Finite-Temperature Study of Bose-Fermi Superfluid Mixtures

Ultra-cold atom experiments offer the unique opportunity to study mixing of different types of superfluid states. Our interest is in superfluid mixtures comprising particles with different statistics- Bose and Fermi. Such scenarios occur naturally, for example, in dense QCD matter. Interestingly, cold atomic experiments are performed in traps with finite spatial extent, thus critically destabilizing the occurrence of various homogeneous phases. Critical to this analysis is the understanding that the trapped system can undergo phase separation, resulting in a unique situation where phase transition in either species (bosons or fermions) can overlap with the phase separation between possible phases. In the present work, we illustrate how this intriguing interplay manifests in an interacting 2-species atomic mixture - one bosonic and another fermionic with two spin components - within a realistic trap configuration. We further show that such interplay of transitions can render the nature of the ground state to be highly sensitive to the experimental parameters and the dimensionality of the system.Comment: 9 pages, 7 figures; Accepted for publication in Phys. Rev.

Signatures of Strong Correlations in One-Dimensional Ultra-Cold Atomic Fermi Gases

Recent success in manipulating ultra-cold atomic systems allows to probe different strongly correlated regimes in one-dimension. Regimes such as the (spin-coherent) Luttinger liquid and the spin-incoherent Luttinger liquid can be realized by tuning the inter-atomic interaction strength and trap parameters. We identify the noise correlations of density fluctuations as a robust observable (uniquely suitable in the context of trapped atomic gases) to discriminate between these two regimes. Finally, we address the prospects to realize and probe these phenomena experimentally using optical lattices.Comment: 4 pages, 2 figure

Analytic models of ultra-cold atomic collisions at negative energies for application to confinement-induced resonances

We construct simple analytic models of the $S$-matrix, accounting for both scattering resonances and smooth background contributions for collisions that occur below the s-wave threshold. Such models are important for studying confinement-induced resonances such as those occurring in cold collisions of $^{133}$Cs atoms in separated sites of a polarization-gradient optical lattice. Because these resonances occur at negative energy with respect to the s-wave threshold, they cannot be studied easily using direct numerical solutions of the Schr\"{o}dinger equation. Using our analytic model, we extend previous studies of negative-energy scattering to the multichannel case, accounting for the interplay of Feshbach resonances, large background scattering lengths, and inelastic processes.Comment: 9 page