Effects of modal dispersion on few-photon–qubit scattering in one-dimensional waveguides

Abstract

We study one-and two-photon scattering from a qubit embedded in a one-dimensional waveguide in the presence of modal dispersion. We use a resolvent based analysis and utilize techniques borrowed from the Lee model studies. Modal dispersion leads to atom-photon bound states which necessitate the use of multichannel scattering theory. We present multichannel scattering matrix elements in terms of the solution of a Fredholm integral equation of the second kind. Through the use of the Lippmann-Schwinger equation, we derive an infinite series of Feynman diagrams that represent the solution to the integral equation. We use the Feynman diagrams as vertex correction terms to come up with closed form formulas that successfully predict the trapping rate of a photon in the atom-photon bound state. We verify our formalism through Krylov-subspace based numerical studies with pulsed excitations. Our results provide the tools to calculate the complex correlations between scattered photons in a dispersive environment.

Inelastic Scattering of Photon Pairs in Qubit Arrays with Subradiant States

“…[40], it has the advantage of a compact matrix formulation valid for any arbitrary spatial arrangement of the qubits. Thus, contrary to other Green-function-based techniques [46,47], we are able to obtain a closed-form answer with a transparent analytical structure. Namely, the S-matrix describing the forward incoherent scattering reads…”

Bound state and non-Markovian dynamics of a quantum emitter around a surface plasmonic nanostructure

“…Recently, a bound state between a QE and surface plasmon polaritons (SPPs) is predicted [61], where the QE does not decay completely to its ground state and part of its excited-state population is trapped in the steady state even in the presence of the lossy metal. Different from the previous investigation [33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48], it is an open quantum system and there is no photonic band gap in the positive frequency domain. The formation of a QE-SPP bound state has been attributed to the strong field confinement which can greatly enhance their interaction.…”

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

“…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.…”