Two-photon scattering in a waveguide by a giant atom

TL;DR

This paper analyzes two-photon scattering in a waveguide coupled to a giant atom with multiple coupling points, revealing how the atom's structure influences photon correlations and scattering properties.

Contribution

It provides a comprehensive theoretical framework for two-photon scattering involving a giant atom with multiple coupling points, including eigenstates, bound states, and the S-matrix, extending previous models.

Findings

Oscillation period and decay rates depend on coupling point distance.

Photon correlation can be enhanced by adjusting coupling point distances.

Increasing the number of coupling points further enhances photon correlations.

Abstract

We study two-photon scattering by a two-level giant atom in a waveguide. We first study the case that the giant atom is coupled to the waveguide via two coupling points, and obtain Bethe ansatz eigenstates and eigenvalues in the Hilbert space of two-excitation. Then we derive bound states by subtracting the states corresponding to Bethe ansatz solutions from the entire two-excitation Hilbert space, and construct the two-photon scattering matrix (S-matrix) by using Bethe ansatz eigenstates and bound states. We further study the properties of output states, which include both the scattering and bound states, for arbitrarily incident two-photon states by using a concrete example. We find that the oscillation period of the scattering states and decay rates of the bound states strongly depend on the distance between two coupling points. Moreover, we find that the two-photon correlation in the bound states can be enhanced by changing such distance when the total energy of two incident photons equals to two times of single photon resonance energy. We also generalize our study to the case that the giant atom is coupled to the waveguide via $N$ coupling points. We obtain all the eigenstates and eigenvalues of the scattering matrix and construct the S-matrix. Comparing with the case of the two coupling points, we find the photon correlation can be further enhanced by increasing the number of the coupling points for the same incident states when the distance of any two nearest neighbor coupling points is half of the wavelength.