How Do Gravitational Wave Detectors Work? (LIGO Fabry-Pérot Interferometry & Squeezed Light)

Einstein’s Ripples in Spacetime and the Strain Metric

In 1916, Albert Einstein published the relativistic field equations predicting that accelerated non-axisymmetric masses (such as orbiting binary black holes or neutron stars) radiate energy in the form of propagating quadrupole ripples in the metric tensor of spacetime—gravitational waves travelling at the speed of light [1,2].

As a gravitational wave passes through space, it creates a transverse differential strain ($h$) that stretches distances along one orthogonal spatial axis while simultaneously compressing the perpendicular axis [1,2,3]. For astrophysical cataclysms occurring hundreds of millions of light-years away, the dimensionless strain reaching Earth is unimaginably minute: $h = rac{Delta L}{L} approx 10^{-21}$ [1,3]. Over a detector arm length of $L = 4 ext{ km}$, this produces a physical displacement $Delta L approx 10^{-18} ext{ meters}$—less than one ten-thousandth the diameter of a proton [1,3,4].

"LIGO detects spacetime stretching smaller than 1/10,000th the width of a proton across four kilometers of ultra-high vacuum."

The Michelson-Fabry-Pérot Optical Architecture

To detect this infinitesimal displacement, the Laser Interferometer Gravitational-Wave Observatory (LIGO) operates twin facilities in Hanford, Washington, and Livingston, Louisiana [1,3,5]. Each detector is an ultra-high vacuum L-shaped Michelson interferometer with 4-kilometer arms [1,3].

A stabilized 1064 nm Nd:YAG infrared laser beam is split into two perpendicular arms by a 50:50 beam splitter [1,4]. Inside each arm, the light is trapped inside a Fabry-Pérot optical cavity between two 40 kg ultra-pure fused silica test-mass mirrors [1,3,4]. The photons bounce back and forth approximately 280 times before escaping back to the beam splitter, effectively extending the optical path length from 4 km to over 1,120 km and magnifying the phase shift caused by spacetime strain [1,3,4].

Under quiescent conditions, the returning beams interfere destructively at the photodetector (the "dark port") [1,4]. When a gravitational wave stretches one arm and compresses the other, destructive interference is disrupted, and a fringe signal proportional to the spacetime strain is recorded [1,3,4].

Isolating the Universe: Quadruple Pendulums and Seismic Attenuation

Because the displacement $Delta L$ is smaller than atomic diameters, thermal vibrations and seismic tremors from ocean waves, trucks, or earthquakes threaten to overwhelm the signal [1,4,6].

LIGO isolates its 40 kg fused silica mirrors using a state-of-the-art quadruple pendulum suspension system hung from active internal seismic isolation platforms [1,4]. The mirrors are suspended by monolithic fused silica fibers thinner than human hair, creating an ultra-high mechanical quality factor ($Q sim 10^8$) that concentrates thermal Brownian noise into extremely narrow resonance spikes outside the detector’s active 10 Hz to 2,000 Hz observational band [1,4,6].

Beating the Quantum Limit with Squeezed Light Injection

At high frequencies (> 100 Hz), sensitivity is fundamentally limited by quantum shot noise caused by Poissonian photon arrival statistics at the photodiode [1,4,7]. Under the Heisenberg uncertainty principle, $Delta phi cdot Delta N ge rac{1}{2}$, where $phi$ is phase and $N$ is photon amplitude [1,7].

In Advanced LIGO’s latest O4 observing runs, physicists inject frequency-dependent quantum squeezed vacuum states produced by non-linear optical parametric oscillators into the dark port [1,7]. This reduces phase fluctuations at high frequencies without increasing radiation pressure noise at low frequencies, allowing LIGO and Virgo to detect binary neutron star mergers out to distances exceeding 500 million light-years [1,3,7].

"Injecting quantum squeezed vacuum states manipulates the Heisenberg uncertainty relation to silence quantum photon noise."