Topics Covered in this Class

Basics of Quantum Optics

We will start by recapitulating important concepts of quantum mechanics and electrodynamics, and how they relate to quantum optics. and how they relate to quantum optics. We will discuss the interaction of light with quantum mechanical objects, concepts like coherent vs. incoherent dynamics, and gnereally how to describe the systems using appropriate quantum mechanical representations.

We will use these to explore the first systems that will be of relevance also to later topics, such as light interaction with individual quantum systems such as two-level and three-level atoms, interactions with many quantum systems and propagation of light in a medium. We discuss the realization of such systems and applications such as slow light, atom cooling and light storage.

Quantum Light

We discuss the quantum description of the light field, or generally bosonic fields, discussing quantum mechanical and classical states of the light field, the properties of the electromagnetic vacuum state, phase-space representations and distribution functions to represent quantized light fields. We also discuss the actual creation and application of quantized light fields for applications such as interferometry and metrology.

Open quantum systems

To correctly take into account the interaction fo a quantum optical system with the open environment, we discuss how to represent effects such as decoherence on the quantum mechanical level using open quantum system. For example, we use the coupling to the vacuum to understand the simplified models of decoherence and why the work the way they do, ad discuss applications to cavity systems, the preparation of quantum states, and the realization of lasers.

1. The master equation
2. Correlation functions and spectra
3. Resonance fluorescence
4. Visualizing decoherence: the Fokker-Planck equation
5. Monte-Carlo wave function and quantum jumps
6. Continuous measurement
7. Composite systems: cavity quantum electrodynamics

Modern applications

During the entire class, a big focus will be on how the concepts are applied to relevant applications, as well as the physical realization of these systems, including important techniques.

In addition to topics directly connected to the bigger blocks of the lecture, we will spend significant time discussin quantum optical topics that are of relevance for current research and applications, such as quantum metrology, quantum optical cooling methods, quantum simulation and quantum information, optomechanical systems and more.

1. How do you prepare objects that behave quantum mechanically?
2. Quantum optics with massive particles
3. Quantum metrology
4. Quantum simulation and computation
5. Optomechanical systems