QUANTUM OPTICS
- Overview
- Assessment methods
- Learning objectives
- Contents
- Bibliography
- Delivery method
- Teaching methods
Knowledge of electromagnetism and basic quantum mechanics.
Final examination, written or oral, depending on student’s choice.
The student is asked to expose two (three) exam topics, concerning subjects covered by the course. The essay is discussed together with the student, and he/she may be asked to deepen some points.
Quantum Optics investigates the quantum-mechanical nature of light and its interaction with matter. Born at the beginning of the last century, this discipline has had over the last 30 years tremendous developments.
The course is a theoretical introduction to the matter The goal is to provide students with the essential formal tools to gain an insight into this fascinating subject, and illustrate the fundamental concepts in the light of some modern experiments.
1.The quantum description of light
-Refresher of classical electromagnetism: Maxwell equations, potentials, wave equation
-Quantization cavity, expansion in normal modes
-The harmonic oscillator in quantum mechanics
-The classical energy and its quantization. Quantized electric and magnetic fields,
-Fock states.
2.The classical and quasi-classical states of the electromagnetic field
-Recall of tthe quantum mechanical formalism, pure and mixed states
-The thermal equilibrium state, definition and properties'
-The coherent states of the e.m field (as eigenstates of the destruction operator, as minimum uncertainty states, as displaced vacuum:statistics of the photon number and of field quadratures.
3.Interferometry with single photons
- The beam-splitter and the Mach Zehnder interferometer in quantum optics.
- The single photon state, the experiment of Grangier et al. (1986).
- Single photon interferometry, wave-particle duality. Weeheler conceptual experiment of delayed choice(2007) and interaction free measurements.
- The Hong-Ou-Mandel effect
4. The non-classical states of the electromagnetic field: squeezed and entangled states
- Squeezed states of the electromagnetic field
- Quasi-classical representations: the Wigner function
- The s squeezed vacuum state
- Squeezed coherent states
- Continuous-variable entanglement : the two-mode squeezed state, quadrature entanglement and EPR paradox
5. Generation of entangled states in non-linear crystals: twin photons and twin beams.
- Elements of Nonlinear Optics.
- Quantum description of parametric frequency down-conversion (PDC)
- State formalism for the PDC process: entangled state, twin beams
- Comparison between correlations of quantum and classical origin
- Examples of quantum metrology applications: high sensitivity interferometry with squeezed light, high sensitivity detection with quantum correlation.
6.Interaction between quantized light and matter.
-Interaction of a two-level atom with a single mode of the radiation field. Regime of the cavity Quantum Elettrodynamics (cavity QED)
-The semiclassical Rabi model
-The quantum-mechanica Jaymes-Cummings model.
-Short outline of some historical experiments of cavity QED.
7.Dissipation and decoherence. The quantum Master Equation in optics.
-The Master Equation in Born and Markov approximations.
-Two level atoms interacting with the continuum of modes of the free electromagnetic field.
-Kramers-Kronig relations for the dissipative and dispersive terms.
-Dissipation coefficients for the two-level
-Approach to equilibrium (rate equations, decoherence, evolution of mean values of observables)
•C.G Gerry and P. L. Knight, Introductory quantum Optics (Cambridge University Press, 2004)
•Notes and slides of the lessons, provided by the teacher during the course
Lectures, carried out on the blackboard or using slides