Interferometers that produce clearer signal by getting rid of light

Photons arrive at random moments. Predict the moment, measure, and win.

 Chris Lee

An interferometer that JPL has sent into space.

JPL

A lot of what I write is about measurement, not because I'm in love with calipers, but because the cutting edge of physics is at the limit of what we can measure. That means that when you want to think about what to do next, you need to consider how a measurement can be made more sensitive.

Many people, including some scientists, don't realize that you can learn a lot about the world simply by developing new or better instruments. Today, I've decided that the measurement you all need to know about is interferometry. Why? Because interferometers are the fezzes (fezzes are cool) of the physics world. And now, a group of international researchers has come up with a way to make interferometers even more sensitive.

To understand why this is significant, you need to understand why I'm not kidding about interferometry being cool. In the past, an interferometer at a Laser Interferometer Gravitational-Wave Observatory (LIGO) was used to detect gravitational waves. The experimenters at LIGO worked hard to gain control over every aspect of the experiment (except for the gravitational waves—they had no control over them), including exquisite control over the light source used. In the end, their results involved measuring physical movements that were less than the diameter of a proton. Surely, very few measurement problems would require an even more sensitive interferometer.

But consider astronomy, where interferometry is used to make measurements on light itself. In this case, the light that nature gives you is dim and has properties not conducive to high-quality measurements. Interferometry under these conditions is challenging.

Have you seen my fez interferometer?

Before I get to the new stuff, let me introduce you to the wonderful world of interferometry and what it has given us. Interferometry is just a way to compare light to itself. You have a source of light, which you pass through a partially reflecting mirror. The reflected part of the beam travels to a second mirror, is reflected, and returns to the first. Likewise, the transmitted part of the beam reflects off yet another mirror and returns to the partially reflective mirror.

Once back at the partially reflective mirror, the two light beams interfere and leave the interferometer. Notice in the picture that the light leaves the interferometer in two directions, but only enters in one. The other direction (or "port" as it is called) also takes in light, but that light has no intensity. Nevertheless it contributes to the signal by adding noise.

Enlarge / Interferometer: light enters the interferometer at the bottom. It is divided by the partially reflective mirror. Half the light travels to the mirror on the left and half continues up to the mirror at the top. These two mirrors reflect the light, which recombines at the partially reflecting mirror. The recombined light either exits in the direction in which it came, toward the detector, or a combination of both. This is symmetrical, so light can also enter from the detector side as well. Even though this light has no intensity, it adds noise.

Imagine that the interferometer is perfectly balanced (so the distance from the partially reflective mirror and the end mirrors is the same for both paths), and the end mirrors are identical. All the light will go in a single direction and the other direction will be completely dark. You can use an interferometer to test whether a mirrored surface is polished and nearly perfectly flat—just use it at one of the end points. Likewise, if you need to make a mirror that has a specific curvature, then the output from the interferometer can tell you exactly how accurate your curvature is. How accurate? Using interferometry, professional optics manufacturers can figure optics with an accuracy that is less than the diameter of an atom.

It's also easy to improve these systems. The more accurate you need to be, the brighter you make the light in the interferometer. This is one of the keys to LIGO's success: the optical power in the interferometer was many kilowatts—signal swamping noise.

Turning the brightness down

Brightness is so effective because of its relationship with noise. For a laser, the noise increases with the square root of the average power. So, if you quadruple the average power of your laser, the noise only increases by a factor of two, giving you a net win. But starlight isn't a laser—it's thermal light. For thermal light, increasing the average power does not give you a net win, because the noise is equal to the average power, at least for bright sources. For dim sources, the random fluctuations are actually greater than the average power.

Given this, you might think that subtracting even more light from the output of an interferometer would make measurements more difficult. But this is exactly what the new work I mentioned earlier involves. And subtracting light works: it makes the interferometer more sensitive. Why? The answer lies in how you use the subtracted light.

For a very dim thermal source, most of the time there are no photons. If you could somehow measure only when there are photons, then you remove a portion of the fluctuations. This is exactly what researchers have done.

At the output of their interferometer, they place a partially reflective mirror that allows them to remove a chosen number of photons. They place a detector in the path of the reflected light to look for those photons. Whenever the detector clicks, they know that there was at least one photon in the interferometer. They can then choose to measure the output of the remaining light from the interferometer.

This sounds simple. Indeed, in electronics, this would be referred to as a box-car integrator. If you have a short signal that comes with a triggering event, you can choose to measure in the tiny interval when the signal is there. Add up the output from all those tiny intervals, reject the noise from all the time in between, and you have a much cleaner signal.

But doing this with photons is complicated because of the statistics of light's behavior.

Photons of a feather flock together

For our purposes, the interferometer accepts light that is in specific modes. Think of modes as a categorization of different photons: wavelength, spatial distribution, electric field orientation, and so on. When we measure the intensity of the light (including at the output of the interferometer), we are asking how many photons are in a particular mode in a particular time interval. And most of the time, for dim light, the answer is zero.

But the statistics of photons are a bit weird, because photons are more likely to arrive in bunches, rather than separately. Why is this? Here's a simple way to think about it: a photon is also a wave and has a spatial extent. Now, if two photons with the same color are traveling together, then they add up in phase to create a brighter light. But, if one photon slips backward with respect to the other, the light gets dimmer and dimmer until it almost vanishes due to interference.

As a result, for a light source above a certain brightness, the probability of measuring two photons arriving at the same time is not just non-zero but is higher than that of individual photons—and much, much, much higher than for two photons that are separated in time by exactly half a wavelength. Essentially, the mixing of the wave-like nature of photons ensures that they travel in little bunches that are well separated from each other. All those photons that would find themselves between these bunches suffer destructive interference and are never emitted.

Because photons are more likely to travel in groups, finding one photon means that there is probably another. Finding two photons means that there is likely a third or fourth to be detected. In other words, if we use the box-car integrator analogy, the trigger signal can be tuned to only measure the interferometer output at those moments when there is the highest number of photons in the mode.

As a result, you get a complicated relationship. Subtracting a single photon improves the ratio between the signal and noise by about 1.4. But subtracting two photons increases the signal-to-noise ratio even further. This increase happens because, by upping the threshold, you only look for those moments when the output intensity will be increasingly high. And the statistics of photons ensure that these moments occur a bit more often than a naive estimate would lead you to expect, which gives you a small net win.

Hurry up and wait

However, don't think you are going to win too much by subtracting light. Imagine that you crank up the threshold so that you don't make any measurements until there are ten photons. For a very dim light, you are going to be waiting a very long time to trigger on a single event. In other words, just like every other measurement in existence, you face a trade-off between measurement time and signal clarity. In this case, the trade-off is more stringent, because the measurement device spends more and more time not actually measuring anything.

Nevertheless, in situations where you can sacrifice time to get a better signal, this may well be worth it.

arXiv.org, 2016, arXiv id: 1605.05424v1