Nonlinear optics for quantum technologies

Nonlinear optics is used for the generation and conversion of quantum states of light, with numerous applications in quantum technologies. In parallel, the development of photonic integrated circuits and micro/nano-cavities offers new opportunities to boost and tailor nonlinear effects. Finally, nonlinear spectroscopy on molecules and nanomaterials is a power ful tool to probe their electronic and vibrational properties. This course covers the fundamental knowledge needed to understand these contemporary developments.

Fundamentals of nonlinear optics

• Reminders: wave propagation in a linear medium with dispersion
• Wave propagation in a nonlinear medium and phase matching conditions
• The nonlinear susceptibility tensor and crystal symmetries
• Generation of coherent states at new frequencies (second harmonic, sum- and difference frequency, etc.)

Quantum theory of nonlinear optics and its applications

• Quantum theory of the nonlinear susceptibility (first quantisation, semi-classical treatment). Particular case of the two-level system.
• Quantization of the electromagnetic field
• Effective Hamiltonian of nonlinear interactions
• Generation of nonclassical states of light: the case of parametric down conversion
• The joint spectral amplitude and the two-mode squeezed state
• Integrated nonlinear optics in waveguides and cavities
• Application to quantum frequency conversion, quantum networks, etc.

Invited seminars and tutorials from researchers active in some of these fields (quantum frequency conversion, integrated quantum optics, etc.) will enrich the course with practical examples from contemporary research.