We study the energetics and dispersion of anomalous dimers that are induced by the Pauli blocking effect in a quantum Fermi gas of majority atoms near interspecies resonances. Unlike in vacuum, we find that both the sign and magnitude of the dimer masses are tunable via Feshbach resonances. We also investigate the effects of particle-hole fluctuations on the dispersion of dimers and demonstrate that the particle-hole fluctuations near a Fermi surface (with Fermi momentum $\ensuremath{\hbar}{k}_{F}$) generally reduce the effective two-body interactions and the binding energy of dimers. Furthermore, in the limit of light minority atoms the particle-hole fluctuations disfavor the formation of dimers with a total momentum $\ensuremath{\hbar}{k}_{F}$, because near $\ensuremath{\hbar}{k}_{F}$ the modes where the dominating particle-hole fluctuations appear are the softest. Our calculation suggests that near broad interspecies resonances when the minority-majority mass ratio
mB/mF is smaller than a critical value (estimated to be
0.136), dimers in a finite-momentum channel are energetically favored over dimers in the zero-momentum channel. We apply our theory to quantum gases of
6Li40K,
6Li87Rb,
40K87Rb, and
6Li23Na near broad interspecies resonances, and discuss the limitations of our calculations and implications.
We investigate theoretically the effects of pairing fluctuations in an ultracold Fermi gas near a Feshbach resonance with a negative effective range. By employing a many-body
T-matrix theory with a coupled fermion-boson model, we show that the single-particle density of states exhibits the so-called pseudogap phenomenon, which is a precursor of superfluidity induced by strong pairing fluctuations. We clarify the region where strong pairing fluctuations play a crucial role in single-particle properties, from the broad-resonance region to the narrow-resonance limit at the divergent two-body scattering length. We also extrapolate the effects of pairing fluctuations to the positive-effective-range region from our results near the narrow Feshbach resonance. Results shown in this paper are relevant to the connection between ultracold Fermi gases and low-density neutron matter from the viewpoint of finite-effective-range corrections.
BCS-Bose-Einstein condensation (BEC) crossover is effected by increasing pairing strength between fermions from weak to strong in the particle-particle channel, and has attracted a lot of attention since the experimental realization of quantum degenerate atomic Fermi gases. Here we study the effect of the (often dropped) particle-hole channel on the zero T gap Δ(0), superfluid transition temperature Tc, the pseudogap at Tc, and the mean-field ratio 2Δ(0)/, from BCS through BEC regimes, using a pairing fluctuation theory which includes self-consistently the contributions of finite-momentum pairs and features a pseudogap in single particle excitation spectrum. Summing over the infinite particle-hole ladder diagrams, we find a complex dynamical structure for the particle-hole susceptibility χph, and conclude that neglecting the self-energy feedback causes a serious over-estimate of χph. While our result in the BCS limit agrees with Gor'kov et al., the particle-hole channel effect becomes more complex and pronounced in the crossover regime, where χph is reduced by both a smaller Fermi surface and a big (pseudo)gap. Deep in the BEC regime, the particle-hole channel contributions drop to zero. We predict a density dependence of the magnetic field at the Feshbach resonance, which can be used to quantify χph and test different theories.