QUANTUM OPTICS

The course is one of the educational activities of the Master Degree in Engineering Physics and enables the student to gain knowledge and understanding of fundamental and applied concepts in the field of quantum optics, which is the description of the quantum features of light.
The objective of the course is to provide a strong background in the field of quantum optics, which is at the foundation of the current applications and implementations in the fields of optical quantum information processing, quantum communication, quantum computing, quantum sensing and quantum technologies.

At the end of the course, the student will:
• Know the basic principles of quantum mechanics
• Know quantum optics methodologies and modern applications (quantum technologies)
• Know how to generate, measure and exploit non-classical light
• Be able to describe the optical (linear and non-linear) systems typically used in modern quantum optics laboratories
• Be able to solve simple quantum mechanical/optical problems and exercises
• Be able to understand scientific literature papers in the field of quantum optics

Knowledge of Calculus, Linear Algebra and Physics I-II is required. Basic knowledge of Quantum Mechanics may be helpful, but it is not necessary since it will be reviewed in the course.

1. Introduction to Quantum Mechanics
The need of a quantum theory
Wave-particle duality
Entities and rules in a physical theory

2. The formalism of Quantum Mechanics
States and observables
Measurement of an observable
Schrödinger and Heisenberg pictures
Composite systems and entanglement
Bell test of local realism

3. Quantum Mechanics with continuous variables
Position and momentum representations and operators
Heisenberg’s uncertainty principle
The quantum harmonic oscillator

4. Quantum states of light
Quantization of the electromagnetic field
Single-mode states (Fock, quadrature, coherent, thermal) and operators
Phase-space picture of quantum states
Quadrature wavefunctions
Minimum-uncertainty states: squeezing

5. Phase-space quasi-probability distributions
Phase-space distribution in classical and quantum optics
The Wigner function: introduction, properties, and examples
Other quasi-probability distributions: Weyl correspondence, s-parametrized quasi-probability distribution, P-function, Q-function

6. Quantum Optics practical tools
Continuous-mode quantum optics
Linear optical devices (multiport, beam splitter)
Interferometry
Encoding quantum information into single photons (polarization and time-bin encoding)
Application: quantum key distribution (BB84 protocol, security of QKD, implementations of QKD)

7. Measuring the quantum state of light
Homodyne detection scheme
Phase-space quantum state tomography
Heterodyne schemes detection scheme

8. Non-classical light
Quadrature squeezed states (description and photon statistics)
Schrödinger cat states
Two-mode squeezed vacuum (description and photon statistics)

9. Generating quantum states of light
Elements of perturbation theory in quantum mechanics (interaction picture)
Elements of non-linear optics
Spontaneous Parametric Down Conversion
How to generate entangled photons and squeezed light

10. Theory of optical coherence
Statistical properties of random light
Classical coherence functions
Quantum coherence functions

• Gerry, Christopher; Knight, Peter, Introductory Quantum Optics. Cambridge: Cambridge University Press, 20041028.
• Leonhardt, Ulf, Measuring the quantum state of light. Cambridge: Cambridge University Press, 1997.

Oral test on the contents of the course (including exercises similar to those done during the course), with the possibility of presenting an essay on a topic agreed with the teacher. No homework will be assigned.
The assessment is based on the understanding of the topics covered in class and on the ability to expose them in a clear and exhaustive manner.

The teaching takes place through frontal lessons on the blackboard or with slides, with the possibility of interaction and involvement.
There will be 3 laboratory activities to experimentally investigate the concepts and techniques described in the course. There will be a visit to the quantum optics laboratories of QuantumFuture research group of the University of Padova.

English

All course topics are presented in the classroom and covered by the lecture notes provided by the teacher.
Lecture notes can be integrated with textbooks.
The list of the topics covered lesson by lesson will be made available, as well as the material (notes, slides, papers, etc) provided by the teacher.