They stand as the last great prediction of general relativity: gravitational waves. They haven't been detected yet, but it seems almost unthinkable for them not to exist. Detecting them though... that is what might be described as a tough problem.

These deformations of space are incredibly tiny. So tiny that making instruments to detect them has produced some of the most challenging engineering problems ever seen. Now, the engineers and physicists can celebrate some progress. Squeezed light has left the lab and is being used to improve a gravitational wave observatory.

What makes gravitational waves so hard to detect?

Gravitational waves are generated by accelerating masses. So, our planet, which is constantly accelerating towards the sun, is sending out a constant stream of gravitational waves. Just really small ones. Likewise, colliding neutron stars will emit a strong burst of gravitational waves. How strong? Well, if the stars were on the other side of our galaxy, a one meter bar on Earth would elongate by about 0.1am (attometer = 10-18m).

It's not really possible to put this in perspective. Even ordinary small numbers, like the orbit of an electron around a hydrogen atom (about 0.05nm), look grossly huge in comparison.

LIGOs, or laser interferometer gravitational wave observatories, use light to detect these tiny deformations. The idea is to split a light beam in two and send each beam off in a different direction. The light beams are then returned to the splitter and recombined. At the point of combination, the light fields interfere, meaning that the measured power in the output of the beamsplitter depends on the difference in the distances each light beam has traveled.

The trick is to make the two paths absolutely identical, which results in absolutely no light exiting at the measurement point due to destructive interference. If the distance changes, this perfect balance is destroyed and the detector sees some light. In a classical world, we would then be ready to roll.

Unfortunately, the world is quantum, and with quantum comes fluctuations. Basically, the place where we measure the light coming out of the interferometer is also a place where light enters the interferometer. So, we aren't adding two light fields together at the beamsplitter. No, we are adding four light fields together. Scientists are not so stupid as to accidentally allow stray light into this device, but nature has its own way of producing strays. The vacuum itself is seething with photons that pop into existence and then disappear again. On average, nothing is there. Unfortunately for LIGO, on average is not good enough.

Let me baffle you with quantum

In a light field, the amplitude (a measure of the brightness of the light) and the phase (which controls how to combine light fields) can't both be measured with absolute accuracy—even if you had the perfect measuring device. You can picture the problem as bunches of photons popping into and out of existence, causing the phase and amplitude of the of the light to jitter around. This doesn't add or subtract energy, but it does continuously redistributes the energy along the light beam.

Now, at the output of the interferometer, we measure the brightness of the light field, and that is defined by how the two fields add together, which determined by their phase. Unfortunately, that means that, no matter how precisely we measure that brightness, it has already been modified by the vacuum fluctuations in the interferometer.

You might think that a photon here or there shouldn't make a difference, but the scaling isn't independent of the laser light entering the interferometer. If you have one photon, you will have a photon of noise. If you have four photons, you will have two photons of noise. The noise increases slower than the signal and the laser power is increased. So, the easiest way to improve the signal to noise ratio is to crank up the power.

That solution, unfortunately, creates its own problems. Powerful and stable lasers are difficult to build. And, all that power has an effect on those optical elements. Some of the light is going to be absorbed, and the optics will deform and expand, increasing the noise rather than decreasing it. It is pretty much certain that the LIGO systems we've already built are close to the limit as far as the benefits of increasing laser power goes.

A quantum mouse trap to catch a noisy quantum mouse

The noise we are trying to defeat is quantum in nature, so researchers have turned to quantum mechanics to solve the problem. The noise in the phase and amplitude of the light is actually a joint minimum. Normally, the noise is distributed evenly between the phase and amplitude. But it is possible to produce light beams that have a phase with noise way below the quantum limit—it just comes at the expense of making the amplitude very noisy. Such light is called squeezed light. There is, unfortunately, no such thing as a high power squeezed light source. So this cannot replace the main light source.

And, in fact, you don't really want to do that. Remember, the source of the noise is from quantum fluctuations; light that we didn't stick into the interferometer. In effect, we made the mistake of letting nature choose that light, and it chooses the vacuum states that satisfy the joint minimum.

The researchers use squeezed light with a very well-defined phase to replace the vacuum contribution. This seeds the vacuum contribution—I use that word deliberately because, although it is not clear, I suspect that the "light" going into the measurement port is actually squeezed vacuum. The squeezing sets the phase of the light far more accurately. This then allows the researchers to sense smaller length deformations and allows less intense gravity waves to be detected.

In the end, technical difficulties limited the degree of squeezing to just over 3dB (basically, the phase has an uncertainty that is a factor of two below that given by the joint minimum). That's not brilliant compared to the 10-13dB (a factor of 10 to 20) that is achieved in quantum optics experiments. But, even with this marginal improvement, the sensitivity of GEO600, a 600m long LIGO, was improved by a factor of three. Much better, but still not good enough to detect anything but the biggest and baddest of astronomical events.

At present, there are two big factors that limit GEO600. First, its operators don't have the degree of squeezing that they really want, and this squeezing is further reduced by the optical absorption and scattering that takes place in the optics between the source and the interferometer. The second limitation is that the squeezing source is only stable over a period of a few hours, so they cannot collect long data runs just yet.

Of these, I would imagine that the optical losses and stability can be improved rather rapidly. It will, unfortunately be a bigger challenge to achieve more squeezing. The issue here is that the amount of squeezing you measure depends on the time period over which you measure it. The most squeezed states last only microseconds, and are measured in the MHz frequency region. But LIGO needs to have sensitivity in the Hz-kHz range, meaning that the squeezed state is the average over milliseconds rather than microseconds. This places quite severe demands on the technical requirements for the laser used to create the squeezed states and the surrounding optics.

In spite of the difficulties, I would imagine that we will see low-frequency squeezed states improve steadily. The LIGO folk have been nothing if not determined.

Nature Physics, 2011, DOI: 10.1038/NPHYS2083