# Topics Covered in this Class

**General introduction**

- What is the plan?
- What are the rules?
- Overview of Quantum Optics
- What are we doing in the lab?

**Basics of Quantum Optics**

We will start by recapitulating the basic concepts of quantum mechanics and quantum optics. We will introduce new aspects and go into much more depth than in last semester’s Quantum Optics lecture. In particular, we will first focus on understanding classical light that interacts with quantum atoms, and explore the role of decoherence in this simple-to-understand framework. This first part of the class sets the stage for what is really new about quantum optics.

- Crash course in quantum mechanics
- Two-level systems: the simplest quantum mechanical system
- Propagation of light in dilute media: many quantum systems interacting with light
- Three-level systems: nonobvious effects of classical light interoacting with quantum systems

**Quantum Light**

The second part of the class explores the effects of the quantization of the light field itself. What effects are new when we introduce photons? The discussion will be kept quite general because these concept can also be applied to massive bosonic and fermionic particles, such as atoms.

- Second quantization
- Example: quantization of the light field
- The electromagnetic vacuum
- Common quantum states and their properties
- Interferometry: measuring and characterizing quantized light fields
- Phase-space representations
- Squeezing

**Open quantum systems**

No quantum system is truly isolated, especially not optical systems. We will now include decoherence systematically and start to couple simple quantum systems to the electromagnetic vacuum and justify the phenomenological treatment known from last semester’ Quantum Optics class.

- The master equation
- Correlation functions and spectra
- Resonance fluorescence
- Visualizing decoherence: the Fokker-Planck equation
- Monte-Carlo wave function and quantum jumps
- Continuous measurement
- Composite systems: cavity quantum electrodynamics

**Modern applications**

The last part of the class will be dedicated to drawing connections to modern applications of quantum optical concepts that you will encounter in your future work. Depending on where your interests lie, we will focus on specific topics such as:

- How do you prepare objects that behave quantum mechanically?
- Quantum optics with massive particles
- Quantum metrology
- Quantum simulation and computation
- Optomechanical systems