# Lecture outline:

## General introduction

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

## Recap: Basics of Quantum Optics

We start by recapitulating the basic concepts of quantum optics, introducing some new aspects not prominently mentioned in last years quantum optics lecture.

- Classical light + quantum atoms
- Quantization of the radiation field
- Beamsplitters, interferometers and homodyne detection
- Quantum atoms interacting with quantum light

## Phase-space representations and quantum state reconstruction

Phase-space representations provide a way to visualize quantum states that has some analogies with classical probability distributions in phase space. They can be used to identify genuine quantum states and they even can be experimentally measured.

- Phase-representation and their use
- Characterizing quantum states of light: Quantum state tomography

## Open quantum systems

No quantum system is truly isolated, especially not optical systems. We will discuss the theoretical treatment of this important aspect here and illustrate applications also justifying phenomenological arguments known from QO1.

- From the master equation to the Focker-Planck equation
- Monte-Carlo wavefunction and quantum jumps
- Langevin equation

## Quantum atom optics / matter waves

Ultracold bosonic atoms can behave very similar to light. We will discuss several experiments generating non-classical matter wave states here.

- Mechanical effects of the atom-light interaction: Laser cooling and trapping.
- Two-mode BEC as collective spin state\
- Spin squeezing, twin atoms and EPR

## Applications: Quantum metrology

Having quantum states with many quanta is advantageous in metrology. Here we discuss applications of non-classical light beams and matter waves in quantum metrology.

- Noise in "classical" interferometry
- Concepts of quantum metrology and applications