Weak measurement: Effect of the detector dynamics

TL;DR

This paper investigates the effects of detector dynamics on weak measurements, emphasizing the importance of probe phase coherence and demonstrating significant imaginary weak value contributions in spin measurements.

Contribution

It introduces a general framework for weak measurement considering detector dynamics and highlights the role of probe phase coherence in the measurement process.

Findings

Probe phase, including Hamiltonian effects, influences weak measurement outcomes.

Imaginary parts of weak values can be substantial in spin measurements.

Detector dynamics are crucial for accurate interpretation of weak measurement results.

Abstract

A general approach to the measurement of an observable with pre- and post-selection is presented. The limit of weak measurement is studied in detail, and it is shown that the phase of the probe, including a Hamiltonian contribution to it, gives rise to observable effects, since the coherence of the probe is essential for the concept of complex weak value to be meaningful. As a particular example, the measurement of a spin component is considered. We find that the contribution of the imaginary part of the weak value is sizeable in this case.