On the Quantum Theory of Direct Detection

Carl W. Helstrom

Alberto Barchielli, Anna Maria Paganoni

Within the quantum theory of measurements continuous in time, a photon detection theory was formulated by using quantum stochastic calculus; this is a purely quantum formulation, where the usual notions of quantum mechanics appear: the dynamics is given by unitary operators and the observables are represented by commuting self-adjoint operators. In this paper we show how this theory can be equivalently developed by means of classical stochastic differential equations for vectors in a Hilbert space and for trace-class operators. This second formulation is linked to Belavkin's equation for a posteriori states and to quantum trajectory theory. A great part of this paper is dedicated to proving this equivalence between the purely quantum formulation and the stochastic one. The theory of direct and heterodyne detection is developed, with emphasis on the fact that the theory of heterodyne detection can be obtained as a limiting case (strong local oscillator) from the theory of direct detection. We discuss also the connections between the quantum Monte Carlo wavefunction method and some of the stochastic equations which appear in the theory of direct detection.

Carl W. Helstrom

Richard Lieu, Michael Stefszky, Chun-Hui Shi

Abstract We report the experimental observation of photon-bunching noise through shot noise measurements made on a pseudo-thermal state of light using balanced detection. A full theory describing the measurement is developed, and, in agreement with the theory, it is found that the shot noise variance in the balanced signal reproduces the time series of the flux of the primary incoherent beam. Moreover, when the average power of the pseudo-thermal light is varied, the balanced detection is seen to track this change. A comparison of direct detection and balanced detection of the thermal field shows that the balanced detection performs at least as well as the direct detection and under some conditions appears to outperform the direct detection. There is not necessarily a contradiction with quantum field theory, which predicts that at best the performance of the balanced detection should be equal to the direct detection because the direct detection process is subject to nonlinearity that has not been excluded by measurements (even though any tests we performed suggest that such effects are small). This is the first time that the bunching noise effect of high occupation number chaotic light via the shot noise of the field has successfully been measured, to the point of using it to infer the flux of the field. The findings may be relevant to radio receiver design, specifically from the viewpoint of sensitivity improvement.

David Thomas Pegg

The recently detected photoelectron antibunching effect is considered to be evidence for the quantised electromagnetic field, i.e. for the existence of photons. Direct-action quantum absorber theory, on the other hand, has been developed on the basis that the quantised field is illusory, with quantisation being required only for atoms. The author shows that photoelectron antibunching is readily explicable in terms of absorber theory and in fact is directly attributable to the quantum nature of the emitting and detecting atoms alone. The physical nature of the reduction of the wavepacket associated with the detection process is briefly discussed in terms of absorber theory.

Masao Osaki