Quantum dynamics of propagating photons with strong interactions: a generalized input-output formalism

TL;DR

This paper introduces a generalized input-output formalism that enables exact calculation of photon dynamics and correlations in strongly interacting one-dimensional photonic systems, facilitating analysis of complex quantum light-matter interactions.

Contribution

The authors develop a novel, exact input-output formalism for analyzing the dynamics of few photons in strongly interacting systems, adaptable to various system configurations.

Findings

Exact calculation of photon dynamics and correlations

Application to systems with infinite-range interactions

Demonstration of selective transmission of correlated multi-photon states

Abstract

There has been rapid development of systems that yield strong interactions between freely propagating photons in one dimension via controlled coupling to quantum emitters. This raises interesting possibilities such as quantum information processing with photons or quantum many-body states of light, but treating such systems generally remains a difficult task theoretically. Here, we describe a novel technique in which the dynamics and correlations of a few photons can be exactly calculated, based upon knowledge of the initial photonic state and the solution of the reduced effective dynamics of the quantum emitters alone. We show that this generalized "input-output" formalism allows for a straightforward numerical implementation regardless of system details, such as emitter positions, external driving, and level structure. As a specific example, we apply our technique to show how atomic systems with infinite-range interactions and under conditions of electromagnetically induced transparency enable the selective transmission of correlated multi-photon states.