Quantum Optical Soliton Dynamics Beyond Linearization: An Open-System Approach

TL;DR

This paper develops two open-system quantum models for optical solitons, capturing complex non-Gaussian dynamics and quantum effects beyond linearization, with applications to stability, phase shifts, and dissipation.

Contribution

It introduces novel methods to analyze quantum soliton dynamics using system-reservoir projections, applicable to non-perturbative regimes and non-Gaussian states.

Findings

Both methods accurately predict quantum phase shifts in solitons.

The LSM approach captures photon loss from non-Markovian effects.

Classical and ME theories underestimate dissipation due to dispersive broadening.

Abstract

We introduce two approaches to modeling the quantum dynamics of optical $\chi^{(3)}$ solitons. Taking an open-system viewpoint, we project the underlying quantum field into system (soliton) and residual reservoir components. The reservoir is treated as either (i) a discrete ``Lanczos supermode'' (LSM) expansion which localizes dynamics to a few-supermode basis, or (ii) a non-local environment which can be traced out by deriving a Markovian master equation (ME). Using these methods, we analyze and identify the quantum structure of both the soliton's stability and its hierarchy of perturbations. Through numerical simulations, we confirm both methods effectively capture quantum-induced soliton phase shifts in a concise few-mode (single-mode for ME) basis, and the LSM approach also captures photon loss which arises from non-Markovian dispersive couplings. As neither method is limited to the linearized regime, our approaches provide powerful computational tools to analyze complex non-Gaussian quantum dynamics of solitons where other commonly-used methods fail, providing insight into such non-perturbative regimes. We also investigate radiation that occurs in the presence of higher-order dispersion with ultrashort pulses, deriving a ME that predicts photon loss consistent with classical theory, but find that both classical and ME theory dramatically underestimate the actual amount of dissipation, which we explain in terms of dispersive coupling-induced soliton broadening.