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

TL;DR

The paper investigates how environment-induced topology can be detected from single-particle dynamics in an SSH chain coupled to local cavity modes. Using Mean Chiral Displacement (MCD) and survival edge probability as dynamical probes, it shows that in the antiadiabatic regime ($\omega_0 > v,w$) the boson–fermion coupling renormalizes hopping and drives a topological transition, evidenced by a discontinuous MCD and nonzero edge survival. When $\omega_0$ is comparable to $v$ and $w$, dissipative effects soften the MCD response but still retain signatures of the induced topology. The work highlights dynamical, bulk-based indicators of environment-driven topology and outlines routes for experimental observation and extensions to richer baths and spinful or non-Hermitian settings.

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.

Figures (14)

• Figure 1: Panel (a): Open SSH chain coupled to inter-cell hopping with several cavity modes at fixed frequency $\omega_0$. The central unit cell is set as the origin of the position reference frame. Panel (b): The dynamics used for the MCD are initialized from a state localized in the central unit cell. Panel (c): The survival edge probability is evaluated for dynamics starting with the electron initially localized at one of the two edges.
• Figure 2: Mean Chiral Displacement (panel (a)) and survival edge probability (panel (b)) for the bare SSH model (described by Eq. \ref{['bare SSH']}) as functions of different ratios of the hopping $v/w$.
• Figure 3: Mean Chiral Displacement (panels (a) and (b)) and survival edge probability (panels (c) and (d)) for the SSH model as functions of dimensionless time, for different values of the coupling $\alpha$ and for $N=201$ unit cells.
• Figure 4: Mean Chiral Displacement (panel (a)) and survival edge probability (panel (b)) as function of time after a sudden quench. Purple curves correspond to $\alpha=0.3$.
• Figure 5: Mean Chiral Displacement (panel (a)) and its FFT (panel (b)) as functions of dimensionless time and frequency respectively, for different values of the frequency $\omega_0$ at coupling $\alpha=0.3$.