Time-Averaged Adiabatic Potentials: Versatile Matter-Wave Guides and Atom Traps

We demonstrate a novel class of trapping potentials, time-averaged adiabatic potentials (TAAP), which allows the generation of a large variety of traps for quantum gases and matter-wave guides for atom interferometers. Examples include stacks of pancakes, rows of cigars, and multiple rings or sickles. The traps can be coupled through controllable tunneling barriers or merged altogether. We present analytical expressions for pancake-, cigar-, and ring-shaped traps. The ring geometry is of particular interest for guided matter-wave interferometry as it provides a perfectly smooth waveguide of widely tunable diameter and thus adjustable sensitivity of the interferometer. The flexibility of the TAAP would make possible the use of Bose-Einstein condensates as coherent matter waves in large-area atom interferometers.

Figure 1

Schematic generation of a TAAP trap; density plots of the potential energy of the atoms for different elements of the TAAP. The darker shades represent smaller values of the potential. Starting with a static magnetic trapping potential (a) we apply an rf field resulting in the dressed potential (b). We now add a modulation field thus periodically shifting the trap up ($t_1$) and down ($t_2$) as shown in (c). We do this at such a high frequency that the atoms are not able to follow the modulation of the dressed potential of (c). This results in the TAAP (d).

Figure 2

Generation of a ring TAAP. (a) Density plot of the TAAP in the $xz$ plane. The dashed lines sketch the points where the atoms are resonant with the rf at times $t_1$ and $t_2$ when the modulation is at its extreme points. (b) Representation of a 3D isopotential surface of the ring TAAP.

Figure 3

Generation of the double-well TAAP. (a) Density plot of the TAAP in the $xz$ plane. The dashed lines sketch the points where the atoms are resonant with the rf for times $t_1$ and $t_2$ where the modulation field has an opposite phase. The curvature has been exaggerated. (b) A 3D representation of an isopotential surface of the resulting TAAP. The surface is rotationally symmetric around the $z$ axis around which the modulation field ${\mathbf{B}}_{\mathrm{m}}(t)$ rotates.