Distant emitters in ultrastrong waveguide QED: Ground-state properties and non-Markovian dynamics

TL;DR

This paper explores the static and dynamic properties of two distant emitters coupled to a waveguide in the ultrastrong coupling regime, revealing non-Markovian effects, modified collective behaviors, and new insights into the Fermi two-atom problem.

Contribution

It introduces an effective Hamiltonian for the two-impurity spin-boson model that captures non-Markovian delay effects in ultrastrong waveguide QED with distant emitters.

Findings

Non-Markovian delay-feedback effects influence emitter dynamics.

Initial correlations cause different evolutions for symmetric and antisymmetric states.

Frequency renormalization affects superradiance and subradiance behaviors.

Abstract

Starting from the paradigmatic spin-boson model (SBM), we investigate the static and dynamical properties of a system of two distant two-level emitters coupled to a one-dimensional Ohmic waveguide beyond the rotating wave approximation. Employing static and dynamical polaron Ans\"atze we study the effects of finite separation distance on the behavior of the photon-mediated Ising-like interaction, qubit frequency renormalization, ground-state magnetization, and entanglement entropy of the two-qubit system. Based on previous works we derive an effective approximate Hamiltonian for the two-impurity SBM that preserves the excitation-number and thus facilitates the analytical treatment. In particular, it allows us to introduce non-Markovianity arising from delay-feedback effects in two distant emitters in the so-called ultrastrong coupling (USC) regime. We test our results with numerical simulations performed over a discretized circuit-QED model, finding perfect agreement with previous results, and showing interesting dynamical effects arising in ultrastrong waveguide QED with distant emitters. In particular, we revisit the Fermi two-atom problem showing that, in the USC regime, initial correlations yield two different evolutions for symmetric and antisymmetric states even before the emitters become causally connected. Finally, we demonstrate that the collective dynamics, e.g., superradiance or subradiance, are affected not only by the distance between emitters, but also by the coupling, due to significant frequency renormalization. This constitutes another dynamical consequence of the USC regime.