The Gravitational-Wave Interferometer

Smaller Than a Proton

Each of LIGO’s arms is about 4 km long. It can measure changes in an arm’s length as small as about 10⁻¹⁹ m.

A proton is about 1.7 × 10⁻¹⁵ m across, more than ten thousand times that. The first gravitational wave detected, in 2015, changed the difference between the arms by about 4 × 10⁻¹⁸ m, about a four-hundredth of a proton’s diameter.

Strain h = ΔL / L · GW150914 peak h ≈ 10⁻²¹ · ΔL ≈ 4 × 10⁻¹⁸ m

One Beam, Two Paths

In the corner station a beam splitter divides the laser light in two, one beam into the X arm and one into the Y arm. Mirrors at the far ends send them back, and they meet again at the beam splitter.

The arms are set so that the two beams cancel at the exit that leads to the detector. That exit is called the dark port.

Laser → beam splitter → two arms → beam splitter → dark port

One Arm Longer, One Shorter

When a gravitational wave passes overhead, one arm gets longer and the other shorter; half a cycle later it is the other way round.

The two beams no longer travel the same distance, they no longer cancel at the exit, and light leaks onto the photodetector. The leaking light rises and falls with the wave. The stretch in the picture is exaggerated; by how much is shown at the top right.

Difference in arm length → phase difference → light at the exit

About 300 Trips Along Each Arm

Each arm has a mirror at both ends, called test masses: the input test mass near the beam splitter and the end test mass at the far end. Together they form a Fabry–Pérot cavity, and the light bounces back and forth about 300 times before it returns to the beam splitter.

That multiplies the wave’s effect on the light’s phase about 300 times, as if the 4 km arms were about 1,200 km long.

Cavity finesse about 450 · phase multiplied about 300 times

Tens of Watts In, Hundreds of Kilowatts in the Arms

The light comes from an Nd:YAG laser at 1064 nm. It is infrared and invisible to the eye; the picture draws it red. It first passes an input mode cleaner, which tidies up the beam.

Almost no light leaves through the dark port, so nearly all of it comes back from the beam splitter towards the laser. A power-recycling mirror there sends it back in, and the power builds up. In the third observing run in 2019, Hanford put in about 34 W, had about 1,500 W at the beam splitter and about 200 kW in each arm. The stronger the light, the smaller, relatively, the flicker from photons arriving at random.

1064 nm · 34 W → about 1,500 W → about 200 kW per arm (2019, Hanford)

Cut Open: Tube and Vacuum

Inside each arm runs a stainless steel tube 1.2 m across with walls only 3 mm thick, under a concrete cover. It is pumped down to about 10⁻⁹ torr, about a trillionth of an atmosphere. Each site holds about 10,000 m³ of vacuum, which LIGO calls the third largest vacuum system in the world.

Baffles in the tube catch light scattered off the beam’s path. The mirrors sit in stainless steel vacuum chambers; the one cut open here holds the X arm’s input test mass.

Tube 1.2 m · wall 3 mm · about 10⁻⁹ torr · about 10,000 m³ per site

Mirrors on a Four-Stage Pendulum

A test mass is a block of fused silica 34 cm across, 20 cm thick and 40 kg, with a reflective coating on the face towards the arm.

It hangs at the bottom of a quadruple pendulum: the top mass hangs from blade springs, then come the upper intermediate mass, the penultimate mass and the test mass. The last stage hangs on four fused-silica fibres 0.4 mm thick. The whole suspension weighs about 360 kg. Behind it hangs a reaction chain: coils push on the two middle stages, and the end reaction mass pushes on the test mass electrostatically, holding the arm cavity at its length.

Fused silica 34 × 20 cm · 40 kg · four 0.4 mm silica fibres

Cut Off From the Ground

The ground never stops moving: ocean waves, wind, passing traffic. The test masses must hardly follow it.

The suspension stands on an active isolation platform, where sensors and actuators cancel most of the shaking first. Each pendulum stage then cuts down shaking faster than its own swing by a large factor. Above 10 Hz the ground’s motion reaches the mirror more than ten orders of magnitude smaller. The shaking in the picture is exaggerated.

Isolation above 10 Hz > 10¹⁰

Squeezed Light

One noise comes from the light itself: photons arrive at random moments, and quantum mechanics does not let that flicker go to zero.

Since 2019 LIGO has injected “squeezed light” at the dark port, making one kind of flicker smaller at the cost of another. Above 50 Hz that lowered the noise by up to 3 dB. Since 2023 the squeezing changes with frequency, using a filter cavity 300 m long.

Since 2019 · up to 3 dB above 50 Hz · since 2023 a 300 m filter cavity

Two Sites, 3,000 km Apart

Hanford and Livingston are about 3,002 km apart in a straight line, about 10 ms for light. A real signal must show up at both, no more than 10 ms apart.

The signal of 14 September 2015 reached Livingston first and Hanford about 6.9 ms later. The delay and the strength at each site told roughly which patch of sky it came from. Today Virgo in Italy and KAGRA, underground in Japan, observe too; both have 3 km arms.

Straight line 3,002 km ≈ 10 ms · GW150914: Livingston 6.9 ms first

14 September 2015

At 09:50:45 UTC both detectors recorded a signal about 0.2 s long: over about 8 cycles its frequency rose from 35 to 150 Hz and its amplitude grew. Two black holes were orbiting each other faster and faster, and merged.

They were about 36 and 29 solar masses, and the black hole they made about 62; about 3 solar masses of energy left as gravitational waves. They were about 1.3 billion light years away. The 2017 Nobel Prize in Physics went one half to Rainer Weiss and the other half jointly to Barry C. Barish and Kip S. Thorne, for decisive contributions to the LIGO detector and the observation of gravitational waves.

36 + 29 → 62 solar masses · about 3 radiated · 410 Mpc

Taken Apart

The quadruple pendulum comes apart: isolation platform, frame, top mass, upper intermediate mass, penultimate mass, test mass and the reaction chain behind. Whichever piece the pointer rests on is lifted out and named.