Beyond Adiabatic Elimination in Topological Floquet Engineering

TL;DR

This paper introduces two novel driven-induced elimination mechanisms in topological Floquet systems, both theoretically and experimentally, challenging traditional adiabatic assumptions and enabling new control over Floquet states.

Contribution

It reports the discovery and experimental demonstration of quasi-adiabatic and high-frequency-limited eliminations in topological Floquet systems, expanding the understanding of spectral reduction under non-adiabatic conditions.

Findings

Experimental observation of driven-induced eliminations in microwave Floquet simulator

Revealed mechanisms between adiabatic and driven-induced eliminations

Potential for advanced Floquet engineering in various physical systems

Abstract

In quantum mechanics, adiabatic elimination is a standard tool that produces a low-lying reduced Hamiltonian for a relevant subspace of states, incorporating effects of its coupling to states with much higher energy. Suppose this powerful elimination approach is applied to quasi-energy states in periodically-driven systems, a critical question then arises that the violation of the adiabatic condition caused by driven forces challenges such a presence of spectral reduction in the non-equilibrium driven system. Here, both theoretically and experimentally, we newly reported two kinds of driven-induced eliminations universal in topologically-protected Floquet systems. We named them "quasi-adiabatic elimination" and "high-frequency-limited elimination", in terms of different driven frequencies that deny the underlying requirement for the adiabatic condition. Both two non-adiabatic eliminations are observed in our recently developed microwave Floquet simulator, a programmable test platform composed of periodically-bending ultrathin metallic coupled corrugated waveguides. Through the near-field imaging on our simulator, the mechanisms between the adiabatic and driven-induced eliminations are revealed, indicating the ubiquitous spectral decomposition for tailoring and manipulating Floquet states with quasi-energies. Finally, we hope our findings may open up profound and applicable possibilities for further developing Floquet engineering in periodically-driven systems, ranging from condensed matter physics to photonics.