Engineering Frequency-dependent Superfluidity in Bose-Fermi Mixtures

TL;DR

This paper proposes a method to control the frequency dependence of superfluid pairing in Bose-Fermi mixtures using inversion symmetry manipulation, aiming to realize exotic odd-frequency superfluidity in ultracold atomic systems.

Contribution

It introduces a symmetry-based approach to engineer frequency-dependent superfluidity and proposes a Bose-Fermi mixture in shaken optical lattices to experimentally realize this.

Findings

Frequency dependence of the order parameter can be tuned by symmetry control.

A Bose-Fermi mixture with asymmetric phonon dispersion can induce frequency-dependent attraction.

Potential realization of odd-frequency superfluidity in cold atom experiments.

Abstract

Unconventional superconductivity or superfluidity are among the most exciting and fascinating quantum states in condensed matter physics. Usually these states are characterized by non-trivial spatial symmetry of the pairing order parameter, such as in $^{3}He$ and high-$T_{c}$ cuprates. Besides spatial dependence the order parameter could have unconventional frequency dependence, which is also allowed by Fermi-Dirac statistics. For instance, odd-frequency pairing is an exciting paradigm when discussing exotic superfluidity or superconductivity and is yet to be realized in the 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 adjusted by controlling the inversion symmetry of the system. Second, taking advantage of the recent rapid developments of shaken optical lattices in ultracold gases, we propose a Bose-Fermi mixture to realize such frequency dependent superfluids. 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 superconductors or superfluids with cold atoms.