Strongly-coupled non-Markovian waveguide QED with input-output HEOM

TL;DR

This paper applies the input-output hierarchical equations of motion (io-HEOM) to model a qubit in a waveguide, capturing non-Markovian effects from non-local coupling and non-linear dispersion with high accuracy.

Contribution

It demonstrates the effectiveness of io-HEOM in accurately modeling non-Markovian waveguide QED beyond perturbative and Markovian approximations.

Findings

io-HEOM captures non-Markovianity from non-local coupling and dispersion.

Bound photon behavior depends on coupling functions and quench dynamics.

Non-linear dispersion causes persistent oscillations due to Van Hove singularities.

Abstract

We consider the problem of modeling a single qubit in contact with a one-dimensional waveguide beyond the standard perturbative and Markovian approximations. Using the recently developed input-output hierarchical equations of motion (io-HEOM), we investigate multiple examples of such waveguides, characterized by different spectral densities. Our examples highlight that the io-HEOM method can accurately capture non-Markovianity in waveguide QED from two distinct origins. The first source of non-Markovianity is spatially non-local coupling between the qubit and the waveguide. By examining two examples with non-local coupling, we show how the coupling function affects the steady-state bound photons, and demonstrate the release of these photons when the qubit energy is quenched. The second source of non-Markovianity is non-linear dispersion. We illustrate this scenario using the example of a cavity array with point-like coupling, where the non-linear dispersion leads to persistent oscillations due to Van Hove singularities in the spectral density.