Quantum transport of strongly interacting photons in a one-dimensional nonlinear waveguide

TL;DR

This paper develops a theoretical method to analyze quantum transport of a few strongly interacting photons in a one-dimensional nonlinear waveguide, revealing phenomena like photon anti-bunching and bunching related to photon interactions and bound states.

Contribution

It introduces a new theoretical approach for solving quantum transport in nonlinear waveguides with tunable interactions, highlighting effects at the single-photon level.

Findings

Strongly interacting photons can be controlled to exhibit anti-bunching or bunching.

Photon interactions lead to suppression or enhancement of multi-photon transmission.

Bound states of photons are responsible for the observed bunching behavior.

Abstract

We present a theoretical technique for solving the quantum transport problem of a few photons through a one-dimensional, strongly nonlinear waveguide. We specifically consider the situation where the evolution of the optical field is governed by the quantum nonlinear Schr\"odinger equation (NLSE). Although this kind of nonlinearity is quite general, we focus on a realistic implementation involving cold atoms loaded in a hollow-core optical fiber, where the atomic system provides a tunable nonlinearity that can be large even at a single-photon level. In particular, we show that when the interaction between photons is effectively repulsive, the transmission of multi-photon components of the field is suppressed. This leads to anti-bunching of the transmitted light and indicates that the system acts as a single-photon switch. On the other hand, in the case of attractive interaction, the system can exhibit either anti-bunching or bunching, which is in stark contrast to semiclassical calculations. We show that the bunching behavior is related to the resonant excitation of bound states of photons inside the system.