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arXiv:1011.5336 · New Journal of Physics

Coexistence of pairing gaps in three-component Fermi gases

O H T Nummi, J. J. Kinnunen, Päivi Törmä

Published May 25, 2011• 7 citations
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Abstract

We study a three-component superfluid Fermi gas in a spherically symmetric harmonic trap using the Bogoliubov–deGennes method. We predict a coexistence phase in which two pairing field order parameters are simultaneously non-zero, in stark contrast to studies performed for trapped gases using local density approximation. We also discuss the role of atom number conservation in the context of a homogeneous system.

DOI
10.1088/1367-2630/13/5/055013

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We study a three-component superfluid Fermi gas in a spherically symmetric harmonic trap using the Bogoliubov–deGennes method. We predict a coexistence phase in which two pairing field order parameters are simultaneously non-zero, in stark contrast to studies performed for trapped gases using local density approximation. We also discuss the role of atom number conservation in the context of a homogeneous system.
Abstract Experiments with ultracold gases on the lattice give the opportunity to realize superfluid fermionic mixtures in a trapping potential. The external trap modifies the chemical potential locally. Moreover, this trap also introduces non-homogeneity in the superconducting order parameter. There are, among other approaches, two methods which can be used to describe the system of two-component mixtures loaded into an optical lattice: the Local Density Approximation (LDA) and the self-consistent Bogoliubov–de Gennes equations. Here, we compare results obtained within these two methods. We conclude that the results can be distinguishable only in the case of a small value of the pairing interaction.
We study the properties of a trapped interacting three component Fermi gas. We assume that one of the components can have a different mass from the other two. We calculate the different phases of the three component mixture and find a rich variety of different phases corresponding to different pairing channels, and simple ways of tuning the system from one phase to another. In particular, we predict coexistence of several different superfluids in the trap, forming a shell structure, and phase transitions from this mixture of superfluids to a single superfluid when the system parameters or temperature is varied. Such shell structures realize superfluids with a nontrivial spatial topology and leave clear observable signatures in the density profile of the gas.
We in this paper investigate the phase diagram associated with the Bardeen-Cooper-Schrieffer--Bose-Einstein-condensate (BCS-BEC) crossover of a three-component ultracold superfluid Fermi gas of different chemical potentials and equal masses in two dimensions. The gap-order parameter and number densities are found analytically by using the functional-path-integral method. The balance of pairing will be broken in the free space due to the unequal chemical potentials. We obtain the same particle-number density and condensed fraction in the BCS-superfluid phase as those in a recent paper [Phys. Rev. A 83, 033630 (2011)] while the Sarma phase of the coexistence of normal and superfluid Fermi gases is characteristic of an inhomogeneous system. The minimum ratio of the BCS-superfluid phase becomes 1/3 in the BCS limit corresponding to the zero ratio in the two-component system in which the critical point of phase separation is ${\ensuremath{\epsilon}}_{B}/{\ensuremath{\epsilon}}_{F}=2$, but it becomes 3 in the three-component case.
We investigate the mean-field ground state of a homogeneous three-component attractive Fermi gas at zero temperature. This is achieved by deriving a set of Bogoliubov--de Gennes (BdG) equations of the three-component system, including pairing both order parameters ${\ensuremath{\Delta}}_{\mathit{ij}}$ and coherence order parameters $\ensuremath{\langle}{\ensuremath{\psi}}_{i}^{\ifmmode\dagger\else\textdagger\fi{}}{\ensuremath{\psi}}_{j}\ensuremath{\rangle}$ ($i\ensuremath{\ne}j$), where ${\ensuremath{\psi}}_{j}$ is the field operator for spin level jjj. Ward-Takahashi identities are obtained to constrain these order parameters. In addition, we present an explicit analytic mean-field solution for symmetric systems and verify that the quasiparticle excitations consist of both gapped and gapless spectra, which correspond to the excitations of paired and unpaired atoms. We further point out that the omission of $\ensuremath{\langle}{\ensuremath{\psi}}_{i}^{\ifmmode\dagger\else\textdagger\fi{}}{\ensuremath{\psi}}_{j}\ensuremath{\rangle}$ in BdG equations could lead to an overestimation of ${\ensuremath{\Delta}}_{\mathit{ij}}$ in the strong coupling regime.
It is quite common that several different phases exist simultaneously in a system of trapped quantum gases of ultra-cold atoms. One example is the strongly interacting Fermi gas with two imbalanced spin species, which has received a great deal of attention owing to the possible occurrence of exotic superfluid phases. By using novel numerical techniques and algorithms, we self-consistently solve the Bogoliubov–de Gennes equations, which describe Fermi superfluids in the mean-field framework. From this study, we investigate the novel phases of spin-imbalanced Fermi gases and examine the validity of local density approximation (LDA), which is often invoked in the extraction of bulk properties from experimental measurements within trapped systems. We show how the validity of the LDA is affected by the trapping geometry, the number of atoms and the spin imbalance.
We study pairing of an interacting three-component Fermi gas in two dimensions. By using a mean-field theory to decouple the interactions between different pairs of Fermi components, we study the free energy landscapes as a function of various system parameters including chemical potentials, binding energies, and temperature. We find that the sss-wave pairing channel is determined by both chemical potentials and the interaction strengths between the three available channels. We find a second-order thermal phase transition and a series of first-order quantum phase transitions for a homogenous system as we change the parameters. In particular, for symmetric parameters, we find the simultaneous existence of three superfluid orders as well as re-entrant quantum phase transitions as we tune the parameters.