Weak value amplification of photon number operators in the optomechanical interaction

TL;DR

This paper proposes an experimental method using weak value amplification and post-selection to enhance the radiation pressure effect of a single photon on a mechanical oscillator in an optomechanical system, enabling larger measurable shifts.

Contribution

It introduces a novel approach combining dark port post-selection and weak measurements to amplify photon-induced mechanical effects in optomechanics.

Findings

Weak value amplification can significantly increase the observable shift in the oscillator's position.

Post-selection leads to larger effects compared to pre-selection alone.

Strong measurement can achieve shifts at the zero-point fluctuation level, with increased back-action.

Abstract

An experimental proposal is presented in which dark port post-selection together with weak measurements are used to enlarge the radiation pressure effect of a single photon on a mechanical oscillator placed in the middle of a Fabry-Perot cavity and initialized in the ground state. By preparing and post-selecting the photon (the system) in two quasi orthogonal states, the weak value of the radiation force operator can lie outside the eigenvalue spectrum, producing a large shift on the wave function of the mechanical oscillator (the measuring device) in the position representation. Consequently, the effect of a single photon on the average position of the oscillator in its final state can be amplified as compared to the effect caused by a photon without post-selection, i.e. only pre-selected. The strong measurement scenario is also analyzed. In this case, a higher amplification effect is achieved and the mean position of the oscillator reaches the level of the zero-point fluctuation, but the back-action on the system is increased and the post-selection probabilities are smaller.