Signal recycled laser-interferometer gravitational-wave detectors as optical springs

TL;DR

This paper analyzes how signal recycling in laser interferometers creates optical spring effects, altering mirror dynamics and potentially improving gravitational wave detection sensitivity beyond the standard quantum limit.

Contribution

It introduces the concept of optical springs in signal recycled interferometers, revealing their impact on mirror dynamics and noise reduction strategies.

Findings

Optical springs modify mirror response to forces, creating oscillatory dynamics.

Signal recycling can enhance noise curve shaping and surpass the standard quantum limit.

Servo systems can suppress instabilities without reducing sensitivity.

Abstract

Using the force-susceptibility formalism of linear quantum measurements, we study the dynamics of signal recycled interferometers, such as LIGO-II. We show that, although the antisymmetric mode of motion of the four arm-cavity mirrors is originally described by a free mass, when the signal-recycling mirror is added to the interferometer, the radiation-pressure force not only disturbs the motion of that ``free mass'' randomly due to quantum fluctuations, but also and more fundamentally, makes it respond to forces as though it were connected to a spring with a specific optical-mechanical rigidity. This oscillatory response gives rise to a much richer dynamics than previously known for SR interferometers, which enhances the possibilities for reshaping the noise curves and, if thermal noise can be pushed low enough, enables the standard quantum limit to be beaten. We also show the possibility of using servo systems to suppress the instability associated with the optical-mechanical interaction without compromising the sensitivity of the interferometer.