Single particle dynamical signature of topology induced by single mode cavities in Su-Schrieffer-Heeger chain

TL;DR

This paper investigates how a single particle in a Su-Schrieffer-Heeger chain coupled to cavity modes exhibits topological phase transitions, detectable through the mean chiral displacement, especially under different frequency regimes.

Contribution

It demonstrates that cavity coupling induces observable signatures in the mean chiral displacement, revealing topological properties in a driven-dissipative quantum system.

Findings

Discontinuous jump in MCD at high frequencies indicating topological transition

Signature in survival edge probability when dynamics start at edges

Smooth MCD behavior at intermediate frequencies due to competition between topology and dissipation

Abstract

Witnessing and tracking topological phase transitions induced by interactions with the environment is a crucial challenge. Among the various experimental approaches to detect topological properties, the Mean Chiral Displacement (MCD) has emerged as a powerful bulk probe in one-dimensional chiral systems, allowing the extraction of the topological invariant from single-particle dynamics. Here we study the dynamics of a single particle in a one-dimensional Su-Schrieffer-Heeger chain coupled to multiple cavity modes via inter-cell hopping terms, focusing on the out-of-equilibrium behavior of the MCD. We show that, whenever the frequency is larger than the static hopping amplitudes, the coupling induces a discontinuous jump in the MCD, already at small times, signaling that such a coupling also leaves a signature in the survival edge probability when the dynamics are initialized at one of the two edges. For frequencies comparable to the static hopping amplitudes, topological order competes with dissipative effects, which makes the MCD behave smoothly, retaining information about the driven-dissipative topology.