Dynamical signatures of bound states in waveguide QED

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

Input-output formalism for few-photon transport: A systematic treatment beyond two photons

“…we will no longer make distinction between the left and right hand side of (32). In what follows, the time evolution of all system operators is considered as that in (34).…”

“…In most of these cases, the methods that were used were tailored to the property of the specific system. In the wavefunction approach for S matrix calculation [12,13,15,16,18,22,23,26,28,30,32], for example, the ansatz for the wavefunction used is specifically related to the local quantum system. As a result, it has been difficult, from these calculations, to identify the general features of S matrices for waveguide QED systems.…”

Characteristic dynamics near two coalescing eigenvalues incorporating continuum threshold effects

“…This result describes the system dynamics near the EP on the longest time scales, for which the t 3 effect is quite typical in open quantum systems [6,11,30,31,[89][90][91]. Hence we see that while the EP dramatically modifies the dynamics on intermediate time scales, the long time dynamics are qualitatively the same as the ordinary case away from the EP; although the time scale T EP at which the long time effect sets in may be modified according to the proximity of the EP2A to the band edge.…”

“…Note that the oscillatory behavior in the survival probability is a result of interference between the contributions from the two band edges; similar oscillatory expressions are obtained for the long time dynamics in the middle of the band (but, unlike the present case, away from any exceptional points) in Refs. [32,91].…”

“…The latter result for the far zone dynamics is fairly well known in the literature; for example, see Refs. [6,11,30,31,[89][90][91].…”