Wavefunction collapse through backaction of counting weakly interacting photons

TL;DR

This paper demonstrates that counting entangled photons in an optical interferometer causes wavefunction collapse, aligning the post-measurement uncertainty with shot-noise limits without environmental decoherence, and preserves momentum information.

Contribution

It provides a formalism showing wavefunction collapse as a measurement backaction from photon counting, without relying on decoherence or spontaneous collapse theories.

Findings

Wavefunction collapses toward a narrow Gaussian at the estimated position.

Post-measurement variance matches shot-noise limited uncertainty.

Initial momentum information is preserved through measurement.

Abstract

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 wavefunction toward a narrow Gaussian wavepacket at the location $x_\mathrm{est}$ 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 $x_\mathrm{est}$. Both the identification of the absolute square of the particle's initial wavefunction as the probability density for $x_\mathrm{est}$ 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.