Theory of coherent interaction-free detection of pulses

TL;DR

This paper introduces a coherent interaction-free detection protocol using a three-level quantum system, achieving higher efficiency and approaching the Heisenberg limit, with robustness against various errors.

Contribution

It formulates a new coherent protocol for interaction-free detection that surpasses traditional projective methods in efficiency and precision.

Findings

Achieves higher detection efficiency than projective protocols.

Reaches the Heisenberg limit for Fisher information at small pulse strengths.

Remains robust under errors, relaxation, and different initial states.

Abstract

Quantum physics allows an object to be detected even in the absence of photon absorption by the use of so-called interaction-free measurements. We provide a formulation of this protocol using a three-level system, where the object to be detected is a pulse coupled resonantly to the second transition. In the original formulation of interaction-free measurements, the absorption is associated with a projection operator onto the third state. We perform an in-depth analytical and numerical analysis of the coherent protocol, where coherent interaction between the object and the detector replaces the projective operators, resulting in higher detection efficiencies. We provide approximate asymptotic analytical results to support this finding. We find that our protocol reaches the Heisenberg limit when evaluating the Fisher information at small strengths of the pulses we aim to detect -- in contrast to the projective protocol that can only reach the standard quantum limit. We also demonstrate that the coherent protocol remains remarkably robust under errors such as pulse-rotation phases and strengths, the effects of relaxation rates and detunings, as well as different thermalized initial states.