BCS-BEC crossover with unequal-mass fermions

We investigate the crossover from BCS pairing to molecular Bose-Einstein condensation (BEC) in an atomic gas with two fermion species with masses m(up arrow) not equal m(down arrow) tuned through a Feshbach resonance. We present results for the T = 0 equation of state as a function of the scattering length including the effects of Gaussian fluctuations about the mean field ground state. We compute the ground state energy as a function of m(up arrow) not equal m(down arrow) at unitarity and find excellent agreement with the quantum Monte Carlo result for m(up arrow) not equal m(down arrow) = 6.67 for a K-40-Li-6 mixture. We show that the dimer scattering length in the BEC limit as a function of m(up arrow) not equal m(down arrow) compares well with the exact four-body results of Petrov et al. [J. Phys. B 38, S645 (2005)]. We also derive the condition for trapping frequencies to obtain an unpolarized gas in a harmonic trap.