Standard quantum limit of angular motion of a suspended mirror and homodyne detection of ponderomotively squeezed vacuum field

TL;DR

This paper derives the quantum noise limits for measuring the angular motion of a suspended mirror, showing that ponderomotive squeezing and homodyne detection can surpass the standard quantum limit.

Contribution

It provides the first explicit expression for quantum noise in angular motion measurement and links Gouy phase shift to homodyne detection for noise cancellation.

Findings

Quantum noise in angular motion measurement is explicitly derived.

First-order Hermite-Gaussian mode vacuum field causes quantum sensing and backaction noise.

Proper detection position can cancel backaction noise and surpass the standard quantum limit.

Abstract

Compared to the quantum noise in the measurement of the translational motion of a suspended mirror using laser light, the quantum noise in the measurement of the angular motion of a suspended mirror has not been investigated intensively despite its potential importance. In this article, an expression for the quantum noise in the angular motion measurement is explicitly derived. The expression indicates that one quadrature of the vacuum field of the first-order Hermite-Gaussian mode of light causes quantum sensing noise and the other causes quantum backaction noise, or in other words the first-order vacuum field is ponderomotively squeezed. It is also shown that the Gouy phase shift the light acquires between the mirror and the position of detection of the light corresponds to the homodyne angle. Therefore, the quantum backaction noise can be cancelled and the standard quantum limit can be surpassed by choosing the appropriate position of detection analogously to the cancellation of quantum radiation pressure noise by choosing an appropriate homodyne angle.