Measuring the Superfluid Fraction of an Ultracold Atomic Gas

We propose a method to measure the superfluid fraction of an atomic gas. The method involves the use of a vector potential generated by optical beams with nonzero angular momenta to simulate uniform rotation. The induced change in angular momentum of the atomic gas can be measured spectroscopically. This allows a direct determination of the superfluid fraction.

Figure 1

Energy levels for the angular motion of an atom under the influence of two-photon Raman coupling via beams with orbital angular momentum difference $\Delta \ell$. The atoms move in a trap of radius $R$, the detuning is $\delta =0.5\hslash (\Delta \ell {)}^2/M{R}^2$, $ϵ=0$, and Rabi frequencies of ${\Omega }_R=0$ (dotted line) and ${\Omega }_R=2\hslash (\Delta \ell {)}^2/M{R}^2$ (solid lines) are shown. The lowest band has its minimum displaced to a nonzero angular momentum ${\ell }^{*}$, equivalent to the effect of an azimuthal vector potential. (The smooth curves interpolate between the allowed integer values of $\ell$.)

Figure 2

Angular momentum ${\ell }^{*}$ at the bottom of the band (dashed line) and change in particle imbalance $\Delta p-\Delta p_0$ (solid line) as a function of $\delta /{\Omega }_R$ for a normal fluid (i.e., centered on ${\ell }^{*}$) for ${\Omega }_R=1000\hslash /M{R}^2$, $\Delta \ell =10$, $ϵ=0$. This illustrates the precision required to distinguish a normal fluid (here $\Delta p-\Delta p_0\sim 3\%$) from a perfect superfluid ($\Delta p-\Delta p_0=0$).