The radial size of the cloud (black dots) is plotted along the vertical axis against time along the horizontal. The data are well fit by a damped sinusoid (blue curve). The long lifetime of the oscillations suggests that the cloud is a superfluid.

False color images of oscillating cloud.

Studies of collective modes in optically trapped gases are useful because they allow us to infer information about microscopic interactions by monitoring macroscopic observables. In our case, we have studied the radial breathing mode in an optically trapped gas of fermions in the strongly-interacting regime [Phys. Rev. Lett. 92, 150402 (2004) and Phys. Rev. A 70, 051401(R) (2004)]. The strength and sign of the interactions between particles is controlled via application of an external magnetic field. After cooling a gas of atoms well into the degenerate regime, we can excite the radial breathing mode of the gas by briefly extinguishing our trapping potential. When the trapping potential is turned off, the cloud begins to expand; when the trap is turned on again, the cloud begins to oscillate. The term "breathing mode" is particularly apt, as the oscillating cloud resembles a balloon that is being rhythmically inflated and deflated [AVI movie (565 kB)].

There are two quantities that are of particular interest: 1. the frequency of the oscillations and  2. how long those oscillations last. The frequency of the oscillations reveals information about the way the particles in the gas interact with each other. We find that the measured frequency is in excellent agreement with predictions for a unitary, hydrodynamic gas when we tune to the region of maximum attractive interactions. Furthermore, we find reasonable agreement with predictions of the oscillation frequency throughout much of the strongly-interacting regime both for attractive and repulsive interparticle interactions.  However, rather unusual behavior begins to appear as we weaken the strength of the attractive interactions [Phys. Rev. A 70, 051401(R) (2004)]. First, the oscillation frequency drops below the predicted value before increasing sharply around a magnetic field of 1080 G. This sharp increase in frequency is accompanied by a very abrupt decrease in the duration of the oscillations.  This type of behavior was first observed by a research group at the University of Innsbruck under the direction of Rudolf Grimm. However, the Innsbruck group observed this unusual behavior at a lower magnetic field of 910 G. At present, there is no definitive explanation for this quantitative discrepancy. However, there is speculation that these abrupt changes in the frequency and duration of the oscillations could be explained by the breaking of fermions that managed to "pair up" when strong interactions were induced in the ultracold gas.

The phenomenon of pairing could be an indication that the Fermi gas has undergone a transition to the long-sought superfluid state.  Further evidence for the existence of this state arises in studies of the duration of the breathing mode oscillations [Phys. Rev. Lett. 92, 150402 (2004)]. At a fixed magnetic field of 870 G, we vary the temperature of the cloud and monitor how long the breathing mode oscillations persist.  As noted above, we find that the oscillation frequency suggests that the cloud of atoms is a hydrodynamic system. Hydrodynamics can arise from both a superfluid state or a very high collision rate between particles.  Unfortunately, frequency information alone does not allow us to make a distinction between superfluid and collisional hydrodynamics. However, charting the duration of the oscillations as a function of temperature indicates that the gas is likely a superfluid at very low temperatures. As the gas is cooled to the lowest temperatures we can achieve in our laboratory, we find that the breathing mode oscillations last longer and longer.  This is an important finding, as we expect that the number of collisions between particles should be decreasing in this regime, according to the rules of quantum mechanics.  Since the oscillations persist longer as the collision rate drops, we believe that the gas is most likely a superfluid at our lowest temperatures.