FUTURE RESEARCH PLANS

I have very broad research interests. In the foreseeable future, I plan to work in the areas outlined below, which will be expanded as time goes on. Having worked on experiment successfully for two years in the past, I always have a strong interest in working closely with experimentalists.

Ultracold atomic Fermi gases in traps: A new branch of condensed matter physics

Superfluidity in ultracold trapped atomic Fermi gases is one of the most exciting research areas in condensed matter and atomic physics. Trapped atomic Fermi gases are very interesting, controlled many-body systems in that one can vary continuously the effective pairing interaction via magnetically tuned Feshbach resonances. This makes it possible to observe Bose-Einstein condensation (BEC) in quantum degenerate Fermi gases directly (in both momentum and real spaces). More excitingly, this brings one the hope that, for the first time, one can study experimentally the BCS-BEC crossover, which has been investigated theoretically for over twenty years. Furthermore, for the condensed matter community, this has created a strong hope that study of whether and how a pseudogap may emerge and evolve in these systems will surely lead to a deeper understanding of the extremely important pseudogap physics in high $T_c$ superconductivity, which physicists have been trying hard, yet still have not succeeded.

Over the past a few years, this field has seen very rapid progress. Experimentalists have been able to cool the atomic Fermi gases down below their quantum degenerate temperatures, and create molecular bosons (diatomic molecules) via Feshbach resonances. Very recently, the Jin group at JILA and the Grimm group at Universität Innsbruck, Austria have made a big breakthrough and observed signatures of the condensation in trapped atomic Fermi gases of $^{40}$K and $^6$Li, respectively, (a story covered by the November 25, 2003 issue of the New York Times).

A number of theorists have been working in this area. However, their work has been based on either the mean-field BCS-Leggett theory at zero temperature or the finite temperature Noziéres-Schmitt-Rink approach at $T_c$. The latter lacks self-consistency and cannot possibly predict a pseudogap. Our pairing fluctuation theory for the pseudogap physics in high $T_c$ superconductors naturally interpolates between the BCS and BEC limits, and can be easily extended to trapped atomic Fermi gases. Indeed, I have recently made great progress in this area. This puts me in a unique position to bridge the high $T_c$ and the atomic physics communities and do better in this area than other competitors.

In particular, I will study the following important topics: (i) possible pseudogap effects and their signatures, (ii) signatures of superfluid transition in the presence of a pseudogap and in generaL, (iii) shrinking of the atomic gas cloud as a function of temperature and magnetic detuning, and (iv) determination of condensate fraction and the phase diagram. At the same time, (v) I will use these systems as a testing ground for various BCS-BEC crossover theories, with the hope of better understanding the pseudogap phenomena in superconductors.

Because we have the theory for the trapped gases at finite temperatures, we will be among the first to address:

• Collective modes at nonzero temperatures;
• Bragg's scattering to measure the excitation spectrum;
• Optical emission and recoil experiments.