title: Nonlinear quantum optics in the (ultra)strong light-matter coupling.
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. The time evolutions for both the field and qubits are computed. The nonlinear character (as a function of N/M) depends on the computed observable. While perfect reflection is obtained for N/M≅1, photon-photon correlations are still resolved for ratios N/M=non-zero. Inter-qubit distance enhances the nonlinear response. Moving to the ultrastrong coupling regime, we observe that inelastic processes are 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 models experiments in circuit QED, photonic crystals and dielectric waveguides.
authors.affiliation: Instituto de Ciencia de Materiales de Aragón y Departamento de Física de la Materia Condensada, CSIC-Universidad de Zaragoza, Zaragoza, E-50009, Spain.
authors.forename: Eduardo
authors.initials: E
authors.lastname: Sánchez-Burillo
authors.forename: Juanjo
authors.initials: J
authors.lastname: García-Ripoll
authors.forename: Luis
authors.initials: L
authors.lastname: Martín-Moreno
authors.forename: David
authors.initials: D
authors.lastname: Zueco