Non-Markovian dynamics of a qubit due to single-photon scattering in a waveguide

Abstract

We investigate the open dynamics of a qubit due to scattering of a single photon in an infinite or semi-infinite waveguide. Through an exact solution of the time-dependent multi-photon scattering problem, we find the qubitʼs dynamical map. Tools of open quantum systems theory allow us then to show the general features of this map, find the corresponding non-Linbladian master equation, and assess in a rigorous way its non-Markovian nature. The qubit dynamics has distinctive features that, in particular, do not occur in emission processes. Two fundamental sources of non-Markovianity are present: the finite width of the photon wavepacket and the time delay for propagation between the qubit and the end of the semi-infinite waveguide.Clarifying the importance of NM effects and the mechanisms behind their onset is thus pivotal in waveguide QED. At the same time, the theory of OQS [34,35] is currently making major advances, yielding a more accurate understanding of NM effects [36][37][38][39]. Through an approach often inspired by quantum information concepts [40], a number of physical properties such as information back-flow [41] and divisibility [42] have been spotlighted as distinctive manifestations of quantum NM behavior and then used to formulate corresponding quantum non-Markovianity measures. These tools have been effectively applied to dynamics in various scenarios [37,38], including in waveguide QED with regard to emission processes [26, 32] 5 such as a single atom emitting into a semi-infinite waveguide [26].Motivated by the need to quantify NM effects in photon scattering from qubits, we present a case study of a qubit undergoing single-photon scattering in an infinite or semi-infinite waveguide (see figure 1), the latter of which is the basis of the proposed controlled-Z [12] and controlled-NOT [13] gates. We aim at answering two main questions: What are the essential features of the qubit open dynamics during scattering? Is such dynamics NM?The key task is to find the dynamical map (DM) of the qubit in the scattering process, which fully describes the open dynamics and is needed in order to apply OQS tools [38]. A distinctive feature of our open dynamics is that the bath (the waveguide field) is initially in a well-defined single-photon state [43,44]. Toward this task, we tackle in full the time evolution of multiple excitations (in contrast to those limited to the one-excitation sector [43,[45][46][47][48]), a problem that has become important recently [30,31,33,[49][50][51][52][53][54][55][56][57].Intuitively, one may expect that the dynamics is fully Markovian in the infinite-waveguide case and NM in the semi-infinite case due to the atom-mirror delay time. We show that this expectation is inaccurate in general, mostly because it does not account for a fundamental source of NM behavior namely the wavepacket bandwidth. This NM mechanism is present in an infinite waveguide, while in a semi-infinite waveguide it augments the natural NM behavior coming from the photon delay time.Recently, NM effects in infi...

Exact Markovian and non-Markovian time dynamics in waveguide QED: collective interactions, bound states in continuum, superradiance and subradiance

“…In Section III, we review previous work on the real-space formalism while clarifying some steps that were omitted in the literature, and construct the time evolution operator for the single-excitation subspace. We review the scattering problem in the realspace formalism [32,34,35] and extend the analysis to multi-qubit systems coupled to a 1D waveguide. We also touch on some interesting many-body physics phenomena such as bound states in continuum (BIC) [36,37]-which had not yet been studied in a linear chain of arbitrary atoms using the real-space approach, nor had they been considered in time evolution-and the related dark and bright states.…”

“…In this paper, we make several fundamental and applied contributions. First, we add the final missing pieces in the theory of single-excitation time dynamics of photon-mediated interactions-in both the Markovian and non-Markovian [5,32,33] regimes-by incorporating bound states in continuum (BIC). We develop the connection between the poles of the scattering parameters and collective decay rates, opening the way to analytic results in a variety of scenarios.…”

Enhancement of spontaneous entanglement generation via coherent quantum feedback

“…Inspired by previous studies, we investigate the spontaneous entanglement generation between two two-level * binzhang220@163.com emitters (qubits) chirally coupled to a 1D semi-infinite waveguide [33][34][35][36][37][38][39]. The finite end of the waveguide is terminated by a perfect mirror, which may reflect photons moving towards it and thus induce time-delayed emitterphoton interaction.…”

“…The finite end of the waveguide is terminated by a perfect mirror, which may reflect photons moving towards it and thus induce time-delayed emitterphoton interaction. Indeed, this system is a very simple example of coherent quantum feedback that suffices for the occurrence of nonexponential atomic decay [36] and non-Markovian dynamics [37,38]. In this paper, we first derive the delay derivative equations (DDEs) for the evolution of the two-qubit reduced system, and study the entanglement dynamics for the qubits.…”

Long-distance dissipation-assisted transport of entangled states via a chiral waveguide

“…In general, long-distance processes in open quantum systems are challenging because of non-Markovian effects due to the non-negligible time delay between the nodes of a quantum network. Non-Markovianity has been shown to be detrimental to both quantum state transfer and entanglement generation between the nodes [5,6].…”