Characterization of Polariton Dynamics in a Multimode Cavity (II): Coherent-Incoherent Transition Driven by Photon Loss

TL;DR

This paper investigates how photon loss influences polariton dynamics in a multimode cavity, revealing a transition from coherent to incoherent behavior and uncovering novel spectral and wave packet features driven by non-Hermitian effects.

Contribution

It provides a detailed spectral and dynamical analysis of non-Hermitian polariton behavior under photon loss, identifying the critical transition and symmetry properties in lossy cavities.

Findings

Identification of an exceptional point at resonance due to photon loss

Observation of reversed propagation and ballistic-to-diffusion transition

Spectral features like level repulsion and bifurcation in polariton dynamics

Abstract

Motivated by the recent advances in optical imaging and tracking of wave-packet propagation in optical cavities, we systematically explore the non-Hermitian polariton dynamics within a decay-tunable multimode cavity model. The complex eigen-spectrum of the model Hamiltonian allows us to predict the incoherent-coherent transition induced by photon losses, which defines an exceptional point at resonance and evolves analytically as the wavevector shifts off-resonantly. The resulting dispersion relation, group velocity, and relaxation rate exhibit striking signatures, such as curve crossing, level repulsion, turnover, bifurcation, and coalescence, as the decay rate crosses the critical transition or the wavevector crosses the resonance. The spectral characterization leads to surprising features in the non-Hermitian wave packet dynamics: (i) maximal population relaxation rate at the critical transition; (ii) reversed propagation in the center-of-mass motion; (iii) ballistic-to-diffusion transition; (iv) contraction in the displacement and width of the polariton wave-packet. These dynamical features have complementary symmetry between the upper-polariton (UP) branch and lower-polariton (LP) branch in the two-dimensional phase diagram spanned by the photon decay rate and wavevector. Thus, the combination of complex spectral characterization and non-Hermitian wave packet propagation establishes the photon decay rate as a powerful control parameter for polariton transport, reveals the underlying symmetry in lossy cavities, and presents a starting point to incorporate other dissipative mechanisms.