We determine the effects of quantum fluctuations about the T = 0 mean-field solution of the BCS-BEC crossover in a dilute Fermi gas using the functional integral method. These fluctuations are described in terms of the zero-point motion of collective modes and the virtual scattering of gapped quasiparticles. We calculate their effects on various measurable properties, including chemical potential, ground-state energy, the gap, the speed of sound and the Landau critical velocity. At unitarity, we find excellent agreement with quantum Monte Carlo and experimental results. In the BCS limit, we show analytically that we obtain Fermi liquid interaction corrections to thermodynamics including the Hartree shift. In the Bose-Einstein condensation ͑BEC͒ limit, we show that the theory leads to an approximate description of the reduction of the scattering length for bosonic molecules and also obtain quantum depletion of the Lee-Yang form. At the end of the paper, we describe a method to include feedback of quantum fluctuations into the gap equation, and discuss the problems of self-consistent calculations in satisfying Goldstone's theorem and obtaining ultraviolet finite results at unitarity.

Published Version

We have analyzed a single vortex at T 0 in a 3D superfluid atomic Fermi gas across a Feshbach resonance. On the BCS side, the order parameter varies on two scales: k ÿ1 F and the coherence length , while only variation on the scale of is seen away from the BCS limit. The circulating current has a peak value j max which is a nonmonotonic function of 1=k F a s implying a maximum critical velocity v F at unitarity. The number of fermionic bound states in the core decreases as we move from the BCS to the BEC regime. Remarkably, a bound state branch persists even on the BEC side reflecting the composite nature of bosonic molecules.

We study the quench dynamics of a two-component ultracold Fermi gas from the weak into the strong interaction regime, where the short time dynamics are governed by the exponential growth rate of unstable collective modes. We obtain an effective interaction that takes into account both Pauli blocking and the energy dependence of the scattering amplitude near a Feshbach resonance. Using this interaction we analyze the competing instabilities towards Stoner ferromagnetism and pairing.Ferromagnetism in itinerant Fermions is a prime example of a strongly interacting system. Most theoretical treatments rely on a mean-field Stoner criterion [1], but whether this argument applies beyond mean-field remains an open problem. It is known that the existence of the Stoner instability is very sensitive to the details of band structure and interactions [2][3][4], however how to account for these details in realistic systems remains poorly understood. Exploring the Stoner instability with ultracold atoms has recently attracted considerable attention. Following theoretical proposals [5], the MIT group made use of the tunability [6] and slow time scales [7-10] of ultracold atom systems to study the Stoner instability [11]. Signatures compatible with ferromagnetism, as understood from mean-field theory [12], were observed in experiments: a maximum in cloud size, a minimum in kinetic energy and a maximum in atomic losses at the transition. However, no magnetic domains were resolved.An important aspect of the MIT experiments is that they were done dynamically: the Fermi gas was originally prepared with weak interactions and then the interactions were ramped to the strongly (repulsive) regime. Dynamic rather than adiabatic preparation was used in order to avoid production of molecules. This raises the question of what are the dominant instabilities of the Fermi gas in the vicinity of a Feshbach resonance.Naively, one would expect that on the BEC-side, molecule production is slow, as it requires a three-body process. Therefore, instability towards Stoner ferromagnetism would dominate over the instability toward molecule production. In this picture, one would expect that quenches to the attractive (BCS) regime always yield an instability towards pairing, whereas quenches to the repulsive (BEC) regime an instability towards ferromagnetism for sufficiently strong interactions.In this Letter, we argue that this picture, which was used to interpret the MIT experiments, is incomplete. Near the Feshbach resonance, even on the BEC side, pair production remains a fast two-body process as long as the Fermi sea can absorb the molecular binding energy. As a result, near the Feshbach resonance, both on the BEC and the BCS side, the pairing and the Stoner instabilities compete directly. We now