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Quantum Optics 1

Module PH7001

This module is offered by Ludwig-Maximilians University Munich (LMU). It is available for TUM students only within a joint degree program (e. g. M. Sc. Quantum Science & Technology).

This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.

Basic Information

PH7001 is a semester module in English language at Master’s level which is offered in winter semester.

This Module is included in the following catalogues within the study programs in physics.

  • Focus Area Experimental Quantum Science & Technology in M.Sc. Quantum Science & Technology

If not stated otherwise for export to a non-physics program the student workload is given in the following table.

Total workloadContact hoursCredits (ECTS)
270 h 90 h 9 CP

Responsible coordinator of the module PH7001 is Immanuel Bloch.

Content, Learning Outcome and Preconditions

Content

This module provides an introduction to quantized light-atom interaction and modern quantum optics experiments. The module starts with a short repetition of the most important phenomena/concepts of semiclassical light-atom interactions. A central part of this module is the quantization of the electromagnetic field, the introduction of field states (Fock states, Coherent states, Squeezed states) and the derivation of the Jaynes-Cummings Model. Fundamental quantum effects and their signatures in experiments will play an important role in the context of cavity quantum electrodynamics. Then, spontaneous emission and the Wigner-Weisskopf-Theory will be introduced. Other important topics of this module will be coherence, correlation functions and photon statistics. For instance, we will discuss the famous Hanbury Brown and Twiss Experiment. After that we continue with entanglement, discussing EPR experiments, Bell’s inequalities and quantum teleportation. Finally, we will provide a short introduction into the realization of quantum gates and basic algorithms.

Learning Outcome

After completing the Module the student is able to:

  1. Explain and calculate the properties of field states.

  2. Discuss various phenomena related to quantized light-atom interaction in two- and three-level systems based on the Jaynes-Cummings-Model.

  3. Explain various experimental settings that can be used to study important quantum phenomena, such as vacuum Rabi oscillations or non-destructive measurements of photons.

  4. Understand coherence phenomena and correlation functions. 

  5. Understand the role of entanglement and the generation of entangled photon pairs.

  6. Explain basic quantum computation algorithms.

Preconditions

No prerequisites beyond the requirements for the Master’s program in Quantum Science and Technology.

Courses, Learning and Teaching Methods and Literature

Learning and Teaching Methods

The module consists of a lecture series (4 SWS) and exercise classes (2 SWS), comprising two lecture sessions and one exercise session per week. 

During lecture the teaching material will be presented on the blackboard. This will be supplemented by power point / keynote presentations to summarize / illustrate important results and discuss state-of-the-art research. As part of the lecture there will be a weekly Journal Club, where original publications related to the module’s content are discussed. Weekly problem sets are offered to obtain a better comprehension of the lecture content and to improve the familiarity with them. The solutions to these problem sets are discussed in weekly exercise sessions.

Participation in the exercise classes is strongly recommended, since the exercises are aids for acquiring a deeper understanding of the core concepts of the course and for practicing to solve typical exam problems.

Media

Power point and One Note presentation.

Literature

Standard textbooks of quantum optics, for example:

  • Introductory Quantum Optics, Christopher Gerry, Peter Knight, Cambridge University Press 2006: Introductory textbook on quantum optics
  • Exploring the quantum, Serge Haroche, Jean-Michel Raimond, Oxford University Press 2006: Focus on cavity-QED, provides a good discussion of fundamental quantum effects, such as entanglement, non-locality and decoherence

  • Quantum Optics, Mark Fox, Oxford University Press: Elementary introduction to quantum optics

  • The Quantum Theory of Light, Rodney Loudon, Oxford University Press: Classic quantum optics textbook, which provides a very good introduction (no discussion of modern experiments)

  • Atom Photon Interactions, C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Wiley-Interscience: Advanced level textbook on light-atom interactions (very detailed)

  • Quantum Optics, Marlan O. Scully, and M. Suhail Zubairy, Cambridge University Press: Advanced textbook on quantum optics (modern notation)

Module Exam

Description of exams and course work

There will be a written exam of 120 minutes duration. Therein the achievement of the competencies given in section learning outcome is tested exemplarily at least to the given cognition level using conceptual questions and computational tasks.

For example an assignment in the exam might be:

  • Discuss the light-atom interaction for a two-level atom interacting with a classical single-frequency light field – describe the evolution of the Bloch vector for resonant/off-resonant illumination, and the effect of spontaneous emission on this evolution.
  • Calculate various properties of field states, for example Fock states and Coherent states.
  • Derivation and discussion of the Jaynes-Cummings model.
  • Computation of correlation functions and discussion of coherence in beam-splitter/interferometer-type setups for classical / non-classical light sources.
  • Entanglement: How can entangled photon pairs be generated? What are the properties of these states? Discuss beam-splitter/interferometer-type settings.

Exam Repetition

The exam may be repeated at the end of the semester.

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