Dan Sheehy: Superfluidity in "magnetized" fermionic atomic gases

Dan Sheehy presented in his talk work on cold atomic gases done in collaboration with L. Radzihovsky (PRL '06, Ann. Phys. '07, PRB '07).

Dan started by reviewing recent results on the BEC-BCS crossover in fermionic gases. Typical experiments are done with Li6 or K40 at temperature of the order 10-100nK (cold) and densities of the order 10^10-10^13/cm^3 (dilute). Two different hyperfine Zeeman states
("spin up" and "spin down") are trapped in a harmonic trap and their interaction is tuned using a Feshbach resonance. In this way strong attractive interactions can be achieved.

QUESTION: Is it only possible to trap two different species?
ANSWER: In principle it's possible to trap more different species and one would expect interesting physics as a result.

QUESTION: How does one measure temperature?
ANSWER: Temperatures aren't very well known experimentally. In the non-interacting case the spatial profile of the atomic cloud can be fit to a Fermi function and thus one can extract the temperature. In the presence of interactions this is, however, not possible.

The attraction between fermions can be considered point-like:

H_int = g(B) \int d^3r psi_up^dagger(r) psi_down^dagger(r) psi_down(r) psi_up(r),

where g(B) is tunable by an external B field. The scattering length varies as

a_S ~ - 1/(B-B_0).

The divergence at B=B_0 signals the appearance of a bound state. The change in sign of a_S does not mean that the interactions switch from attractive to repulsive. At B > B_0 the attraction between fermions is weak (BCS regime). At B <> n_down. He presented a phase diagram as a function of the inverse scattering length and the polarization

P = (N_up - N_down)/(N_up + N_down).

By contrast to conventional condensed matter experiments where one fixes the magnetic field, in cold atomic gases the number of spin up and spin down particles can be fixed, i.e., one works at fixed P.

In the BCS limit it is known that a Zeeman field kills superconductivity if h = h_c = Delta_0 / sqrt 2 (Clogston limit). The transition is first order. Therefore, at fixed P one finds phase
separation. The BCS state exists only for P = 0. At finite P, three different phases occur:
1. phase separation at small P
2. FFLO state in a small region of intermediate P and far enough away from the resonance
3. normal Pauli paramagnet at large P

Experimentally phase separation is indeed observed by the Rice & MIT groups: in the middle of the trap a condensate forms while the excess up spins accumulate towards the edges of the trap.

QUESTION: Is the normal region at the edge of the trap fully polarized?
ANSWER: No, it is only partially polarized according to the conditions for chemical equilibrium.

Far enough on the BEC side, instead of phase separation a magnetic superfluid is predicted consisting of molecules (singlets) mixed with the excess spin up fermions. This is to be compared to He3 - He4 mixtures. No experiments in the deep BEC limit testing this exist so far.

COMMENT: For non-s-wave pairing a quantum critical point exists between the BEC and the BCS regime.

QUESTION: What about the formation of quartets predicted by Nozieres et al?
ANSWER: There is no experimental evidence for that.

QUESTION: How can one measure the FFLO phase?
ANSWER: It has not been observed, yet, but it should be visible in the density profile.

QUESTION: In He3-He4 mixtures the solubility limit depends on the nature of interactions. Is this true here as well?
ANSWER: Within mean field theory the transition to the polarized superfluid depends on the interaction strength. So far there are no results beyond mean field available.