Radio Frequency Response of the Strongly Interacting Fermi Gases at Finite Temperatures

The radio frequency spectrum of the fermions in the unitary limit at finite temperatures is characterized by the sum rule relations. We consider a simple picture where the atoms are removed by radio frequency excitations from the strongly interacting states into a state of negligible interaction. We calculate the moments of the response function in the range of temperature $0.08 \epsilon_F < T < 0.8 \epsilon_F$ using auxiliary field Monte Carlo technique (AFMC) in which continuum auxiliary fields with a density dependent shift are used. We estimate the effects of superfluid pairing from the clock shift. We find a qualitative agreement with the pairing gap - pseudogap transition behavior. We also find within the quasiparticle picture that in order for the gap to come into quantitative agreement with the previously known value at T=0, the effective mass has to be $m^* \sim 1.43 m$. Finally, we discuss implications for the adiabatic sweep of the resonant magnetic field.Comment: 2 figure

Unitary Fermi Gas in a Harmonic Trap

We present an {\it ab initio} calculation of small numbers of trapped, strongly interacting fermions using the Green's Function Monte Carlo method (GFMC). The ground state energy, density profile and pairing gap are calculated for particle numbers $N = 2 \sim 22$ using the parameter-free "unitary" interaction. Trial wave functions are taken of the form of correlated pairs in a harmonic oscillator basis. We find that the lowest energies are obtained with a minimum explicit pair correlation beyond that needed to exploit the degeneracy of oscillator states. We find that energies can be well fitted by the expression $a_{TF} E_{TF} + \Delta {\rm mod}(N,2)$ where $E_{TF}$ is the Thomas-Fermi energy of a noninteracting gas in the trap and $\Delta$ is a pairing gap. There is no evidence of a shell correction energy in the systematics, but the density distributions show pronounced shell effects. We find the value $\Delta= 0.7\pm 0.2\omega$ for the pairing gap. This is smaller than the value found for the uniform gas at a density corresponding to the central density of the trapped gas.Comment: 2 figures, 2 table