Collective excitation profiles and the dynamics of photonic condensates

Abstract

Photonic condensates are complex systems exhibiting phase transitions due to the interaction with their molecular environment. Given the macroscopic number of molecules that form a reservoir of excitations, numerical simulations are expensive, even for systems with few cavity modes. We present a systematic construction of molecular excitation profiles with a clear hierarchical ordering, such that only modes in the lowest order in the hierarchy directly affect the cavity photon dynamics. In addition to a substantial gain in computational efficiency for simulations of photon dynamics, the explicit spatial shape of the mode profiles offers a clear physical insight into the competition among the cavity modes for access to molecular excitations.

Noncritical Slowing Down of Photonic Condensation

“…The system dynamics is described well in terms of rate equations for the occupations n i of cavity modes and a vector f characterizing the inhomogeneous fractional excitation of all dye molecules [17]. A suitable construction of collective modes of molecular excitations [18] enables the reduction of the molecular environment to its most relevant degrees of freedom. To this end, the vector f is decomposed into a hierarchy of several components f j ¼ P j f with suitably defined projectors P j .…”

“…By construction the cavity dynamics depends only on the level-0 component f 0 , and the level-(j þ 1) component f jþ1 affects the cavity dynamics only indirectly via its influence on the level-j component f j . A truncation after two or three levels provides an excellent description of the system dynamics with substantial gain in numerical efficiency [18].…”

“…The level-0 component f 0 can be expanded into a set of vectors e i such that the equation of motion [17,18]…”

“…, the vector x with elements ½x j ¼ P þ P i g ij A i n i , the pump rate P, and the decay constant Γ ↓ for nonradiative decay or emission into free space [17,18].…”

Learning the Fuzzy Phases of Small Photonic Condensates

“…( 2) and ( 4) can be greatly reduced by approximating the full spatial resolution of the model with a hierarchy of collective molecular modes F m . 48,49 Sufficiently accurate results can be obtained by truncating the hierarchy after a few orders. In the collective mode picture, Eq.…”