Session N6: Fermi Superfluid Gases : Non-equal Spin Polarization (FFLO State) and p-Wave pairing

Phase Diagram of Cold Polarized Fermi Gas

We propose the phase diagram of cold polarized atomic Fermi gas with zero-range interaction. We identify four main phases in the plane of density and polarization: the superfluid phase, the normal phase, the gapless superfluid phase, and the modulated phase. We argue that there exist a Lifshitz point at the junction of the normal, the gapless superfluid and the modulated phases, and a splitting point where the superfluid, the gapless superfluid and the modulated phases meet. We show that the physics near the splitting point is universal and derive an effective field theory describing it. We also show that subregions with one and two Fermi surfaces exist within the normal and the gapless superfluid phases.   

Superfluid stability in polarized Fermi atomic gases

For a two-species atomic Fermi gas with equal populations, it is now widely accepted that a smooth BCS-BEC cross-over occurs when the Feshbach resonance is crossed. However, the situation is very different if the populations of the two species are different. In particular, the uniform state is stable only either (a) for sufficiently negative detuning, where the system is a gapless mixture of Bose condensed pairs and unpaired normal Fermions, or (b) for sufficiently positive detuning, where Fermions are unpaired and the system is in the normal state. No uniform state is stable in between. Phase transition(s) must therefore occur when the resonance is crossed. We discuss the theoretical phase diagram of this system in this talk.   

Pairing and Phase Separation in a Polarized Fermi Gas

BCS pairing can only occur when the Fermi energies of the individual particles are equal. There has been great interest, however, in the consequences of mismatched Fermi energies that may arise in several important situations, including magnetized superconductors or cold dense quark matter at the core of neutron stars. Pairing is qualitatively altered by the Fermi energy mismatch, and there has been considerable speculation regarding the nature and relative stability of various proposed exotic phases. We have created a two-component gas of $^6$Li atoms in which the relative Fermi energies are altered by changing the relative numbers of each component \footnote{G.B. Partridge \textit{et al.}, cond-mat/0511752.}. The BEC/BCS crossover with tunable interactions is realized via a Feshbach resonance. Above a critical number polarization, which depends on the interaction energy, the gas separates into a superfluid paired core surrounded by a shell of normal unpaired atoms. Below the critical polarization the gas exists in a paired state with asymmetric Fermi surfaces. The critical polarization is largest in the BEC regime, and becomes small in the BCS regime. We also measure the universal interaction parameter $\beta$ for a strongly interacting Fermi gas to be -0.54 (5), in good agreement with recent Monte-Carlo calculations.   

Fermi superfluids with p-wave pairing near a Feshbach resonance

Fermi superfluids with s-wave pairing near an s-wave Feshbach resonance are being extensively studied both theoretically and experimentally. Recently, Feshbach resonances in the p-wave channel have been observed in both $^{40}$K and $^6$Li, raising the possibility that fermionic superfluids with p-wave pairing could be attained at low temperatures. Since the pairing wavefunction in this case breaks rotational symmetry, the superfluid properties of this system in the BEC-BCS crossover will be much different from the s-wave case. In particular, I will discuss the symmetry of the ground state as well as the experimental signatures of these novel superfluids as a function of the parameters defining the resonance. Other new results on resonance physics will also be reported.   

Evolution from BCS to BEC Superfluidity in Dilute Fermi Gases

I will review briefly some old results [1,2] of the evolution from BCS to BEC superfluidity in dilute Fermi gases, including critical temperature, order parameter amplitude, chemical potential and time dependent Ginzburg-Landau theory for the s-wave channel in three dimensions. Following this discussion, I will present new results for the BCS to BEC evolution of Fermi gases in the p-wave channel [3]. I will make comparisons between s-wave and p-wave superfluidity and point out the main differences between the two cases. Lastly, I will discuss supefluidity of s-wave and p-wave Fermi gases in a restricted two-dimensional geometry (one dimensional optical lattice), where a Berezinkii-Kosterlitz-Thouless-type transition is proposed as the system evolves from the weak to the strong attraction limit. In this case, I will show that spontaneous vortex-antivortex pairs form and that they can condense into a vortex-antivortex lattice at lower temperatures [4]. [1] C. A. R. Sa de Melo, M. Randeria, and J. R. Engelbrecht, PRL 71, 3202 (1993). [2] J. R. Engelbrecht, M. Randeria, and C. A. R. Sa de Melo, PRB 55, 15153 (1997). [3] M. Iskin, and C. A. R. Sa de Melo, cond-mat/0510300 (2005). [4] S. S. Botelho, and C. A. R. Sa de Melo, cond-mat/0509387 (2005).