Cavity-induced superconducting and $4k_F$ charge-density-wave states

TL;DR

This paper proposes experimental setups using optical resonators to induce and observe superconducting and charge-density-wave states in fermionic atoms, highlighting cavity feedback as a mechanism for self-organization.

Contribution

It introduces novel cavity-assisted methods to realize and study s-wave superconductivity and 4k_F charge density waves in cold atom systems, combining experimental design with theoretical analysis.

Findings

Cavity feedback induces s-wave pairing in fermionic chains.

Self-organization into 4k_F charge density wave in ladder structures.

Theoretical identification of steady states using density matrix renormalization group.

Abstract

We propose two experimental setups for fermionic atoms in a high-finesse optical resonator in which either a superconducting state with s-wave symmetry of the pairs or a 4k F charge density wave can self-organize. In order to stabilize the s-wave pairing, a two component attractively in- teracting fermionic gas is confined to a one dimensional chain structure by an optical lattice. The tunneling of the atoms along the chains is suppressed initially by an energy offset between neighbor- ing sites. A Raman transition using the cavity mode and a transversal pump laser then reintroduces a cavity-assisted tunneling. The feedback mechanism between the cavity field and the atoms leads to a spontaneous occupation of the cavity field and of a state of the fermionic atoms which is dominated by s-wave pairing correlations. Extending the setup to a quasi-one-dimensional ladder structure where the tunneling of atoms along the rungs of the ladder is cavity-assisted, the repul- sively interacting fermionic atoms self-organize into a 4k F charge density wave. We use adiabatic elimination of the cavity field combined with state-of-the-art density matrix renormalization group methods in finite systems in order to identify the steady state phases of the system.