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We study three-dimensional Bose and Fermi gases in the upper branch, a phase defined by the absence of bound states in the repulsive interaction regime, within an approximation that considers only two-body interactions. Employing a formalism based on the S matrix, we derive useful analytic expressions that hold on the upper branch in the weak coupling limit. We determine upper branch phase diagrams for both bosons and fermions with techniques valid for arbitrary positive scattering length. [ABSTRACT FROM AUTHOR]

We study the virial expansion for three-dimensional Bose and Fermi gases at finite temperature using an approximation that only considers two-body processes and is valid for high temperatures and low densities. The first virial coefficients are computed and the second is exact. The results are obtained for the full range of values of the scattering length, and the unitary limit is recovered as a particular case. A weak coupling expansion is performed and the free case is also obtained as a proper limit. The influence of an anisotropic harmonic trap is considered using the local density approximation (LDA), analytical results are obtained, and the special case of the isotropic trap is discussed in detail. [ABSTRACT FROM AUTHOR]

We show that an ansatz based on independent composite bosons [Phys. Rep. 463, 215 (2008)] accurately describes the condensate fraction of molecular Bose-Einstein condensates in ultracold Fermi gases. The entanglement between the fermionic constituents of a single Feshbach molecule then governs the many-particle statistics of the condensate, from the limit of strong interaction to close to unitarity. This result strengthens the role of entanglement as the indispensable driver of composite-boson behavior. The condensate fraction of fermion pairs at zero temperature that we compute matches excellently previous results obtained by means of fixed-node diffusion Monte Carlo methods and the Bogoliubov depletion approximation. This paves the way towards the exploration of the BEC-BCS crossover physics in mixtures of cold Fermi gases with an arbitrary number of fermion pairs as well as the implementation of Hong-Ou-Mandel-like interference experiments proposed within coboson theory. [ABSTRACT FROM AUTHOR]

We study both Bose and Fermi gases at finite temperature and density in an approximation that sums an infinite number of many-body processes that are reducible to two-body scatterings. This is done for arbitrary negative scattering length, which interpolates between the ideal and unitary gas limits. In the unitary limit, we compute the first four virial coefficients within our approximation. The second virial coefficient is exact, and we extend the previously known result for fermions to bosons and also for both bosons and fermions for the upper branch on the other side of unitarity (infinitely large positive scattering length). Assuming bosons can exist in a metastable state before undergoing mechanical collapse, we map out the critical temperatures for strongly coupled Bose-Einstein condensation as a function of scattering length. [ABSTRACT FROM AUTHOR]