Open Quantum Optical Systems by Carlos Navarrete-Benlloch, 2017/2018 WS

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Quantum optics treats the interaction between light and matter. You may think of light as the optical part of the electromagnetic spectrum, and matter as atoms. However, modern quantum optics covers a wild variety of systems, so that a general definition of it could be "quantum electrodynamics at low energies". Such scenario includes, for example, superconducting circuits, confined electrons, excitons in semiconductors, defects in solid state, or the center-of-mass motion of micro-, meso-, and macroscopic systems. Moreover, quantum optics is at the heart of the exponentially-growing field of quantum information processing and communication, both at the conceptual level and at the level of technological implementations. The ideas and experiments developed in quantum optics have also allowed us to take a fresh look at many-body problems of relevance for condensed matter and even high-energy physics. In addition, quantum optics holds the promise of testing foundational problems in quantum mechanics as well as physics beyond the standard model in table-sized experiments.

One of the distinct features of quantum optics is that it deals with systems which are not isolated, that is, they leak out energy and information to their surrounding environment. While this is actually the most common situation in real physical systems, it is not the one students usually encounter in their standard quantum mechanics courses. The biggest part of this course will be devoted to fill this gap: we will go through the many tools and methods that have been developed to describe open quantum optical systems. Apart from their practical use, these methods also have deep physical interpretations which will make you understand quantum mechanics much better.

Quantum optics and open systems are therefore topics that no future researcher in quantum physics should miss.

Basic information

  • Teacher: Carlos Navarrete-Benlloch.
  • Questions: email to
  • Type: 5 ECTS credits as an elective course in physics (bachelor from 5th semester on and master).
  • Time: Mondays 14:00-16:00 (theory) and Tuesdays 14:15-15:15 (practical, but don't miss it, it will contain lots of important concepts).
  • Location on MONDAYS: Hörsaal F
  • Location on TUESDAYS: Room SRLP 0.179 (Seminar of Laser Physics, Prof. Peter Hommelhoff chair: in this building).
  • Starting date: Monday, October 16th.
  • UnivIS site here.
  • Evaluation method:
Written exam with two parts:
Multiple-choice test for basic concepts worth up to 30% points.
Essay-type questions and exercises worth up to 70% points. You'll be able to choose between several options.
• You can increase your grade by up to 0.7 by preparing and discussing the exercises provided below (resources section).
  • Prerequisites: The course will be understandable to any student who has passed at least one course in basic quantum mechanics. Ideal for last year bachelor students, master students, and PhD students.
  • Important dates:
March 27, exam date, at 2pm in Hörsaal F.
March 2, deadline to submit exercises (better scanned or with a high-resolution picture, but you can give me originals in class or in my office until February 23; afterwards I'm travelling). While I encourage you to try to work out all the exercises, I will give 0.3 and 0.7 extra points to anyone who invests time in one or more exercises, respectively. I will not judge them according to how well done they are, it is enough to convince me that you thought about them and tried your best.
March 2, I will release the solutions to the exercises.
March 12-23, meetings to discuss the exercises (contact me by email from March 1 to fix some time).

Content of the course

The course will contain a selection of topics from the following list:

  • Review of classical mechanics, Hilbert spaces, and quantum mechanics
  • Quantization of the electromagnetic field as a collection of harmonic oscillators: quantum states (number, coherent, squeezed, thermal,entangled,...); phase-space visualization through the Wigner function; other technologically relevant systems captured by the harmonic oscillator model.
  • Quantum theory of atoms and the two-level approximation: atomic energy spectrum; two-level approximation, dynamics, and visualization in the Bloch sphere; other systems that act as "artificial" or "engineered" atoms.
  • Atom-light interaction: Hamiltonian in the dipolar approximation; Jaynes-Cummings model; Rabi oscillations, collapses, and revivals.
  • Light in a nonlinear dielectric: Basic second-order processes and frequency generation; Hamiltonian under the independent dipole approximation; Bogoliubov diagonalization and unstable Hamiltonians.
  • Quantum optics in open systems: Open optical cavities, the master equation and the quantum Langevin equation; incoherent atomic processes, spontaneous emission, Lamb shift, and dephasing; some paradigmatic open models such as the degenerate parametric oscillator and the laser.
  • Numerical and analytical techniques for open quantum-optical systems: Superspace approach; the method of quantum-state trajectories; phase-space techniques; small quantum fluctuations around the classical state; light-matter decorrelation.
  • Detection of the output field: Input-output relations; quantum regression theorem; photodetection, bunching, and antibunching; homodyne detection and squeezing.
  • Elimination of spurious degrees of freedom: Effective Hamiltonians and master equations; projection-operator and -superoperator techniques; examples: effective motional optical potentials on a detuned atom and sideband cooling with a driven cavity mode.

An exhaustive list of topics can be found here. Don't let yourself be intimidated by the length of the list: the course will include only a small selection among these topics. Students can choose amongst the remaining topics for the oral and written presentations, as well as propose topics themselves.


I am developing lecture notes and exercise sheets (with the key questions of the chapter and an exercise that students can work out for extra points) while teaching the course. I will be updating them here:

Lecture Notes (status: all course content except for some figures and proofs).

Exercise sheets (status: all course content).

The lecture notes are self-contained, but a list of books which I encourage students to read is provided there.

Other useful resources that I have written are my PhD thesis and my book on quantum information with continuous variables.

Special lectures:

  • Quantum optics with quantum dots by Petru Tighineanu.
  • Superconducting circuits by Hugo Ribeiro.
  • Mechanical systems by Talitha Weiss (no slides, blackboard lecture).