Weak measurement amplification based on thermal noise effect

TL;DR

This paper demonstrates that thermal noise can be exploited in weak measurement amplification, allowing displacement sensitivities at room temperature to be enhanced by nearly seven orders of magnitude, surpassing traditional limits.

Contribution

It introduces a novel amplification mechanism using thermal states as pointers, extending weak measurement amplification beyond pure Gaussian states.

Findings

Amplification limit reaches thermal fluctuation level with increasing temperature.

Two schemes achieve nearly seven orders of magnitude displacement amplification.

Sensitivity to 0.26 nm displacement at room temperature is attained.

Abstract

Most studies for postselected weak measurement focus on using pure Gaussian state as a pointer, which can only give an amplification limit reaching the level of the ground state fluctuation. When the pointer is initialised in a thermal state, we find that the amplification limit after the postselection can reach the level of thermal fluctuation, indicating that the amplification effect achieving the level of thermal fluctuation is also increased with the temperature grow, and also give the amplification mechanism different from the one with pure Gaussian state pointer. To illustrate these results, we propose two schemes to implement room temperature amplification of the mechanical oscillator's displacement caused by a single photon in optomechanical system. The two schemes can both enhance the mechanical oscillator's original displacement by nearly seven orders of magnitude, attaining sensitivity to displacements of $ 0.26$ nm. Such amplification effect can be used to observe the impact of a single photon on a room temperature mechanical oscillator which is hard to detect in traditional measurement.