Quantum correlations of the photon fields in a waveguide quantum electrodynamics

TL;DR

This paper provides a quantum dynamical analysis of photon correlations in waveguide QED, revealing interference effects in second-order correlations for single-photon scattering on a two-level atom.

Contribution

It offers an analytical expression for the electric field operator and explores photon correlation functions in a waveguide QED setup with up to two excitations.

Findings

Second order correlation function shows interference effects.

Photon measurements are correlated similar to Hanbury Brown and Twiss.

Analytic expressions for electric field operators in this system.

Abstract

We present a time-dependent quantum calculations of the first order and second order photon correlation functions for the scattering of a single-photon pulse on a two-level atom (qubit) embedded in a one-dimensional open waveguide. Within Markov approximation we find the analytic expression for the quantum operator of positive frequency electric field. We restricted Hilbert space of initial states by the states with one and two excitations and show that the photon probability amplitudes are given by the off-diagonal matrix elements of the electric field operator between these states. For two-excitation initial state where the atom is excited and there exists a single photon in a waveguide we calculate the second order correlation function which describes the measurements by two detectors at two different space-time points. The second order correlation function exhibits the interference term showing that the measurements of two detectors are correlated. This interference is similar to that found in the Hanbury Brown and Twiss correlation experiment with two indistinguishable photons.