Nonlinear quantum optics in the (ultra)strong light-matter coupling

TL;DR

This paper investigates the nonlinear optical response of multiple photons interacting with multiple qubits in waveguides, revealing how coupling strength, qubit arrangement, and ultrastrong regimes influence photon correlations and inelastic processes.

Contribution

It introduces a numerical approach using Matrix Product States to analyze nonlinear quantum optics in strong and ultrastrong coupling regimes, modeling experimental setups.

Findings

Perfect reflection occurs at N/M ≈ 1.

Photon-photon correlations persist at N/M= 2/20.

Ultrastrong coupling enhances inelastic processes and modifies qubit interactions.

Abstract

The propagation of $N$ photons in one dimensional waveguides coupled to $M$ qubits is discussed, both in the strong and ultrastrong qubit-waveguide coupling. Special emphasis is placed on the characterisation of the nonlinear response and its linear limit for the scattered photons as a function of $N$, $M$, qubit inter distance and light-matter coupling. The quantum evolution is numerically solved via the Matrix Product States technique. Both the time evolution for the field and qubits is computed. The nonlinear character (as a function of $N/M$) depends on the computed observable. While perfect reflection is obtained for $N/M \cong 1$, photon-photon correlations are still resolved for ratios $N/M= 2/20$. Inter-qubit distance enhances the nonlinear response. Moving to the ultrastrong coupling regime, we observe that inelastic processes are \emph{robust} against the number of qubits and that the qubit-qubit interaction mediated by the photons is qualitatively modified. The theory developed in this work modelises experiments in circuit QED, photonic crystals and dielectric waveguides.