# COMPUTATIONAL QUANTUM OPTICS

**Academic Year 2022/2023**- Teacher:

**Alessandro Ridolfo**

## Expected Learning Outcomes

The course as the aim to present selected topics of Quantum Physics in the context of Modern Quantum Optics, from the theoretical point of view, within the related computational methods developed with a dedicated software (Mathematica) as numerical tool. This course aims to train students in numerical modeling and in solving advanced Quantum Mechanics problems, with a certain impact in theoretical and applicative research both in the cavity and in the circuit-QED research field.

Knowledge and understanding.Knowledge of the fundamental ideas and theoretical/numerical techniques for the representation of complex quantum system and the study of their dynamics. Knowledge of the working principles of state of the art physical systems.

Applying knowledge and understanding.Ability in applying the logical abstraction of physical concepts through analogies in order to code the phenomenona. Exploit the acquired knowledge in the context of Modern Quantum Optics and advanced Quantum Physics.

Marking judgements. Ability to develop her/his own interpretations of physical phenomena, and to relate with a collaborating research group. Ability to find her/his own responsibility for a proper choice of the courses and final thesis, with particular respect to the possibility to invest the acquired knowhow for job opportunities or post-doc positions.

Communication skills. Ability to discuss (in Italian and English), elaborate and modeling the learned physical concepts.

Learning skills. Ability to acquire skills allowing a continuous upgrade of the knowledge, by accessing the research environment and specialized literature. Ability to exploit the bibliographic research with the use of databases in order to develop his/her own scientific research.

## Course Structure

Frontal lessons (5 CFU - 35 hours) and computer laboratory (1 CFU computer training - 15 hours).

If the teaching is given in a mixed or remote mode, the necessary changes with respect to what was previously stated may be introduced, in order to comply with the program envisaged and reported in the syllabus.

## Required Prerequisites

Essential knowledge: Electromagnetism and fundamentals of Quantum Mechanics

Important knowledge: Condensed Matter Physics

## Attendance of Lessons

## Detailed Course Content

Modeling of quantum systems: quantum harmonic oscillator, LC quantum circuit, Fock number basis, cavity field quantization, two level systems, numerical modeling in the Hilbert space, eigenvalues problem.

Coherent dynamics: driven systems, rotating frame and rotating wave approximation, Rabi oscillations, Jaynes-Cummings model, vacuum Rabi oscillations.

Quantum Optics tools: photodetector, Mach-Zender interferometer, Hanbury Brown-Twiss setup, beam splitter, phase shifter, single photon interference, wich-way information, Elitzur-Weidman experiment.

Statistical properties of light: concept of photodetection, input-output relations, photon statistics, coherent and thermal light, photon antibunching, squeezed light, Wigner function.

Open quantum systems: system-bath interaction, Heisenberg-Langevin equations, density matrix, optical master equation and its derivation, thermal steady state solutions, atom in a lossy cavity, numerical implementation of master equation for interacting systems.

selected topics: Fokker-Planck equation, Monte Carlo Quantum Jump.

## Textbook Information

[1] Mark Fox, Quantum Optics - An Introduction, Oxford University Press (2006)

[2] D.F. Walls, Gerard J. Milburn, Quantum Optics, Springer (2008)

## Learning Assessment

### Learning Assessment Procedures

The examination is divided into two parts:

1) an elaborate on a topic of the course that will be presented as a seminar, within a numerical implementation of the topic dealt with

2) an oral interview on a topic chosen by the teacher. The learning verification can also be carried out electronically (telematically), should the conditions require it.

### Examples of frequently asked questions and / or exercises

The questions below are not an exhaustive list but they are just a few examples:

- Find the statistical distribution of the number of photons of a coherent state

- What characterizes the Elitzur-Weidman experiment?

- What do vacuum Rabi oscillations depend on?

- Find the average number of photons of a cavity in thermal equilibrium with its environment