QUANTUM AND SEMICLASSICAL OPTICS
- Overview
- Assessment methods
- Learning objectives
- Contents
- Bibliography
- Teaching methods
- Contacts/Info
Basic knowledge of electromagnetism and of quantum mechanics
The examination consists in an oral examination which will last 60-90 minutes.
The scope of the course is to introduce the student to the field of modern optics. In the first part of the course, the interaction between matter and radiation is described within the semiclassical model, where only the atomic system is treated within the quantum theory while the interacting field is treated in a classical framework. In the second part of the course we introduce the students to the field of quantum optics, which is based on a fully quantum description of the electromagnetic field. We also illustrate some simple applications in the field of quantum metrology and interferometry, where the sensitivity of the measurement can be improved beyond the standard quantum limit by exploiting quantum correlations of the light source.
First part: semiclassical theory
The optical Bloch equations for a two level atomic system
- Interaction of the 2-level atom with the e.m. field. Interaction Hamiltonian in the dipole
approximation.
- Density matrix formalism - Liouville Von Neuman evolution equation
- Derivation of the Optical Bloch equations.
- Solution of the Bloch equations driven by a monochromatic plane wave – precession of
the Bloch vector on the Bloch sphere - comparison with the results of the perturbative model.
Second part: Quantum Optics
Quantization of the electromagnetic field in the vacuum.
Equivalence between the electromagnetic field and an infinite set of indipendent harmonic oscillator. The harmonic oscillator in the quantum theory. Field quantization. The electric and magnetic field operator. The heisenberg and the Schroedinger picture. The Fock states basis.
The coherent states as quasi-classical states of the e.m. field. Definitions and general properties. Photon statistics of a coherent state. Uncertainty relation for the fluctuations of the field quadratures.
The density matrix formalism. Pure and mixed states of the e.m. field. Photon statistics of a thermal state.
Quantum optics with a beamsplitter. Classical and quantum description of a beamsplitter. Input-output formalism. Photon number correlation function from the two output port of a beam splitter. Criteria of non-classicality for a light source.
Some appplications
-The hong Ou Mandel effect.
-The Mach-zehnder infterferometer.
-High-sensitivity absorption measurement exploiting twin beams correlations.
- High-sensitivity interferometry using squeezed states.
L. Lugiato, F. Prati M. Brambilla, Nonlinear Optical Systems, Cambridge University Press (2015).
C.G Gerry and P. L. Knight, Introductory quantum Optics (Cambridge University Press, 2004)
Lecture notes from the teacher on the e-learning platform
Others references
A. Yariv, Quantum Electronics, Cap, 15, Wiley & sons, 3rd ed. (1989)
R. W. Boyd, Nonlinear Optics, cap. 3, 6 e 7, 3rd ed., Accademic,Press (2008)
Classroom lectures at the dashboard. The teacher will also provide lecture notes to the students through the e-learning platform.
Receive under appointment (office V4.7 fourth floor via Valleggio 11)
e-mail: enrico.brambilla@uninsubria.it