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arXiv:cond-mat/0604638 · Physical Review Letters

Surface Tension in Unitary Fermi Gases with Population Imbalance

Theja N. De Silva, Erich J. Mueller

Published Aug 17, 2006• 87 citations
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Abstract

We study the effects of surface tension between normal and superfluid regions of a trapped Fermi gas at unitarity. We find that surface tension causes notable distortions in the shape of large aspect ratio clouds. Including these distortions in our theories resolves many of the apparent discrepancies among different experiments and between theory and experiments.

DOI
10.1103/physrevlett.97.070402

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We study the effects of surface tension between normal and superfluid regions of a trapped Fermi gas at unitarity. We find that surface tension causes notable distortions in the shape of large aspect ratio clouds. Including these distortions in our theories resolves many of the apparent discrepancies among different experiments and between theory and experiments.
We show that the maximum population imbalance ratio PCCP_\mathrm{CC}PCC​ for a two-component Fermi gas near the unitarity limit to condense does not increase with the trap aspect ratio λλλ, by two methods of 1) solving the Bogoliubov-de Gennes equations with coupling-constant renormalization, and 2) studying the pairing susceptibility by the real-space self-consistent TTT-matrix approximation. The deviation of the cloud shape from what is expected from the trap shape increases but stays minor with increasing λλλ up to 50. This finding indicates that despite the apparent discrepancy between the MIT and Rice experiments over the value of PCCP_\mathrm{CC}PCC​ and the validity of local density approximation, the equilibrium state of the system for the aspect ratio in the Rice experiment should be consistent with that of MIT.
We present a series of theoretical studies of the boundary between a superfluid and a normal region in a partially polarized gas of strongly interacting fermions. We present mean-field estimates of the surface energy in this boundary as a function of temperature and scattering length. We discuss the structure of the domain wall, and use a previously introduced phenomonological model to study its influence on experimental observables. Our microscopic mean-field calculations are not consistent with the magnitude of the surface tension found from our phenomonological modeling of data from the Rice University experiments. We conclude that one must search for novel mechanisms to explain the experiments.
This thesis presents a theoretical study of strongly-interacting Fermi systems with population imbalance, which is motivated by some differences in cold atoms experiments. We calculate the energy of a single fermion interacting resonantly with a Fermi sea of different species fermions in anisotropic traps, and show that finite particle numbers and the trap geometry impact the phase structure and the critical polarization, the limit of resonance superfluidity in traps. Our findings contribute to understanding some experimental discrepancies as finite-size and confinement effects. For an imbalanced gas in the uniform system, we calculate the energy of adding an impurity, and construct the equation of state of the partially-polarized normal Fermi liquid. Finally, we study the properties of a spin-down polaron in a trapped gas containing arbitrary numbers of spin-up and spin-down fermions, and derive a self-consistent equation for the polaron energy.