Odd-frequency pairing in a binary mixture of bosonic and fermionic cold atoms

Abstract

We study fermionic superfluidity in a boson-single-species-fermion cold-atom mixture. We argue that apart from the standard p-wave fermion pairing mediated by the phonon field of the boson gas, the system also exhibits s-wave pairing with the anomalous correlator being an odd function of time or frequency. We show that such a superfluid phase can have a much higher transition temperature than the p-wave and may exist for sufficiently strong couplings between fermions and bosons. These conditions for odd-frequency pairing are favorable close to the value of the coupling at which the mixture phase separates. We evaluate the critical temperatures for this system and discuss the experimental realization of this superfluid in ultracold atomic gases.

Phase separation and collapse in Bose-Fermi mixtures with a Feshbach resonance

“…Finally, we note that in this work we have neglected the possibility of fermionic superfluidity induced by density fluctuations of the bosonic condensate: For a spin polarized Fermi gas, boson-mediated p-wave 9 and s-wave odd-frequency 10 Cooper pairing have been recently analyzed for the single-channel model. In both cases it has been found that the conditions for Cooper pairing are favorable for a repulsive enough Bose-Fermi interaction strength U BF .…”

“…Even richer scenarios are expected for heteronuclear resonances in Bose-Fermi mixtures, because one can in principle destroy the BEC by binding bosons and fermions into fermionic molecules. 5 Moreover, a host of novel phenomena has been predicted, such as spatial separation of bosons and fermions induced by interspecies repulsive interactions, 6,7 boson-mediated Cooper pairing, 8,9,10 density wave phases in optical lattices, 11 and the formation of polar molecules with dipolar interactions.…”

On the Puzzle of Odd-Frequency Superconductivity

“…This is the source of various drawbacks of the odd-frequency pairing. However, since the anomalous green function should be defined with respect to the given meanfield gap function with broken U(1) gauge symmetry, we must first set up the relation between ∆ ↑↑ (k) and ∆ ↑↑ (k) by the minimum condition of the free energy as (10), and the anomalous green functions are determined afterward. With this procedure, we always obtain ∆ ↑↑ (k) = ∆ ↑↑ (k) * and F ↑↑ (k) = F ↑↑ (k) * both for the even-frequency and the odd-frequency pairing.…”

Possible Odd-Frequency Superconductivity in Strong-Coupling Electron–Phonon Systems

“…A universal feature of superconductivity so far stimulates to discuss the OF pairing in connection with experimental reality in the heavyfermion systems, 15,16) superconducting junctions, [17][18][19][20][21][22][23][24][25][26][27][28][29][30] vortex core, 31,32) proximity effect of superfluid 3 He 33) and the cold atoms. 34) Aside from the intensive studies, the homogenous state of the OF pairing has struggled against the fundamental difficulties such as the thermodynamic instability 7,35,36) and the unphysical Meissner effect. 4) These difficulties have hampered further investigation on the property of the superconducting state except a determination of the transition temperature T c .…”