Course Coordinator: 
Hiroki Takahashi
Quantum Optics for Qubits
This course introduces basic notions of quantum optics and prepares a theoretical foundation that facilitates understanding the working principles of modern quantum devices, such as linear optical quantum computers, ion traps, superconducting circuits etc. In many cases physical systems used in quantum technology applications can be described by simple quantum physics of spins (two level systems) and harmonic oscillators. We start from basic algebras of a, a^dagger and Pauli, and then move on to topics such as coherent states, squeezed states, (anti-)bunching, photon statistics, Rabi oscillation, Bloch sphere, Ramsey interference,  cavity QED, master equations, quantum input-output relation, two-qubit entangling gate, ion traps, Josephson junctions, circuit QED.
Target students
Students who are or will be working on applied quantum physics.
Students who wish to understand the working principles of quantum technologies.
Students successfully completing this course will be able to: • Apply basic concepts in quantum optics to interpret various quantum phenomena. • Solve dynamics of quantum systems using master/Schroedinger equations. • Explain working principles of important quantum devices and protocols. • Critically read academic papers in the relevant field.
Course Content: 
1 Basic algebra: bras and kets
Quantized EM field

Quantum harmonic oscillator: Fock states, Coherent states, squeezed states

3 Beam splitter and interferometer

Photon statistics: bunching and anti-bunching

4 Two-level systems interacting with classical fields
Rabi oscillation
5 Two-level systems interacting with quantum fields
Cavity QED
6 Open quantum systems
Master equation
Spontaneous emission
Ramsey interference
7 Quantum input-output relation

Qubit realization: photonics


Qubit realization: ion trap 1


Qubit realization: ion trap 2


Qubit realization: superconducting circuit 1


Qubit realization: superconducting circuit 2


Student self-working week for presentation

14 Presentation by students: Reviewing selected papers
Course Type: 
Problem sheet assignments 60%, Final presentation about selected papers 40%
Reference Book: 
1. “Measuring quantum state of light” by Ulf Leonhardt.
2. “An open systems approach to quantum optics” by H Carmichael.
3. “Methods in theoretical quantum optics” by Barrett and Radmore.
Prior Knowledge: 

Basic knowledge about
・Undergrad-level quantum mechanics
・Undergrad-level linear algebra