Amplification effects in optomechanics via weak measurement

TL;DR

This paper analyzes the exact dynamics of weak measurement in optomechanics, revealing amplification effects in mirror displacement influenced by Kerr phase and phase shifters, beyond traditional weak measurement explanations.

Contribution

It provides an exact solution to the weak measurement scheme in optomechanics, highlighting amplification effects caused by Kerr phase and phase modulation.

Findings

Positive and negative amplification effects observed.

Amplification modulated by phase shifter.

Maximal displacement occurs in short evolution time.

Abstract

We revisit the scheme of single-photon weak-coupling optomechanics using post-selection, proposed by Pepper, Ghobadi, Jeffrey, Simon and Bouwmeester [Phys. Rev. Lett. 109, 023601 (2012)], by analyzing the exact solution of the dynamical evolution. Positive and negative amplification effects of the displacement of the mirror's position can be generated when the Kerr phase is considered. This effect occurs when the post-selected state of the photon is orthogonal to the initial state, which can not be explained by the usual weak measurement results. The amplification effect can be further modulated by a phase shifter, and the maximal displacement state can appear within a short evolution time.