Crossover from 2D to 3D in a Weakly Interacting Fermi Gas

We have studied the transition from two to three dimensions in a low temperature weakly interacting ${}^6\mathrm{Li}$ Fermi gas. Below a critical atom number $N_{2\mathrm{D}}$ only the lowest transverse vibrational state of a highly anisotropic oblate trapping potential is occupied and the gas is two dimensional. Above $N_{2\mathrm{D}}$ the Fermi gas enters the quasi-2D regime where shell structure associated with the filling of individual transverse oscillator states is apparent. This dimensional crossover is demonstrated through measurements of the cloud size and aspect ratio versus atom number.

Figure 1

One-dimensional density profiles for clouds at 992 G as a function of atom number in the tight (a) and weakly confined (b) directions after $500\mu \mathrm{s}$ expansion. Solid black lines are contours of equal density and the dashed red lines show the predicted rms cloud width for an ideal Fermi gas. The color bar indicates line density in units of $\mathrm{atoms}/\mu \mathrm{m}$.

Figure 2

Measured rms cloud widths (data points) and theoretical predictions for a weakly interacting (solid lines) and ideal (dashed lines) Fermi gas. Radial cloud width is plotted in the main panel and the inset shows the transverse cloud width after $500\mu \mathrm{s}$ expansion. Theoretical curves are scaled as described in the text.

Figure 3

Cloud aspect ratio in the 2D-3D crossover (points) and theoretical predictions for a weakly interacting (solid line) and ideal (dashed line) Fermi gas. Arrows indicate predicted atom numbers at which new transverse states become accessible. Inset: Gradient of the experimental and theoretical aspect ratios showing the signature of shell filling.