A Superradiant Topological Peierls Insulator inside an Optical Cavity

TL;DR

This paper demonstrates that a spinless ultracold Fermi gas in an optical cavity can undergo a superradiant transition to a topological Peierls insulator with observable edge states, driven by light-matter interactions and symmetry breaking.

Contribution

It reveals a novel topological phase transition in a cavity QED system with fermions, showing how superradiance induces a topological insulator with measurable edge states.

Findings

Topological Peierls insulator forms at a specific Fermi momentum.

Edge states are detectable via cavity spectrum broadening.

Zak phase correlates with the cavity field phase.

Abstract

We consider a spinless ultracold Fermi gas tightly trapped along the axis of an optical resonator and transversely illuminated by a laser closely tuned to a resonator mode. At a certain threshold pump intensity the homogeneous gas density breaks a $\mathbf{Z}_2$ symmetry towards a spatially periodic order, which collectively scatters pump photons into the cavity. We show that this known self-ordering transition also occurs for low field seeking fermionic particles when the laser light is blue-detuned to an atomic transition. The emergent superradiant optical lattice in this case is homopolar and possesses two distinct dimerizations. Depending on the spontaneously chosen dimerization the resulting Bloch bands can have a non-trivial topological structure characterized by a non-vanishing Zak phase. In the case the Fermi momentum is close to half the cavity-mode wavenumber, a Peierls-like instability here creates a topoloical insulator with a gap at the Fermi surface, which hosts a pair of edge states. The topological features of the system can be non-destructively observed via the cavity output: the Zak phase of the bulk coincides with the relative phase between laser and cavity field, while the fingerprint of edge states can be observed as additional broadening in a well defined frequency window of the cavity spectrum.