroidal trap designed for ultracold atoms. It relies on a combination of a magnetic trap for rf-dressed atoms, which creates a bubble-like trap, and a standing wave of light. This trap is well-suited for investigating questions of low dimensionality in a ring potential. We study the trap characteristics for a set of experimentally accessible parameters. A loading procedure from a conventional magnetic trap is also proposed. The flexible nature of this ring trap, including an adjustable radius and adjustable transverse oscillation frequencies, will allow the study of superfluidity in variable geometries and dimensionalities.

Figure 1

Energy of the dressed levels in the magnetic quadrupole trap described in the paper, plotted along the radial coordinate, in the vicinity of the potential minimum at $\rho =r_0$. The five dressed sublevels for a $F=2$ spin state are plotted, as well as two bare states for comparison (bare state $m_F=-1$ is shown dashed and $m_F=2$ dash-dotted). The ring trap we discuss in this paper is based on the upper dressed potential $m_F=F=2$, for the radial trapping (bold solid line). Values for the field gradient and rf and Rabi frequencies are given in Table .

Figure 2

(Color online) A view of the ring trap. An isopotential surface is plotted for the parameters of Table , in the harmonic approximation. The length unit is $1\mathrm{\mu }\mathrm{m}$. The vertical direction was amplified ten times for clarity. The overall trap shape is that of a Saturnian ring.

Figure 3

(Color online) Outline illustration of stages in the loading of the ring trap. The $z$ axis is in the vertical direction and we assume a cylindrical symmetry about this axis. In (b)–(f) the elliptical line indicates the location (in the $y$-$z$ plane) of the rf resonance. In (d)–(f) the horizontal bands indicate the presence of the standing light wave. Then: (a) We take as the starting point a BEC in a magnetic trap. (b) Shortly after transfer to the dressed rf trap the condensate fills a location around the rf resonance, but is not yet excluded from the trap center. (c) After rf expansion [stage (ii)] the condensate lies at the bottom of the “egg shell.” (d) The application of the optical standing wave results in a potential which confines the condensate to a couple of potential wells (corrugations). (e) The standing wave is moved upwards and the condensate ring is formed and expanded outwards and upwards. (f) Final position of the condensate ring at maximum radius. All three potentials, magnetic, dressed rf, and optical are required to maintain the ring.

Figure 4

(Color online) Coils and laser configuration for producing and exciting the ring trap. The trap is the combination of a vertical light standing wave (blue beam on the figure) and an egg shell rf trap (see Sec. 2). This egg shell trap relies on a magnetic field gradient (produced by the quadrupole coils) and rf coupling between Zeeman sublevels (two rf coils in quadrature as described in Sec. 6). The additional “spinning” coils could be used for exciting the rotation of the atoms inside the ring trap (see Sec. 7).