Our paper was the first one to present a theoretical study of the superfluidity in the fermion system with spin population imbalance across Feshbach resonance. Together with two impressive experimental works of this system in a trap potential, which were reported in the same year (2004) when we submitted the paper, these works stimulated intense theoretical activity in this field. The imbalanced fermion system also has important implications in other areas of physics such as quark matter and superconductivity.

“Our paper was the first one to present a theoretical study of the superfluidity in the fermion system with spin population imbalance across Feshbach resonance.”

With two types of fermions of equal numbers under a Feshbach resonance, the system smoothly changes from BCS to BEC from above to below the resonance. We, however, show that for a fermion system with unequal spin populations, there is no smooth BCS-BEC crossover.

The uniform state is stable only when either (a) beyond a critical coupling strength, where it is a gapless superfluid, or (b) when the coupling strength is sufficiently weak, where it is a normal Fermi gas mixture. Phase transition(s) must therefore occur when the resonance is crossed.

Equal numbers of two spin states with a weak attractive interaction may form loose Cooper pairs at low temperature. These pairs flow through one another without resistance, giving rise to superfluidity or superconductivity if these fermions carry charges. When the coupling between these two spin states is strong, a tightly bound "molecule" is stable and the molecular Bose-Einstein condensation can occur at low temperature.

For an imbalanced fermion system, leftover fermions need to coexist with the "molecule" or loose Cooper pairs. The stability of the superfluidity in these Bose-Fermi mixtures is the key question which we are interested in. In the present paper, we found, in an imbalanced fermion system, that normal fluid is the stable homogeneous phase in the weak-coupling BCS side. In the strong coupling BEC regime, the homogeneous superfluid is stable. The system, however, is unstable in the intervening region. Thus, a phase transition must occur in between.

Our work on this problem was initiated by studying the instability of the interior-gap state which results from a mismatched Fermi surface. This work was done by two of us (Shin-Tza Wu and Sungkit Yip) and was published in early 2003.

During 2003 and 2004, several groups reported the observations of the molecular BEC and/or BCS superfluid with equal spin populations across the Feshbach resonance. These experimental results motivated us to investigate the superfluid phase diagram across the resonance in an imbalanced fermion system.

Our work has actually left open the question as to what phases actually exist in the intermediate region near the resonance. Experiments seemed to have indicated phase separation closed to resonance, but it is still an unsettled question whether more exotic phases, such as the Fulde-Ferrell-Larkin-Ovchinnikov phase(s), exist in some part of the phase diagram. Indeed many theoretical papers have been written on this subject, including a recent one by our group (N. Yoshida and S.-K. Yip, "Larkin-Ovchinnikov state in resonant Fermi gas," Phys. Rev. A 75, 2007).

There is also a question of the effects of finite temperatures, and also how this phase diagram would be modified if the two species of fermions have different masses, a system which also seems to be experimentally accessible. Many groups, including ours, are investigating these questions (Shin-Tza Wu, C.-H. Pao and S.-K. Yip, "Resonant pairing between fermions with unequal masses," Phys. Rev. B 74, 2006).

Dr. Chien-Hua Pao
Associate Professor
Department of Physics
National Chung Cheng University
Chiayi, Taiwan

Dr. Shin-Tza Wu
Assistant Professor
Department of Physics
National Chung Cheng University
Chiayi, Taiwan

Dr. Sungkit Yip
Research Fellow
Institute of Physics
Academia Sinica
Taipei, Taiwan