Chiral gain-induced time-reversal symmetry breaking in quantum systems

Structured light offers a powerful approach to tailor light--matter interactions in quantum systems with chiral properties. While chirality has been extensively studied in passive platforms, the role of optical gain in controlling chiral quantum dynamics remains largely unexplored. In this work, we develop a general theoretical framework to describe the dynamics of an atomic system interacting with structured gain environments, where amplification depends on the light's polarization or momentum. By quantizing the electromagnetic field in linear bianisotropic media with gain and extending the Lindblad formalism to these settings, we derive a master equation governing the atom's irreversible evolution. We show that chiral gain can break time-reversal symmetry and drive the system toward a symmetry-broken steady state with nonreciprocal properties. This effect is illustrated in detail for moving plasmonic substrates, which exhibit inherently chiral gain that selectively amplifies transitions of a given handedness. Our results establish chiral gain as a novel mechanism for engineering nonreciprocal quantum steady states.