Coherence

The concept of coherence is widely used in different areas of physics like in optics, in quantum optics or in neutron and X-ray scattering, however with subtle differences in meaning for the different communities. In quantum optics it is mainly the source of photons and its characterization in terms of coherence functions which is of concern. In a scattering experiment, on the other hand, the source is supposed to be characterized and it is the internal degrees of freedom of the sample which are studied via their influence on the detected interference pattern. It is one of the purposes of this paper to clarify the different concepts and to show how they are interrelated. The paper is organized as follows. First, we will discuss what interferes in a physical event. This will be treated according to the Feynman formulation of quantum mechanics in terms of probability amplitudes and we will describe nine rules on how to calculate with these amplitudes. Then we will discuss what destroys interference. The main part of the paper treats a number of applications from quantum optics and X-ray and neutron scattering. These include quantum beats, Hanbury Brown and Twiss interferometry, entangled states, Einstein–Podolsky–Rosen paradox and speckle from coherently illuminated samples.