Abstract
We consider a quantum emitter ("atom") radiating in a one-dimensional (1D) photonic waveguide in the presence of a single mirror, resulting in a delay differential equation for the atomic amplitude. We carry out a systematic analysis of the non-Markovian (NM) character of the atomic dynamics in terms of refined, recently developed notions of quantum non-Markovianity such as indivisibility and information back-flow. NM effects are quantified as a function of the round-trip time and phase shift associated with the atom-mirror optical path. We find, in particular, that unless an atom-photon bound state is formed a finite time delay is always required in order for NM effects to be exhibited. This identifies a finite threshold in the parameter space, which separates the Markovian and non-Markovian regimes.
Highlights
The distinction between Markovian and non-Markovian regimes has long been considered a basic one in the study of open system dynamics, i.e., when the system of interest is in contact with an external environment
We have studied the occurrence of non-Markovianity in the emission process of an atom coupled to a one-dimensional field, in the presence of a single mirror which imposes a hard-wall boundary condition on the latter
Adopting the nondivisibility of time evolution as the chosen definition of non-Markovianity, and the NM quantifier proposed in Ref. [7], we have studied the strength of NM effects in our system as a function of the two effective parameters characterizing the model: the rescaled round-trip time γ td and the phase φ
Summary
The distinction between Markovian and non-Markovian regimes has long been considered a basic one in the study of open system dynamics, i.e., when the system of interest is in contact with an external environment. Within the limits of validity of the model, our study clearly illustrates how the non-Markovianity of the atomic emission is affected by imposing simple boundary conditions on the radiation field In this spirit it is worth recalling that, even in the light of modern NM measures, spontaneous emission of a single atom (in vacuum) embodies the paradigmatic Markovian open dynamics: the emitted radiation travels away from the atom, so that the latter has no chance to retrieve information about its past dynamics from the electromagnetic field (i.e., the environment). Further details on the treatment of the atom-mirror dynamics are given in the Appendix
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