Quantum Dynamics of Dissipative Polarizable Media

Classical polarizable models have long been the standard for simulating multiscale condensed-phase systems, yet their inherently dissipative nature calls for a rigorous quantum treatment. We aim to provide a unified framework for describing dissipative media and quantum optics—an approach relevant to nanophotonics, quantum plasmonics, and condensed-matter systems.

In this talk, I will present a Hamiltonian framework for the quantum dynamics of polarizable sources, built on a generalized theory of the damped harmonic oscillator and formulated using pseudo-boson theory to capture coherent-state behavior. This formalism naturally situates polarizable media within the language of open quantum systems.

We apply this theory to analyze the optical response of two distinct plasmonic systems, highlighting new insights that emerge from our perspective. Utilizing the phase-space formulation of quantum mechanics and the integrability of quadratic Hamiltonians, I will derive a self-consistent relation for the emitted electric field under a semiclassical approximation, using exact expressions for the medium's polarization.

To conclude, I will present a master equation describing the open dynamics of a quantum system interacting with such a polarizable medium, along with analytical expressions for correlation functions evaluated over arbitrary Gaussian states.

Reference: https://link.aps.org/doi/10.1103/nxs1-rhqx , arXiv:2501.12070 [quant-ph]

Acknowledgments: The authors (FEQR, Piero Lafiosca, Tommaso Giovannini, Chiara Cappelli) acknowledge funding from MUR-FARE Ricerca in Italia: Framework per l'attrazione ed il rafforzamento delle eccellenze per la Ricerca in Italia - III edizione. Prot. R20YTA2BKZ.