Waveguide QED: Power Spectra and Correlations of Two Photons Scattered Off Multiple Distant Qubits and a Mirror

TL;DR

This paper investigates how two photons interact with multiple distant qubits and a mirror in a waveguide, revealing complex photon correlations and spectral features influenced by interference and non-Markovian effects.

Contribution

It provides a detailed analysis of two-photon scattering in waveguide QED with multiple qubits and non-Markovian dynamics, extending previous Markovian models.

Findings

Reflected photons are initially bunched due to stimulated emission.

Correlations exhibit rapid oscillations with increasing qubits.

Resonant driving leads to sharp spectral features and band gap localization.

Abstract

We study two-level systems (2LS) coupled at different points to a one-dimensional waveguide in which one end is open and the other is either open (infinite waveguide) or closed by a mirror (semi-infinite). Upon injection of two photons (corresponding to weak coherent driving), the resonance fluorescence and photon correlations are shaped by the effective qubit transition frequencies and decay rates, which are substantially modified by interference effects. In contrast to the well-known result in an infinite waveguide, photons reflected by a single 2LS coupled to a semi-infinite waveguide are initially bunched, a result that can be simply explained by stimulated emission. As the number of 2LS increases (up to 10 are considered here), rapid oscillations build up in the correlations that persist for a very long time. For instance, when the incoming photons are slightly detuned, the transmitted photons in the infinite waveguide are highly antibunched. On the other hand, upon resonant driving, incoherently reflected photons are mostly distributed within the photonic band gap and several sharp side peaks. These features can be explained by considering the poles of the single particle Green function in the Markovian regime combined with the time delay. Our calculation is not restricted to the Markovian regime, and we obtain several fully non-Markovian results. We show that a single 2LS in a semi-infinite waveguide can not be decoupled by placing it at the node of the photonic field, in contrast to recent results in the Markovian regime. Our results illustrate the complexities that ensue when several qubits are strongly coupled to a bus (the waveguide) as might happen in quantum information processing.