Gravitational wave detectors from an experimental perspective

TL;DR

This work presents an experimental perspective on gravitational-wave detectors, detailing how detector noise limits sensitivity and how interferometric configurations translate gravitational-wave signals into measurable outputs. It combines a rigorous noise theory framework with a practical detector model that includes Michelson readout, Fabry-Perot arm cavities, and power recycling, then derives the dominant noise contributions—seismic, thermal, and quantum—through both classical and quantum optics formalisms. The chapter provides explicit expressions for transfer functions, PSDs, and shot-noise-limited strain sensitivity, highlighting the trade-offs between intracavity power, finesse, and bandwidth, and discusses advanced techniques such as PDH locking and vacuum squeezing to enhance performance. The resulting sensitivity curve demonstrates the balancing of signal amplification and noise suppression, informing realistic upgrades for future detectors and underpinning the practical impact of resonant cavities, stabilization loops, and quantum noise control on gravitational-wave astronomy.

Abstract

This chapter introduces the fundamental principles of gravitational wave detectors in a simple and comprehensive manner. Because these instruments aim for extremely high sensitivity, it is essential to understand their various noise sources, how such noise couples to the detector output, and the strategies used to mitigate them. These noises contributions are computed in the frame of the Virgo detector and a sensitivity curve is calculated. Although a simplified layout of a gravitational wave detector is considered, it takes into account the most dominant effects and yields in a sensitivity estimate close to the what is observed in real detectors.

Figures (20)

• Figure 1: Two examples of noises: white and colored. On the temporal profile (left), these two noises are hardly distinguishable, whereas their auto-correlation functions (right) have different behaviors.
• Figure 2: Usual representation of the GW polarizations
• Figure 3: a) Schematics of a Michelson interferometer. Light coming from a laser source is split by a beamsplitter into two orthogonal arms and fully reflected back to the beamsplitter. Depending on the interference, part of the light is reflected back to the laser and part is transmitted to a photodetector. b) Fields in reflection (green arrows) and transmission (orange arrows) of a beamsplitter represented by the real convention, where the reflected light field acquires a minus sign in one (here the left) of the surfaces of the beamsplitter.
• Figure 4: Representation of a Fabry-Perot cavity. The mirrors are characterized by their transmission and reflection coefficients $\sqrt{T_1},\sqrt{R_1}$ and $\sqrt{T_2}, \sqrt{R_2}$ and they are placed at a distance $L$. A polarized laser is injected in the cavity. $E_i, E_r, E_c$ and $E_t$ are respectively the input, reflected, circulating and transmitted complex electric fields.
• Figure 5: Squared modulus of the enhancement function as function of the round-trip phase $\varphi$ for $\sqrt{R_1} = 0.9$ and $\sqrt{R_2} = 0.914$. The spacing between the resonant peaks is noted as $\Delta\varphi_\text{FSR}$ and their full width at half maximum (FWHM) as $\delta\varphi_\text{FWHM}$.