Measurement of Wave Fields

Abstract

Wave flelds are the fundamental entities in both classical electrodynamics and quantum mechanics. The similarity of their governing dynamical equations suggests that similar strategies may be used to measure both classical and quantum flelds. Indeed, numerous experiments in the recent past have demonstrated just this. But it is not this similarity alone that makes it important to consider their measurement within a single context, it is the very notion of manipulation of quantum systems (the idea of quantum state preparation or control) that demands it. Consider, for example the generation of a single 'on demand, using the prescription, say, of Eberly and Law's photon pistol [1]. What does this mean, precisely? Nothing more than the specification of the quantum state of the field (a Fock state with eigenvalue unity) and a classical state of the field (the temporal mode in which the excitation is generated). Both pieces of information are necessary to appropriately specify what one means by the time of production of a photon. This problem resurfaces in all quantum measurement problems one needs to know both the basis in which one is making the measurement and the degree of freedom (or the mode) for which the measurement is defined. To the extent that quantum state measurement is the same as state preparation, it might be argued that there is no need to consider state measurement procedures separately. Of course, in practice most measurement schemes end up being of the demolition variety — one infers from the detected signal what the state must have been at the detector before a signal was registered. This is quite a different situation than the ideal envisioned by von Neumann. But this aside, the situation may perhaps be likened to one of quality control, if one may adopt the industrial, metaphor used by the state engineers. That is, the consumer needs to determine whether she has been sold the quantum system that meets her needs, in the state that she ordered. Thus she needs both a classical and a quantum field measurement apparatus. Of course in practice one must order (and measure) an ensemble of identically prepared states, and then use the apparatus to determine