Optique non-linéaire, ultra-rapide et quantique

Enseignants : François HACHE et Nicolas TREPS
Chargé de TD :
ECTS : 3
Langue d’enseignement  : Anglais
Site web :


Objective of this lecture is to study non-linear interaction between light and mater, from classical to quantum effects. The natural regime, even if non-exclusive, is the femtosecond regime, where effects are macroscopic and experiments are usually performed. Beyond giving the essential ingredients of non-linear and quantum optics, this lecture will focus on recent applications and experiments, spreading for microscopy and spectroscopy to non-classical state generation and quantum metrology.

PART I : Nonlinear Optics

1- Introduction

  • Course : Introduction to nonlinear optics Nonlinear susceptibilities Propagation equation
  • Training : Self-phase modulation, Solitons

2- Second order effects

  • Course :Two-wave mixing, Manley-Rowe relation Second harmonic generation (SHG) Phase-matching, quasi-phase matching
  • Training : Parametric gain, OPO’s, thresholds of SROPO and DROPO

3- Ultrashort pulses

  • Course : Short pulse generation : mode-locking Characterization methods Femtosecond spectroscopy Nonlinear microscopy
  • Training : Kerr-Lens Mode-Locking

4- Quantum calculation of nonlinear susceptibilities

  • Course : Liouville equation, perturbative response Calculation of χ(2)
  • Training Non résonnant χ(2)

5- Response-functions – Two-dimensional spectroscopy

  • Course : Rotating-wave approximation, resonant Feynman diagrams Pump-probe experiments
  • Training : Fluorescence / resonant Raman

6- Training Third-harmonic generation for Gaussian beams – Application to microscopy

PART II : Femtosecond quantum optics

1- Introduction

  • Course : Quantum nature of light and pioneer experiments Single and two photons experiments, EPR states

2- Multimode quantum electromagnetic field

  • Course : Field quantization (time and frequency domains) – Coherent states Multimode homodyne detection Continuous variable regime
  • Training : Position measurement and standard quantum limit

3- Non-classical states

  • Course : Gaussian states : squeezing and entanglement Wigner function and non-gaussian states
  • Training : Generation of a non-gaussian state, Kraus operators

4- Multimode entanglement in the frequency domain

  • Course : Introduction to symplectic algebra, Schmidt and Bloch Messiah decomposition Pulsed single mode single photons
  • Training : Parametric down conversion for multimode quantum states

5- The frequency comb : a metrological tool

  • Course : Frequency comb and metrology
  • Training : Quantum noise limited metrology with frequency combs

6- Time and frequency measurements

  • Course : Quantum Cramér Rao bound : ultimate quantum limit for metrology
  • Training : Pulse shaping for quantum coherent control