## Admission Requirements

In addition to enthusiasm for quantum physics: B.Sc. level quantum mechanics and mathematics, and you should be familiar with the content of the M.Sc. course on quantum theory.

## Description

Quantum optics is the foundation of many present-day quantum technologies like single molecule superresolution imaging and time-resolved spectroscopy, but of course also key for emerging 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 and qubits. 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, also by the cutting-edge papers that students prepare and discuss.

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

Coupled quantum oscillators: Jaynes-Cummings model and dressed-states picture of strongly coupled systems, opto-mechanical interaction

Cavity QED: (Rydberg) atoms, quantum dots and color centers, Purcell effect, Schrödinger cat states, decoherence and quantum jumps

Quantum applications: quantum teleportation, remote entanglement generation, Bell inequality, quantum key distribution, qubits for quantum computing.

## 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

Use quadrature representation or quasi-probability distribution to desribe 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 interaction Hamiltonian generating the state

Compute and interpret the second-order correlation function of states of light and indicate the boundary between classical and quantum light

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

Give operator expressions for the quantum optical output of arbitrary multiports and interferometers using the input-output formalism (s-matrix) of beamsplitters

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 in terms of their density matrix

Calculate and explain the eigenstates of the Jaynes-Cummings Hamiltonian in the dressed-state picture

Explain and design simple setups used to prepare and manipulate the quantum state of an atomic qubit using the interaction of the Rabi-model

Describe how entanglement can be generated and tested in experiments that involve spontaneous parametric down-conversion or atomic cascades

The following soft skills will be trained during the course:

We will continuously train analytic thinking by interactive lectures and exercise classes.

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

You will find the timetables for all courses and degree programmes of Leiden University in the tool MyTimetable (login). Any teaching activities that you have sucessfully registered for in MyStudyMap will automatically be displayed in MyTimeTable. Any timetables that you add manually, will be saved and automatically displayed the next time you sign in.

MyTimetable allows you to integrate your timetable with your calendar apps such as Outlook, Google Calendar, Apple Calendar and other calendar apps on your smartphone. Any timetable changes will be automatically synced with your calendar. If you wish, you can also receive an email notification of the change. You can turn notifications on in ‘Settings’ (after login).

For more information, watch the video or go the the 'help-page' in MyTimetable. Please note: Joint Degree students Leiden/Delft have to merge their two different timetables into one. This video explains how to do this.

## Mode of instruction

Reading assignment (Gerry & Knight sections), lectures, student presentations, homework and exercise classes, discussions, exam.

See Brightspace

## Assessment method

Doing the homework assignments is essential, and you can get a bonus point.

Student presentations are graded for each group based on the presentation and questions asked.

Written or oral examination, with questions modeled after the exercises from the tutorials, and about conceptual topics.

There is a possibility to retake the exam. The date and format (oral or written examination) of the retake will be discussed.

## 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

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

## Registration

From the academic year 2022-2023 on every student has to register for courses with the new enrollment tool MyStudyMap. There are two registration periods per year: registration for the fall semester opens in July and registration for the spring semester opens in December. Please see this page for more information.

Please note that it is compulsory to both preregister and confirm your participation for every exam and retake. Not being registered for a course means that you are not allowed to participate in the final exam of the course. Confirming your exam participation is possible until ten days before the exam.

Extensive FAQ's on MyStudymap can be found here.

## Contact

Lecturer: Dr. W. Löffler

## Remarks

Following Quantum Optics, Theory of Condensed Matter, and Quantum Field Theory, at the same time, has proven to be very challenging. Don't hesitate to drop by to discuss your plans!