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arXiv:0806.0419 · Physical Review B

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

Ryan M. Kalas, Alexander V. Balatsky, Dmitry Mozyrsky

Published Nov 18, 2008• 19 citations
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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.

DOI
10.1103/physrevb.78.184513

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We consider a system of repulsively interacting Bose-Fermi mixtures of spin-polarized uniform atomic gases at zero temperature. We examine possible realization of ppp-wave superfluidity of fermions due to an effective attractive interaction via density fluctuations of Bose-Einstein condensate within mean-field approximation. We find the ground state of the system by direct energy comparison of the ppp-wave superfluid state in a single uniform mixed phase and normal Fermi gas state in a phase-separated phase, and suggest an occurrence of the ppp-wave superfluidity for a strong boson-fermion interaction regime. We study some signatures of the ppp-wave superfluid, such as anisotropic energy gap and quasiparticle energy in the axial state, that have not been observed in spin-unpolarized superfluid of atomic fermions. We also show that a Cooper pair is a tightly bound state, such as a diatomic molecule in the strong boson-fermion coupling regime, and suggest an observable indication of the ppp-wave superfluid in the real experiment.
Unconventional superconductivity and superfluidity are among the most exciting and fascinating quantum phenomena in condensed-matter physics. Usually such states are characterized by nontrivial spin or spatial symmetry of the pairing order parameter, such as ``spin triplet'' or ``ppp wave.'' However, besides spin and spatial dependence the order parameter may have unconventional frequency dependence which is also permitted by Fermi-Dirac statistics. Odd-frequency fermionic pairing is an exciting paradigm when discussing exotic superfluidity or superconductivity and is yet to be realized in experiments. In this paper we propose a symmetry-based method of controlling frequency dependence of the pairing order parameter via manipulating the inversion symmetry of the system. First, a toy model is introduced to illustrate that frequency dependence of the order parameter can be achieved through our proposed approach. Second, by taking advantage of recent rapid developments in producing spin-orbit-coupled dispersions in ultracold gases, we propose a Bose-Fermi mixture to realize such frequency-dependent superfluid. The key idea is introducing the frequency-dependent attraction between fermions mediated by Bogoliubov phonons with asymmetric dispersion. Our proposal should pave an alternative way for exploring frequency-dependent superfluids with cold atoms.
We investigate many-body phase diagrams of atomic boson-fermion mixtures loaded in the two-dimensional optical lattice. Bosons mediate an attractive, finite-range interaction between fermions, leading to fermion pairing phases of different orbital symmetries. Specifically, we show that by properly tuning atomic and lattice parameters it is possible to create superfluids with sss-, ppp-, and ddd-wave pairing symmetry as well as spin and charge density wave phases. These phases and their stability are analyzed within the mean-field approximation for systems of $^{40}\mathrm{K}\text{\ensuremath{-}}^{87}\mathrm{Rb}$ and $^{40}\mathrm{K}\text{\ensuremath{-}}^{23}\mathrm{Na}$ mixtures. For the experimentally accessible regime of parameters, superfluids with unconventional fermion pairing have transition temperature around a percent of the Fermi energy.
Cooper pairing caused by an induced interaction represents a paradigm in our description of fermionic superfluidity. Here, we present a strong coupling theory for the critical temperature of p-wave pairing between spin polarized fermions immersed in a Bose-Einstein condensate. The fermions interact via the exchange of phonons in the condensate, and our self-consistent theory takes into account the full frequency and momentum dependence of the resulting induced interaction. We demonstrate that both retardation and self-energy effects are important for obtaining a reliable value of the critical temperature. Focusing on experimentally relevant systems, we perform a systematic analysis varying the boson-boson and boson-fermion interaction strength as well as their masses, and identify the most suitable system for realizing a p-wave superfluid. Our results show that such a superfluid indeed is experimentally within reach using light bosons mixed with heavy fermions.
We reveal that the ppp-wave superfluid can be realized in a mixture of fermionic and F=1F=1F=1 bosonic gases. We derive a general set of the gap equations for gaps in the sss and ppp channels. It is found that the spin-spin Bose-Fermi interactions favor the ppp-wave pairing and naturally suppress the pairing in the sss channel. The gap equations for the polar phase of ppp-wave superfluid fermions are numerically solved. Our study suggests a way to realize a pure ppp-wave superfluid in a well-controlled environment of atomic physics.