Dynamical signatures of bound states in waveguide QED

TL;DR

This paper investigates how the energy of an impurity affects the emitted photon and decay dynamics in waveguide QED, revealing complex temporal behaviors and robustness against losses.

Contribution

It provides a detailed analysis of the decay process and emitted photon properties in waveguide QED, highlighting the influence of impurity energy and the robustness of phenomena.

Findings

Photon frequency depends on impurity energy and band position.

Decay exhibits exponential, power-law, and oscillatory regimes.

Phenomenology remains stable with system losses.

Abstract

We study the spontaneous decay of an impurity coupled to a linear array of bosonic cavities forming a single-band photonic waveguide. The average frequency of the emitted photon is different from the frequency for single-photon resonant scattering, which perfectly matches the bare frequency of the excited state of the impurity. We study how the energy of the excited state of the impurity influences the spatial profile of the emitted photon. The farther the energy is from the middle of the photonic band, the farther the wave packet is from the causal limit. In particular, if the energy lies in the middle of the band, the wave packet is localized around the causal limit. Besides, the occupation of the excited state of the impurity presents a rich dynamics: it shows an exponential decay up to intermediate times, this is followed by a power-law tail in the long-time regime, and it finally reaches an oscillatory stationary regime. Finally, we show that this phenomenology is robust under the presence of losses, both in the impurity and the cavities.