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arXiv:0901.2945 · Physical Review A

Theory of the normal-superfluid interface in population-imbalanced Fermi gases

Stefan K. Baur, Sourish Basu, Theja N. De Silva, Erich J. Mueller

Published Jun 24, 2009• 22 citations
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Abstract

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.

DOI
10.1103/physreva.79.063628

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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.
Transport in strongly interacting Fermi gases provides a window into the nonequilibrium behavior of strongly correlated fermions. In particular, the interface between a strongly polarized normal gas and a weakly polarized superfluid at finite temperature presents a model for understanding transport at normal-superfluid and normal-superconductor interfaces. An excess of polarization in the normal phase or a deficit of polarization in the superfluid brings the system out of equilibrium, leading to transport currents across the interface. We implement a phenomenological mean-field model of the unitary Fermi gas, and investigate the transport of spin and mass under nonequilibrium conditions. We consider independently prepared normal and superfluid regions brought into contact, and calculate the instantaneous spin and mass currents across the normal-superfluid (NS) interface. For an unpolarized superfluid, we find that spin current is suppressed below a threshold value in the driving chemical potential differences, while the threshold nearly vanishes for a critically polarized superfluid. The mass current can exhibit a threshold in cases where Andreev reflection vanishes, while in general Andreev reflection prevents the occurrence of a threshold in the mass current. Our results provide guidance to future experiments aiming to characterize spin and mass transport across NS interfaces.
In the first part of this thesis, we present an inhomogeneous theory for the low-temperature properties of a resonantly interacting Fermi mixture in a trap that goes beyond the local-density approximation. We compare a Bogoliubov-de Gennes and a Landau-Ginzburg approach that both include mean-field-like self-energy effects to account for the strong interactions at unitarity. We conclude that the Landau-Ginzburg approach is more appropriate when dealing with a first-order phase transition. We show diagrammatically how these self-energy effects arise from fluctuations in the superfluid order parameter. Gradient terms of the order parameter are included to account for inhomogeneities. This approach incorporates the state-of-the-art knowledge of the homogeneous mixture with a population imbalance exactly and gives good agreement with the experimental density profiles of Shin et al. [Nature 451, 689 (2008)]. We calculate the universal surface tension due to the observed interface between the equal-density superfluid and the partially polarized normal state of the mixture. We find that the exotic and gapless superfluid Sarma phase can be stabilized at this interface, even when this phase is unstable in the bulk of the gas. We also discuss the possibility of a metastable state to explain the deformation of the superfluid core that is seen in the experiment of Partridge et al. [Science 311, 503 (2006)]. In the second part, we show that a two-channel mean-field theory for a Bose gas near a Feshbach resonance allows for an analytic computation of the chemical potential, and therefore the universal constant β, at unitarity. To improve on this mean-field theory, which physically neglects condensate depletion, we study a variational Jastrow ansatz for the ground-state wavefunction and use the hypernetted-chain (HNC/0) approximation to minimize the energy for all positive values of the scattering length. We also show that other important physical quantities such as Tan's contact and the condensate fraction can be directly obtained from this approach.
We argue that, for the recent experiments with imbalanced fermion gases, a temperature difference may occur between the normal (N) and the gapped superfluid (SF) phase. Using the mean-field formalism, we study particle scattering off the N-SF interface from the deep BCS to the unitary regime. We show that the thermal conductivity across the interface drops exponentially fast with increasing h/kBTh/{k}_{B}Th/kB​T, where hhh is the chemical potential imbalance. This implies a blocking of thermal equilibration between the N and the SF phase. We also provide a possible mechanism for the creation of gap oscillations [Fulde-Ferrell-Larkin-Ovchinnikov (FFLO)-like states] as seen in recent studies on these systems.