Energy-Based Weak Measurement

TL;DR

This paper explores a novel weak measurement process where a photon transfers energy to an absorber without absorption, revealing insights into energy transfer and measurement in quantum systems.

Contribution

It introduces an energy-based weak measurement framework where unabsorbed photons influence an absorber's energy, expanding understanding of quantum measurement processes.

Findings

The absorber's energy increase equals its weak value.

Photon energy distribution shifts opposite to the absorber's energy.

Analysis includes non-scattering and interaction-free energy transfer cases.

Abstract

When a well-localized photon is incident on a spatially superposed absorber but is not absorbed, the photon can still deliver energy to the absorber. It is shown that when the transferred energy is small relative to the energy uncertainty of the photon, this constitutes an unusual type of weak measurement of the absorber's energy, where the energy distribution of the unabsorbed photon acts as the measurement device, and the strongly disturbed state of the absorber becomes the effective pre-selection. Treating the final state of the absorber as the post-selection, it is shown that the absorber's energy increase is the weak value of its translational Hamiltonian, and the energy distribution of the photon shifts by the opposite amount. The basic case of non-scattering is examined, followed by the case of interaction-free energy transfer. Details and interpretations of the results are discussed.