Superfluidity in ultracold atomic Fermi gases has been one of the most
exciting, fast developing research areas in recent years. Atomic Fermi
gases provide a controlled many-body system with a tunable pairing
strength via Feshbach resonances so that BCS-Bose-Einstein condensation
(BEC) crossover can be studied experimentally. These systems have been
expected to provide experimental tests on various BCS-BEC crossover
theories, and shed light on the pseudogap physics in high 
superconductivity. However, since the atoms are charge neutral, it is
much more difficult to detect the superfluid transition experimentally
than detecting the superconducting transition in superconductors.
Another question is to what extent the Feshbach resonance induced
superfluidity tuned via magnetic field is similar to the usual BCS-BEC
crossover physics tuned via a single paramter of pairing interaction?
In collaboration with the groups at the University of Chicago, JILA, and
the Duke University, I have recently studied the nature of the onset of
the superfluidity in such systems, in particular, in the pseudogap
regime. Given the difficulty to perform phase sensitive measurements on
these systems, we have shown that one can determine the onset of the
superfluidity via the sharp change in the density of states across
in the pseudogap regime. This is thus far the first theoretical
study of the possible pseudogap effects in atomic Fermi gases,
preceeding the recent experimental study of the pseudogap using RF
spectroscopy.
Furthermore, we have shown that the Feshbach resonance induced molecular bosons have an important influence on the BCS-BEC crossover, leading to a far more non-interacting Bose gas in the BEC regime, and hence a more pronounced narrowing of the density profile of an atomic Fermi gas in a trap. Very recently, we have found that the superfluidity tuned via a Feshbach resonance is very different from that of regular BCS-BEC crossover. Surprisingly, the importance of the resonance induced molecular bosons are inversely proportional to the coupling strength between the ``open channel'' atoms and the ``closed channel'' molecules. The most important finding is that the harmonic trap potential can be dramatically renormalized by the effective interaction between pairs or Feshbach molecules so that it becomes essentially flat in the entire condensate region. As a consequence, the thermodynamcs behaves like a homogeneous system in this region. This finding has such a huge impact that essentially all condensate fraction and phase diagram related measurements need to be reanalyzed.
In our latest work, we have addressed the thermodynamics of trapped Fermi gases in the strongly interacting regime, where the system is the most interesting but the least understood. This has been the first theoretical attempt on thermodynamics in this regime. Our results are in perfect quantitative agreement with experimental data. More importantly, our work has provided for the first time a theoretical basis for implementing the much needed thermometry in strongly interacting Fermi gases.
The future in this field is wide open, with obvious connections with fields as diverse as nanosuperconductors and quantum computing.