Quantum Optics 2

The module starts with a short repetition of the most important phenomena/concepts of quantum mechanics important for the understanding of quantum optics. A central part of this module is the systematic treatment of decoherence in experiments through an open-systems approach. The first part of the module starts with a detailed overview of two-level-systems (qubits) and how to control them for applications in spectroscopy and quantum science. We discuss adiabatic control, Berry’s phase, and the extension to dilute media of two-level-systems in this context. At this stage, decoherence is still treated phenomenologically to put the focus on the physical effects rather than the mathematics. The discussion moves on to the new effects that can be discovered in three-level systems, with a focus on Raman transitions, electromagnetically induced transparency, and stimulated Raman adiabatic passage. We introduce the important concept of adiabatic elimination. Three-level systems in ions are then used to discuss the quantum Monte-Carlo wave function method, as a first introduction to treating decoherence systematically. In the second part of the module, we begin with a review of second quantization for bosons and fermions and review the quantization of the electromagnetic field as an example. In this context, we discuss effects of the quantum vacuum, such as the Casimir force and how to observe them. We review how to measure the quantized light field, discuss homodyne detection, and introduce the spin description of beam splitters and interferometers. We show the equivalence of Mach-Zehnder interferometry to Ramsey spectroscopy and introduce phase-space representations of the density matrix. These are used to discuss metrology beyond the standard quantum limit. In the third part of the module, we formally derive how to treat decoherence with the Master and Langevin equations, and use cavity quantum electrodynamics as an example to introduce quantum state tomography, Fokker-Planck equations as a visualization tool, and continuous measurement. We finally extend this treatment to the scattering of light and show how to treat mechanical effects of light in an open-systems approach. The module ends with an overview of state-of-the-art laser cooling techniques.

After completing the Module the student is able to:

1. Understand the simplest quantum optical systems (two- and three-level systems, harmonic oscillators) and how to control them at a fundamental level.

2. Use these systems as building blocks to model composite quantum systems.

3. Understand and model decoherence by coupling quantum systems to environments analytically and numerically.

4. Understand how to measure and characterize the quantum properties of quantum optical systems.

5. Read, understand, and critique current research papers in quantum science that use quantum optics concepts in experiments with photons, atoms, ions, molecules, solid-state qubits, and electromechanical quantum systems.

Quantum Optics (PH7001)

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

The main 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 contents and to improve their familiarity with them. The solutions to the problem sets are discussed in weekly exercise classes.

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.

Blackboard and Powerpoint.

We cover selected material from all of the books below, and additional material from review articles and current research papers.

• The Quantum Theory of Light, by R. Loudon

• Optical Resonance and Two-Level atoms by L. Allen and J. H. Eberly

• Frequency Standards by F. Riehle

• Quantum Optics by M. Scully and S. Zubairy

• Photons and Atoms by C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg

• Atom-Photon interactions by C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg

• Introduction to Quantum Optics by G. Grynberg, A. Aspect, C. Fabre, and C. Cohen-Tannoudji

• The Quantum Vacuum by P. Milonni

• Exploring the Quantum by S. Haroche and J.-M. Raimond

• Optical Coherence and Quantum Optics by L. Mandel and E. Wolf

• Elements of Quantum Optics by P. Meystre and M. Sargent

• Quantum Optics by D. Walls and G. Milburn

• The Quantum World of Ultra-cold Atoms and Light, Books I, II, and III by C. Gardiner and P. Zoller

• Quantum Noise by C. Gardiner and P. Zoller

• Handbook of Stochastic Methods by C. Gardiner

• Statistical Methods in Quantum Optics by H. Carmichael

• The theory of Open Quantum Systems by H.-P. Breuer and F. Petruccione

• Quantum Measurement by V. B. Braginsky and F. Ya. Khalilii

There will be an oral exam of 30 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 a specific example of a quantum optical system in which to realize a qubit. Discuss how to control and how to characterize this qubit.
• Discuss the difference between decoherence and ensemble inhomogeneities that lead to dephasing, and what to do about them.
• Discuss how to take advantage of three-level systems to realize effective two-level systems with reduced decoherence.
• Discuss a quantum stochastic trajectory for a specific example and how to interpret it.
• Discuss how to measure the full quantum state of light, and how to visualize it.
• Discuss interferometry beyond the standard quantum limit.
• Discuss a simple open system, e.g. a single cavity mode coupled to the electromagnetic vacuum, and how to model and visualize the resulting dynamics.
• Discuss Doppler cooling of a specific atom and its limitations