Lifetime of angular momentum in a rotating strongly interacting Fermi gas

We investigate the lifetime of angular momentum in an ultracold strongly interacting Fermi gas, confined in a trap with controllable ellipticity. To determine the angular momentum we measure the precession of the radial quadrupole mode. We find that in the vicinity of a Feshbach resonance, the deeply hydrodynamic behavior in the normal phase leads to a very long lifetime of the angular momentum. Furthermore, we examine the dependence of the decay rate of the angular momentum on the ellipticity of the trapping potential and the interaction strength. The results are in general agreement with the theoretically expected behavior for a Boltzmann gas.

Figure 1

(Color online) Oscillation of the cloud after excitation of the radial quadrupole mode. For a rotating hydrodynamic gas, the principal axes of the quadrupole mode oscillation precess with a frequency determined by the angular momentum of the gas. To follow the precession we measure the angle of the long axis of the cloud. Note that every half oscillation period this angle changes by $\pi /2$ because of the mode oscillation; see also Fig. 2. The oscillation of the cloud shape is determined by measuring the widths along the short $\left(W_S\right)$ and the long axis $\left(W_L\right)$ of the cloud.

Figure 2

(Color online) Evolution of the quadrupole mode in a rotating Fermi gas in the unitarity limit. The upper panel shows the precession of the principal axes of the mode. The experimental data are shown by the dots. The solid line represents a fit according to Eq. (A1). The dashed lines correspond to the idealized precession of the angle when there is no damping present in the mode. Whenever the oscillation of the difference in widths $\Delta W^2/W_0^2$ (lower panel) has a local maximum, the observed precession angle coincides with the idealized precession. The parameter $W_0$ is the average width of the cloud. The finite value of $\varphi$ at zero wait time results from the precession of the cloud during expansion. Here $L_z=1.7\hslash$ and $T/T_F\approx 0.2$.

Figure 3

The angular momentum $L_z$ as a function of the rotation frequency ${\Omega }_t$ of the elliptic trap. Here we spin up the gas for $t_{\text{rot}}=60\text{ms}$. The temperature is $T/T_F\approx 0.2$. The gas is in the unitarity limit.

Figure 4

(Color online) Decay of the angular momentum $L_z$ for a gas in the unitarity limit. The temperature is $T/T_F=0.22\left(3\right)$. We fit an exponential decay behavior (solid lines) to the experimental data points. For low ellipticity $ϵ=0.009$ (open dots) the lifetime is 1.4 s, while at higher ellipticity $ϵ=0.1$ (filled dots) the lifetime is only 0.14 s. To better see the difference of the lifetime for the two ellipticities, we normalized $L_z$ by its initial value $L_0$. For the lower ellipticity $L_0=2.2\hslash$ and for the higher ellipticity $1.6\hslash$.

Figure 5

(Color online) Normalized decay rate of the angular momentum as a function of the ellipticity for a gas in the unitarity limit. The temperatures are $T/T_F=0.22\left(3\right)$ (filled dots) and 0.35 (2) (open dots). The solid lines are fits based on the expected behavior for a Boltzmann gas [16]. The inset shows the low ellipticity region.

Figure 6

Lifetime of the angular momentum versus interaction parameter $1/k_{F}a$ for $ϵ=0.09$. The temperature for $1/k_{F}a=0$ is $T/T_F=0.22\left(3\right)$.