Wave Functionals for the Photon Field

Abstract

Given a Hilbert space of quantum mechanical states, in principle any basis is as good as any other if we are capable of doing exact calculations for processes. However, as is well-known, in practice it is advantageous to choose a certain basis in preference to others for a particular problem. The photon even at this basic level is still stimulating new theoretical work¹. On the experimental front there is impressive progress in realizing some of these new calculated states². On using the rules of quantum mechanics, it is of course possible to calculate accurately correlation functions which describe photodetection in these experiments. However in non-cavity situations such as parametric down-conversion we would like to understand to what extent we can think of localised photons flying through space. It is not simple to characterise such states since there is no position operator for the photon.