# Introduction

## Flux quantization

In superconductors, electrons condense into a quantum coherent state at low temperatures. The continuity of the macroscopic wavefunction of this condensate implies that a superconducting ring can only be threaded by a magnetic flux which is a multiple of the flux quantum, $$\Phi_0 = 2.068~\textrm{fWb}$$.

The quantization of flux was predicted by Fritz London in 1948 and verified by Deaver, Fairbank, Doll, and Näubauer more than ten years later.

## Josephson junctions

When two superconductors are separated by a sufficiently thin barrier, Cooper pairs can tunnel across in a quantum coherent manner. This effect was predicted by Brian Josephson in 1962, for which he later won the Nobel prize. The superconductor-insulator-superconductor sandwich in which it occurs is called a Josephson junction.

The foundation for most of the research conducted in the group is the AC Josephson effect, which states that a Josephson junction with a DC voltage bias $$V$$ will emit photons of energy $$h\nu = 2eV$$. The proportionality constant between (\nu\) and $$V$$ is the inverse of the flux quantum and is called the Josephson constant, $$K_J = 2e/h = 483.6~\textrm{THz/V}$$.