Quantum theory of light scattering in a one-dimensional channel: Interaction effect on photon statistics and entanglement entropy

TL;DR

This paper provides an exact quantum analysis of light scattering in a one-dimensional channel, revealing how photon statistics and entanglement are affected by system parameters and detuning.

Contribution

It introduces a comprehensive quantum scattering approach that accounts for spatial and temporal parameters, offering new insights into photon statistics and entanglement in 1D light-matter interactions.

Findings

Reflected photon statistics can switch from sub- to super-Poissonian with detuning.

Transmitted photon statistics are always super-Poissonian.

Entanglement entropy follows area laws and is bounded by a four-level system entropy.

Abstract

We provide a complete and exact quantum description of coherent light scattering in a one-dimensional multi-mode transmission line coupled to a two-level emitter. Using recently developed scattering approach we discuss transmission properties, power spectrum, the full counting statistics and the entanglement entropy of transmitted and reflected states of light. Our approach takes into account spatial parameters of an incident coherent pulse as well as waiting and counting times of a detector. We describe time evolution of the power spectrum as well as observe deviations from the Poissonian statistics for reflected and transmitted fields. In particular, the statistics of reflected photons can change from sub-Poissonian to super-Poissonian for increasing values of the detuning, while the statistics of transmitted photons is strictly super-Poissonian in all parametric regimes. We study the entanglement entropy of some spatial part of the scattered pulse and observe that it obeys the area laws and that it is bounded by the maximal entropy of the effective four-level system.