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

Area of Science:

• Quantum optics
• Solid-state physics
• Quantum information science

Background:

• Investigating light-matter interactions is crucial for quantum technologies.
• Understanding photon propagation in waveguide-coupled qubit systems is key for quantum computing and communication.

Purpose of the Study:

• To analyze the nonlinear response of scattered photons in a system of N photons and M qubits.
• To explore the impact of varying photon numbers, qubit numbers, inter-qubit distances, and coupling strengths on quantum dynamics.
• To characterize the transition from strong to ultrastrong qubit-waveguide coupling regimes.

Main Methods:

• Numerical simulation of quantum evolution using the matrix product states technique.
• Computation of time evolutions for both the photonic field and the qubits.
• Analysis of scattered photon properties, including nonlinear response and photon-photon correlations.

Main Results:

• Perfect reflection is achieved when the ratio of photons to qubits (N/M) is approximately one.
• Photon-photon correlations remain observable even for non-zero N/M ratios.
• Increased inter-qubit distance enhances the nonlinear response of the system.
• In the ultrastrong coupling regime, inelastic processes are robust to the number of qubits, and qubit-mediated interactions are significantly altered.

Conclusions:

• The nonlinear response is tunable via the N/M ratio and inter-qubit distance.
• The study provides a theoretical framework applicable to experiments in circuit Quantum Electrodynamics (QED), photonic crystals, and dielectric waveguides.
• Findings offer insights into controlling quantum correlations and interactions in scalable quantum systems.