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arXiv:0908.3733 · Physical Review Letters

Induced Interactions and the Superfluid Transition Temperature in a Three-Component Fermi Gas

J.-P. Martikainen, J. J. Kinnunen, Päivi Törmä, C. J. Pethick

Published Dec 28, 2009• 23 citations
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Abstract

We study many-body contributions to the effective interaction between fermions in a three-component Fermi mixture. We find that effective interactions induced by the third component can lead to a phase diagram different from that predicted if interactions with the third component are neglected. As a result, in a confining potential a superfluid shell structure can arise even for equal populations of the components. We also find a critical temperature for the BCS transition in a 6Li mixture which can deviate strongly from the one in a weakly interacting two-component system.

DOI
10.1103/physrevlett.103.260403

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We study many-body contributions to the effective interaction between fermions in a three-component Fermi mixture. We find that effective interactions induced by the third component can lead to a phase diagram different from that predicted if interactions with the third component are neglected. As a result, in a confining potential a superfluid shell structure can arise even for equal populations of the components. We also find a critical temperature for the BCS transition in a 6Li mixture which can deviate strongly from the one in a weakly interacting two-component system.
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.
Many-body effects on superfluidity and transition temperatures are calculated for optical lattices and uniform systems with ultracold multi-component Fermi gases. The induced interactions depend sensitively on the interactions between the multi-components and their densities. The s- and d-wave pairing gaps and critical temperatures are calculated for optical lattices at low (dilute) filling as well as near half filling to leading orders in the interaction strength with and without induced interactions. They can deviate strongly from dilute two-component systems and affect the phase diagram. In two dimensional optical lattices the induced interactions are singular at half filling and strongly affect s- and d-wave superfluidity.
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 calculate the effects of induced interactions on the transition temperature to the BCS state in dilute Fermi gases. For a pure Fermi system with two species having equal densities, the transition temperature is suppressed by a factor (4e)(1/3) approximately 2.2, and for nu fermion species, the transition temperature is increased by a factor (4e)(nu/3-1) approximately 2.2(nu-3). For mixtures of fermions and bosons the exchange of boson density fluctuations gives rise to an attractive interaction, and we estimate the increase of the transition temperature due to this effect.
After an introduction into 100 years of research on superfluidity and the concept of the BCS-BEC crossover, we describe recent experimental studies of a spin-polarized Fermi gas with strong interactions. Tomographically resolving the spatial structure of an inhomogeneous trapped sample, we have mapped out the superfluid phases in the parameter space of temperature, spin polarization, and interaction strength. Phase separation between the superfluid and the normal component occurs at low temperatures, showing spatial discontinuities in the spin polarization. The critical polarization of the normal gas increases with stronger coupling. Beyond a critical interaction strength all minority atoms pair with majority atoms, and the system can be effectively described as a boson-fermion mixture. Pairing correlations have been studied by rf spectroscopy, determining the fermion pair size and the pairing gap energy in a resonantly interacting superfluid.
We investigate a three-component fermion mixture in the presence of weak attractive interactions. We use a combination of the equation of motion and the Gaussian variational mean-field approaches, which both allow for simultaneous superfluid and magnetic ordering in an unbiased way, and capture the interplay between the two order parameters. This interplay significantly modifies the phase diagram, especially the superfluid-normal phase boundaries. In the close vicinity of the critical temperature and for small chemical potential imbalances, strong particle-hole symmetry breaking leads to a phase diagram similar to the one predicted by Cherng et al. [Phys. Rev. Lett. 99, 130406 (2007)], however, the overall phase diagram is markedly different: additional chemical potential-driven first- and second-order transitions and triple points emerge as well as more exotic second-order multicritical points, and bicritical lines with O(2,2)\text{O}(2,2)O(2,2) symmetry. We identify the terms which are necessary to capture this complex phase diagram in a Ginzburg-Landau approach, and determine the corresponding coefficients.