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Journal of Physics B Atomic Molecular and Optical Physics

Pairing in cold Fermi gases and Fermi–Bose mixtures

Jordi Mur-Petit, A. Polls, M. Baldo, H.-J. Schulze

Published Mar 24, 2004• 7 citations
Publisher

Abstract

The possibilities of pairing in a low-density, cold Fermi gas interacting either through the interaction with another fermionic species or through a bosonic gas are analysed. In the latter case, special attention is devoted to the study of the experimentally relevant situation of a two-dimensional system. Estimates for the gaps at zero temperature in experimental conditions are presented.

DOI
10.1088/0953-4075/37/7/062

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The possibilities of pairing in a low-density, cold Fermi gas interacting either through the interaction with another fermionic species or through a bosonic gas are analysed. In the latter case, special attention is devoted to the study of the experimentally relevant situation of a two-dimensional system. Estimates for the gaps at zero temperature in experimental conditions are presented.
An effective interaction between fermions in a Bose-Fermi mixture is derived. It is induced by density fluctuations of the bosonic background. The contributions from states containing both one and two virtual phonons are taken into account self-consistently. The time dependence of the effective interaction has been removed by assuming that the velocity of the fermions at the Fermi surface is much larger than the sound velocity in the Bose gas. This assumption is more appropriate for the actual experimental situations than the usual approximation of neglecting retardation effects. The effective interaction turns out to be attractive and, as a consequence, can give rise to a superconducting phase in the Fermi component of the mixture. The fermions are considered in only one magnetic state, so that pairing can be effective only in odd-lll channels. It has been found that the onset of the superconducting phase can occur at temperatures (>100nK)(>100\mathrm{nK})(>100nK) of the same order of magnitude as the Fermi temperature $(\ensuremath{\sim}300\mathrm{nK}),$ and the energy gap in the excitation spectrum is a small fraction $(\ensuremath{\sim}1%)$ of the Fermi energy.
Ultracold atom experiments offer the unique opportunity to study mixing of different types of superfluid states. Our interest is in superfluid mixtures comprising of particles with different statistics---Bose and Fermi. Such scenarios occur naturally, for example, in dense quantum chromodynamics (QCD) matter. Interestingly, cold atomic experiments are performed in traps with finite spatial extent, thus critically destabilizing the occurrence of various homogeneous phases. Critical to this analysis is the understanding that the trapped system can undergo phase separation, resulting in a unique situation where phase transition in either species (bosons or fermions) can overlap with the phase separation between possible phases. In the present work, we illustrate how this intriguing interplay manifests in an interacting two-species atomic mixture---one bosonic and another fermionic with two spin components---within a realistic trap configuration. We further show that such interplay of transitions can render the nature of the ground state to be highly sensitive to the experimental parameters and the dimensionality of the system.
We consider a model of a Fermi-Bose mixture with strong hard-core repulsion between particles of the same sort and attraction between particles of different sorts. In this case, besides the standard anomalous averages of the type ⟨b⟩⟨b⟩⟨b⟩, ⟨bb⟩⟨bb⟩⟨bb⟩, and ⟨cc⟩⟨cc⟩⟨cc⟩, a pairing between fermions and bosons of the type bcbcbc is possible. This pairing corresponds to the creation of composite fermions in the system. At low temperatures and equal densities of fermions and bosons composite fermions are further paired in quartets. At higher temperatures trios, which consist of composite fermions and elementary bosons, are also present in the system. Our investigations are important in connection with the recent observation of weakly bound dimers in magnetic and optical dipole traps at ultralow temperatures and with the observation of the collapse of a Fermi gas in an attractive Fermi-Bose mixture of neutral particles.
We study the role of the Bose–Fermi (BF) pair correlations in the cold BF-mixture of atomic gases. After summarizing the previous results on the formation of composite BF-pairs in the uniform BF mixture, we present an exactly solvable model where bosons and fermions are distributed over finite number of orbits and interact via attractive pairing-type interaction. We show that, as the interaction strength increases, BF pairs with different quantum numbers are gradually created in the ground state through a series of level crossings, until finally the system becomes a Fermi sea of BF-pairs.
We consider the model of a Fermi-Bose mixture with strong hard-core repulsion between particles of the same sort and attraction between particles of different sorts. In this case, in addition to the standard anomalous averages of the type 〈 b 〉, 〈 bb 〉, and 〈 cc 〉, pairing between fermions and bosons of the type 〈 bc 〉 is possible. This pairing corresponds to creation of composite fermions in the system. At low temperatures and equal densities of fermions and bosons, composite fermions are further paired into quartets. At higher temperatures, trios consisting of composite fermions and elementary bosons are also present in the system. Our investigations are important in connection with the recent observation of weakly bound dimers in magnetic and optical dipole traps at ultralow temperatures and with the observation of collapse of a Fermi gas in an attractive Fermi-Bose mixture of neutral particles.
Similar to what has recently been achieved with Bose-Bose mixtures [G. Lamporesi, J. Catani, G. Barontini, Y. Nishida, M. Inguscio, and F. Minardi, Phys. Rev. Lett. 104, 153202 (2010)], mixed-dimensional Fermi-Fermi mixtures can be created by applying a species-selective one-dimensional optical lattice to a two-species Fermi gas ($\ensuremath{\sigma}\ensuremath{\equiv}{\ensuremath{\uparrow},\ensuremath{\downarrow}}$), in such a way that both species are confined to quasi--two-dimensional geometries determined by their hoppings along the lattice direction. We investigated the ground-state phase diagram of superfluidity for such mixtures in the BCS-BEC evolution, and found normal, gapped superfluid, gapless superfluid, and phase separated regions. In particular, we found a stable gapless superfluid phase where the unpaired $\ensuremath{\uparrow}$ and $\ensuremath{\downarrow}$ fermions coexist with the paired (or superfluid) ones in different momentum space regions. This phase is in some ways similar to the Sarma state found in mixtures with densities, but in our case, the gapless superfluid phase is unpolarized and most importantly it is stable against phase separation.