QUANTUM AND SEMICLASSICAL OPTICS

Degree course: 
Corso di Second cycle degree in PHYSICS
Academic year when starting the degree: 
2022/2023
Year: 
1
Academic year in which the course will be held: 
2022/2023
Course type: 
Compulsory subjects, characteristic of the class
Credits: 
6
Period: 
First Semester
Standard lectures hours: 
48
Detail of lecture’s hours: 
Lesson (48 hours)
Requirements: 

Basic knowledge of electromagnetism and of quantum mechanics

Final Examination: 
Orale

The oral examination , which will last 60-90 minutes, consists in an in-depth verification of the knowledge acquired by the student during the course.
In addition to questions on the basic theory developed in the lectures, the student will be asked to present in more details one of the more advanced topics developed during the lessons, which will be previously assigned by the teacher.

Assessment: 
Voto Finale

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.

At the end of the course the student is expected to acquire a basic knowledge in semiclassical and quantum optics, as well as to tackle simple problems in this field.

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.

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

Professors

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