Wavefunction collapse through backaction of counting weakly interacting photons

We apply the formalism of quantum measurement theory to the idealized measurement of the position of a particle with an optical interferometer, finding that the backaction of counting entangled photons systematically collapses the particle's wave-function toward a narrow Gaussian wavepacket at the location x(est) determined by the measurement without appeal to environmental decoherence or other spontaneous collapse mechanism. Further, the variance in the particle's position, as calculated from the post-measurement wavefunction, agrees precisely with shot-noise limited uncertainty of the measured x(est). Both the identification of the absolute square of the particle's initial wavefunction as the probability density for x(est) and the de Broglie hypothesis emerge as consequences of interpreting the intensity of the optical field as proportional to the probability of detecting a photon. Linear momentum information that is encoded in the particle's initial wavefunction survives the measurement, and the pre-measurement expectation values are preserved in the ensemble average. (C) 2016 AIP Publishing LLC.