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arXiv:cond-mat/0603498 · Physical Review A

Pairing in a three-component Fermi gas

Tomi Paananen, J.-P. Martikainen, Päivi Törmä

Published May 10, 2006• 69 citations
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Abstract

We consider pairing in a three-component gas of degenerate fermions. In particular, we solve the finite-temperature mean-field theory of an interacting gas for a system where both interaction strengths and fermion masses can be unequal. At zero temperature, we find the possibility of a quantum phase transition between states associated with pairing between different pairs of fermions. On the other hand, finite-temperature behavior of the three-component system reveals some qualitative differences from the two-component gas: for a range of parameters it is possible to have two different critical temperatures. The lower one corresponds to a transition between different pairing channels, while the higher one corresponds to the usual superfluid-normal transition. We discuss how these phase transitions could be observed in ultracold gases of fermionic atoms.

DOI
10.1103/physreva.73.053606

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We consider pairing in a three-component gas of degenerate fermions. In particular, we solve the finite-temperature mean-field theory of an interacting gas for a system where both interaction strengths and fermion masses can be unequal. At zero temperature, we find the possibility of a quantum phase transition between states associated with pairing between different pairs of fermions. On the other hand, finite-temperature behavior of the three-component system reveals some qualitative differences from the two-component gas: for a range of parameters it is possible to have two different critical temperatures. The lower one corresponds to a transition between different pairing channels, while the higher one corresponds to the usual superfluid-normal transition. We discuss how these phase transitions could be observed in ultracold gases of fermionic atoms.
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.
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 s-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.
We investigated possible superfluid phases at finite temperature in a two-component Fermi gas with density imbalance. In the frame of a general four-fermion interaction theory, we solved in the BCS region the gap equations for the pairing gap and pairing momentum under the restriction of fixed number densities and analyzed the stability of different phases by calculating the superfluid density and number susceptibilities. The homogeneous superfluid is stable only at high temperature and low number asymmetry, the inhomogeneous Larkin-Ovchinnikov-Fudde-Ferrell state survives at low temperature and high number asymmetry, and in between them there exists another possible inhomogeneous phase, that of phase separation. The critical temperatures and the orders of the phase transitions among the superfluid phases and normal phase are calculated analytically and numerically. The phase diagram we obtained in the temperature and number asymmetry plane is quite different from the one in the temperature and chemical potential difference plane for a system with fixed chemical potentials.
Ultracold three-component atomic Fermi gases in one dimension are expected to exhibit rich physics due to the presence of trions and different pairing states. Quantum phase transitions from the trion state into a paired phase and a normal Fermi liquid occur at zero temperature. We derive the analytical thermodynamics of strongly attractive three-component one-dimensional fermions with SU(3) symmetry via the thermodynamic Bethe ansatz method in unequal Zeeman splitting fields H1{H}_{1}H1​ and H2{H}_{2}H2​. We find explicitly that for low temperature the system acts like either a two-component or a three-component Tomonaga-Luttinger liquid dependent on the system parameters. The phase diagrams for the chemical potential and specific heat are presented for illustrative values of the Zeeman splitting. We also demonstrate that crossover between different Tomonaga-Luttinger-liquid phases exhibit singular behavior in specific heat and entropy as the temperature tends to zero. Beyond Tomonaga-Luttinger-liquid physics, we obtain the equation of state which provides a precise description of universal thermodynamics and quantum criticality in three-component, strongly attractive Fermi gases.
We develop a pairing-field formalism for ab initio studies of non-relativistic two-component fermions on a (d+1)-dimensional spacetime lattice. More specifically, we focus on theories where the interaction between the two components can be described by the exchange of a corresponding pairing field. The introduction of a pairing field may indeed be convenient for studies of, e.g., the finite-temperature phase structure and critical behavior of, e.g., ultracold atomic Fermi gases. Moreover, such a formalism allows to directly compute the momentum and frequency dependence of the pair propagator, from which the pair-correlation function can be extracted. For a first illustration of the application of our formalism, we compute the density equation of state and the superfluid order parameter for a gas of unpolarized fermions in (0+1) dimensions by employing the complex Langevin approach to surmount the sign problem.
We develop a pairing-field formalism for ab initio studies of non-relativistic two-component fermions on a (d+1)-dimensional spacetime lattice. More specifically, we focus on theories where the interaction between the two components can be described by the exchange of a corresponding pairing field. The introduction of a pairing field may indeed be convenient for studies of, e.g., the finite-temperature phase structure and critical behavior of, e.g., ultracold atomic Fermi gases. Moreover, such a formalism allows to directly compute the momentum and frequency dependence of the pair propagator, from which the pair-correlation function can be extracted. For a first illustration of the application of our formalism, we compute the density equation of state and the superfluid order parameter for a gas of unpolarized fermions in (0+1) dimensions by employing the complex Langevin approach to surmount the sign problem.