SCC1120 - QUANTUM AND SEMICLASSICAL OPTICS

courses

ID:

SCC1120

Duration (hours):

56

CFU:

SSD:

FISICA DELLA MATERIA

Year:

2025

Date/time interval

Primo Semestre (22/09/2025 - 16/01/2026)

Course Objectives

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. By the end of this course, students should be able to explain basic concepts in semiclassical and quantum optics and solve simple problems in this field.

Course Prerequisites

Basic knowledge of electromagnetism and of quantum mechanics

Teaching Methods

Classroom lectures at the blackboard. The teacher will also provide lecture notes to the students through the e-learning platform. 42 hours of the course will be taught by Prof. Brambilla, while the remaining 14 hours by Prof. Caspani, who will cover the last Quantum Optics topics (quantum optics with a beam splitter, input-output formalism, non-classicality criteria, squeezed states, and some applications, etc.).

Assessment Methods

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 lessons, the student will be asked to present in more details one of the more advanced topics developed during the lectures, which will be previously assigned by the teacher. Full mark with laude is assigned only to students that - accomplish all the aims and outcomes discussed above - are able to re-elaborate the different topics and to establish connections and comparisons

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. Optical resonators and the two-level atom laser. Calculation of the transmission function of a ring cavity. Stationary solutions of the two-level atom laser. Laser dynamics in the low transmission limit and the mean field approximation. The Lorenz Haken instability for class C lasers. Second part: Quantum Optics Quantization of the electromagnetic field in the vacuum. Equivalence between the electromagnetic field and an infinite set of independent harmonic oscillators. The harmonic oscillator in the quantum theory. Field quantization. The electric and magnetic field operator. The Heisenberg and the Schrödinger 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. Cavity quantum electrodynamics - the Jaynes Cumming model The JC Hamiltonian - The bare and dressed states description. The Haroche experiment: generation of atom-cavity mode entangled states - Collapses and revivals of the Rabi oscillations. Quantum optics with a beamsplitter. Classical and quantum description of a beamsplitter. Input-output formalism. Photon number correlation function from the two output ports of a beam splitter. Criteria of non-classicality for a light source. Squeezed states. Some applications: -The Hong-Ou-Mandel effect. -The Mach-Zehnder interferometer. -High-sensitivity absorption measurement exploiting twin beams correlations. - High-sensitivity interferometry using squeezed states.

Course Language

English

More information

The lecturers receive by appointment: Prof. Brambilla, office V4.3 fourth floor via Valleggio 11, e-mail: enrico.brambilla@uninsubria.it Prof. Caspani, office V4.7 fourth floor via Valleggio 11, e-mail: lucia.caspani@uninsubria.it