## Admission Requirements

B.Sc. level quantum mechanics and mathematics, and you should be familiar with the content of the M.Sc. quantum theory course!

## Description

Quantum optics is the foundation not only of many present-day quantum technologies like single molecule superresolution imaging and time-resolved spectroscopy, but also of near-future quantum technologies: From quantum computing with superconducting qubits in microwave resonators, to quantum communications with single and entangled photons. All these examples require knowledge of the core of this course: light-matter interaction at the fundamental quantum level.

To understand quantum light-matter interactions, both the atom and the electromagnetic field need to be quantized (second quantization), and we show how this enables quantum control, manipulation and detection of quantum systems. Many interesting and highly relevant questions can be addressed within the framework of quantum optics because the calculations are relatively simple compared to other quantum field theories. This makes quantum optics ideally suited to test the foundations of quantum mechanics and probe the crossover between the microscopic realm of quantum physics to the macroscopic domain of classical physics.

Throughout the course a strong link is made between theoretical concepts and modern experimental research by discussing the important experiments using scientific articles. Key historical papers are given as background, while the students present a relevant article in small groups. The discussion of these experiments helps to illustrate and understand essential differences between a classical and quantum mechanical description.

The course covers the following subjects and topics:
* **Basics:** quantization of the electromagnetic field, field quadratures, quantum measurement, operator ordering theorems
* **States of light:** coherent states, thermal states, photon number states, quantum phase space distributions, Wigner functions, quantum phase operator
* **Sources of quantum light:** squeezed light, single and entangled photon sources
* **Correlation functions:** quantum and classical coherence, Hanbury-Brown and Twiss experiment
* **Quantum interference:** quantum beamsplitter, Hong-Ou-Mandel effect, interferometers, homodyne detection, backaction and noise, quantum erasure
* **Coupled quantum oscillators:** Jaynes-Cummings model and dressed-states picture of strongly coupled systems, opto-mechanical interaction
* **Cavity QED:** (Rydberg) atoms, quantum dots and diamond color center, Purcell effect, Schrödinger cat states, decoherence and quantum jumps
* **Applications of entanglement:** quantum teleportation, remote entanglement generation, Bell’s inequality, and quantum key distribution

## Course objectives

At the end of the course you will be able to:

- Understand and being able to analyze complex quantum optics experiments, extract and understand the underlying physics.
- Apply the formalism of creation and annihilation operators for the electromagnetic field to describe quantum states of light
- Name the different quasiprobability distributions and use these to draw a phase-space picture of the various quantum states of light
- Calculate and explain the fluctuations and correlations of different quantum states of light
- Calculate the photon number distribution of different quantum states of light from the Hamiltonian that describes the interaction that generates the state
- Compute and interpret the second-order correlation function of states of light and indicate the boundary between classical and quantum light
- Explain Bell’s theorem and experimental tests done with entangled photons
- Explain and calculate the contribution of quantum fluctuations in measurements involving light
- Formulate decoherence of quantum states using the quantum-jump method
- Calculate and explain the eigenstates of the Jaynes-Cummings Hamiltonian in the dressed-state picture
- Explain the concept of Schrödinger cat states and name several different ways of creating such macroscopic quantum states
- Describe and calculate the properties of squeezed states
- Explain the Hong-Ou-Mandel effect as quantum interference related to which-path-information
- Calculate the visibility of quantum interference effects
- Explain the quantum erasure effect and the role of which-path information
- Give operator expressions for the quantum optical output of arbitrary multiports and interferometers using the input-output formalism (s-matrix) of beamsplitters
- Explain and design simple setups used to prepare and manipulate the quantum state of an atomic qubit using the interaction of the Rabi-model
- Verify if a given quantum state is pure or mixed and if the quantum state is entangled or not
- Describe how entanglement can be generated and tested in experiments that involve spontaneous parametric down-conversion or atomic cascades

## Soft Skills

The following soft skills will be trained during the course: * Presentation skills are trained by the short (~10 min.) presentations about a relevant recent article in the field of experimental quantum optics * Scientific collaboration and team work during preparation of the presentation in a small group, as well as during discussions during the exercise classes.

## Timetable

Physics Schedule

For detailed information go to Timetable in Brightspace

## Mode of instruction

Lectures, student presentations, exercise classes, discussions, exam.

See Brightspace

## Assessment method

- 1/3: Student presentations are graded for each group based on the presentation and questions asked.
- Written examination, with questions modeled after the exercises from the tutorials.
- There is a possibility to retake the exam. The date and format (oral or written examination) of the retake will be decided in consultation.

## Reading list

C. Gerry and P. Knight, Introductory Quantum Optics, Cambridge University Press, Cambridge, UK (2005), ISBN 0 521 52735 X (paperback). Also available via the Library

Additional lecture notes and papers will be distributed via blackboard

Suggested additional reading for a more experimental perspective: M.Fox, Quantum Optics: An Introduction, Oxford University Press, Oxford, UK (2001), ISBN 0198566735 (paperback). Also available via the Library

## Brightspace

Registration for Brightspace occurs via uSis

How to sign up for classes: click here

## Contact

Lecturer: Dr. W. Löffler