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We consider the problem of a single # atom in the presence of a Fermi sea of " atoms, in the vicinity of a Feshbach resonance. We calculate the chemical potential and the effective mass of the # atom using two simple approaches: a many-body variational wave function and a T-matrix approximation. These two methods lead to the same results and are in good agreement with existing quantum Monte Carlo calculations performed at unitarity and, in one dimension, with the known exact solution. Surprisingly, our results suggest that, even at unitarity, the effect of interactions is fairly weak and can be accurately described using single particle-hole excitations. We also consider the case of unequal masses. DOI: 10.1103/PhysRevLett.98.180402 PACS numbers: 05.30.Fk, 03.75.Ss, 71.10.Ca, 74.72.ÿh The investigation of ultracold Fermi gases with two unbalanced hyperfine states (which we shall denote as " and # ) has been through an impressive expansion last year. This subfield is of great interest both on practical and on theoretical grounds. Indeed, on one hand, it is related to other fields of physics, namely, superconductivity, astrophysics, and high-energy physics, where similar situations arise [1]. On the other hand, the additional parameter provided by the population imbalance should provide a tool to deepen our understanding of the Bose-Einstein condensation (BEC)-BCS crossover in these systems and contribute to improving our control of many-body theory. This recent activity has been started by striking experimental results [2] which have given rise to a considerable number of theoretical works [3]. Experiments performed on trapped systems have observed equal density superfluid states as well as partially and fully polarized regions.The analysis of the T 0 phase separation requires the knowledge of the properties of both the superfluid and the partially polarized normal phase [4 -6]. This has been developed in the recent work of Lobo et al. [6], where, at unitarity, the properties of the partially polarized phase have been obtained by calculating through a quantum Monte Carlo (QMC) approach the parameters which characterize a single # atom immersed in a Fermi sea of " atoms, with density n " k 3 F =62 . In this way, they were able to obtain very good agreement with experimental results.Here we consider the general problem of a single # atom in a completely polarized " atom Fermi sea. The " -# interaction is characterized by an s-wave scattering length a, whose value can be tuned via a Feshbach resonance from the BEC (1=k F a 1) to the BCS (1=k F a ÿ1) limits. The Fermi gas is ideal due to the suppression of higher angular momentum scattering at low temperatures. This problem is a much simpler one than the case of two equal spin populations in the BEC-BCS crossover, although still quite nontrivial due to the absence of a small parameter in the strongly interacting regime. It is the simplest realization of the moving impurity problem, and it bears a strong similarity with other old, famous, and notoriously difficult...

We perform a detailed study of the collective mode across the whole BEC-BCS crossover in fermionic gases at zero temperature, covering the whole range of energy beyond the linear regime. This is done on the basis of the dynamical BCS model. We recover first the results of the linear regime in a simple form. Then specific attention is payed to the non linear part of the dispersion relation and its interplay with the continuum of single fermionic excitations. In particular we consider in detail the merging of collective mode into the continuum of single fermionic excitations. This occurs not only on the BCS side of the crossover, but also slightly beyond unitarity on the BEC side. Another remarkable feature is the very linear behaviour of the dispersion relation in the vicinity of unitarity almost up to merging with the continuum. Finally, while on the BEC side the mode is quite analogous to the Bogoliubov mode, a difference appear at high wavevectors. On the basis of our results we determine the Landau critical velocity in the BEC-BCS crossover which is found to be largest close to unitarity. Our investigation has revealed interesting qualitative features which would deserve experimental exploration as well as further theoretical studies by more sophisticated means.

We consider a single atom within a Fermi sea of atoms. We elucidate by a full many-body analysis the quite mysterious agreement between Monte Carlo results and approximate calculations taking only into account single particle-hole excitations. It results from a nearly perfect destructive interference of the contributions of states with more than one particle-hole pair. This is linked to the remarkable efficiency of the expansion in powers of hole wave vectors, the lowest order leading to perfect interference. Going up to two particle-hole pairs gives an essentially perfect agreement with known exact results. Hence our treatment amounts to an exact solution of this problem.

We present an analytical treatment of a single ↓ atom within a Fermi sea of ↑ atoms, when the interaction is strong enough to produce a bound state, dressed by the Fermi sea. Our method makes use of a diagrammatic analysis, with the involved diagrams taking only into account at most two particle-hole pairs excitations. The agreement with existing Monte-Carlo results is excellent. In the BEC limit our equation reduces exactly to the Skorniakov and Ter-Martirosian equation. We present results when ↑ and ↓ atoms have different masses, which is of interest for experiments in progress.

The non elementary-boson nature of excitons controls Bose-Einstein condensation in semiconductors. Composite excitons interact predominantly through Pauli exclusion; this produces dramatic couplings between bright and dark states. In microcavities, where bright excitons and photons form polaritons, they force the condensate to be linearly polarized-as observed. In bulk, they also force linear polarization, but of dark states, due to interband Coulomb scatterings. To evidence this dark condensate, we thus need indirect processes, like the shift it induces on the (bright) exciton line.

We present a simple derivation of the energy formula found by Tan, relative to the single channel hamiltonian relevant for ultracold Fermi gases. This derivation is generalized to particles with different masses, to arbitrary mixtures, and to two-dimensional space. We show how, in a field theoretical approach, the 1/k 4 tail in the momentum distribution and the energy formula arise in a natural way. As a specific example, we consider quantitative calculations of the energy, from different formulas within the ladder diagrams approximation in the normal state. The comparison of the results provides an indication on the quality of the approximation.

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