One-Dimensional Waveguide Coupled to Multiple Qubits: Photon-Photon Correlations

TL;DR

This paper investigates photon-photon correlations in a 1D waveguide coupled to multiple qubits, revealing complex behaviors influenced by frequency and qubit separation, with implications for quantum microwave experiments.

Contribution

It provides a detailed analysis of photon correlations in multi-qubit waveguide systems, including both non-Markovian and Markovian models, highlighting conditions where simplified approaches are accurate.

Findings

Photon correlations depend sensitively on qubit separation and frequency.

Transmitted and reflected photons can exhibit initial bunching followed by anti-bunching.

Markovian approximation is accurate for small qubit separations.

Abstract

For a one-dimensional (1D) waveguide coupled to two or three qubits, we show that the photon-photon correlations have a wide variety of behavior, with structure that depends sensitively on the frequency and on the qubit-qubit separation $L$. We study the correlations by calculating the second-order correlation function $g_2(t)$ in which the interference among the photons multiply scattered from the qubits causes rich structure. In one case, for example, transmitted and reflected photons are both bunched initially, but then become strongly anti-bunched for a long time interval. We first calculate the correlation function $g_2(t)$ including non-Markovian effects and then show that a much simpler Markovian treatment, which can be solved analytically, is accurate for small qubit separation. As a result, the non-classical properties of microwaves in a 1D waveguide coupled to many superconducting qubits with experimentally accessible separation $L$ could be readily explored with our approach.