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

Abstract

We develop a formalism for modelling exact time dynamics in waveguide quantum electrodynamics (QED) using the real-space approach. The formalism does not assume any specific configuration of emitters and allows the study of Markovian dynamics fully analytically and non-Markovian dynamics semi-analytically with a simple numerical integration step. We use the formalism to study subradiance, superradiance and bound states in continuum. We discuss new phenomena such as subdivision of collective decay rates into symmetric and anti-symmetric subsets and non-Markovian superradiance effects that can lead to collective decay stronger than Dicke superradiance. We also discuss possible applications such as pulse-shaping and coherent absorption. We thus broaden the range of applicability of real-space approaches beyond steady-state photon transport.

Non-Markovian super-superradiance in a linear chain of up to 100 qubits

“…This phenomenon, predicted when the distance between emitters is small compared to the wavelength of radiation, can be understood as collective behaviour of the entire system. Curiously, enhanced emission can also occur when the emitters are macroscopically separated [6][7][8][9]; a regime in which collective behaviour might not be expected. What's more, the emission can become more enhanced than Dicke superradiance; earning it the name super-superradiance (SSR) [8].…”

“…Curiously, enhanced emission can also occur when the emitters are macroscopically separated [6][7][8][9]; a regime in which collective behaviour might not be expected. What's more, the emission can become more enhanced than Dicke superradiance; earning it the name super-superradiance (SSR) [8]. This highly counter-intuitive phenomenon can be explained by an effect that has recently gained attention in other contexts [10][11][12][13][14][15][16]: time-delayed coherent quantum feedback.…”

“…One must, therefore, take into account non-Markovian dynamics of qubit-light interactions. This was done in waveguide QED for a single qubit in [13,[25][26][27] for two qubits in [6,7] and three qubits in [8]. Here, we consider up to 100 qubits.…”

“…Here, T is the transfer matrix corresponding to a unit cell, which consists of inter-qubit propagation and single qubit-light interaction. Following [8], T can be written as where L is the distance between two adjacent qubits, ∆ k = E k −Ω is the detuning between the photon energy E k and the qubit energy separation Ω, and γ 0 is the decay rate of a single qubit to the 1D waveguide. When deriving this transfer matrix, we use the realspace Hamiltonian [8,20,28], where the light-matter interactions take the form of a delta-function at the qubit position.…”

“…In the Markovian regime, the propagation phase acquired by the photon between two qubits can be linearized, kL ΩL [6,8]. In this regime, f (∆ k ) can be approximated by an N th degree polynomial in ∆ k , since the exponential terms in the transfer matrix can be replaced by a constant e ikL e iΩL .…”