A quantum beamsplitter that relies on dust

Researchers divide photons when they should group together.

Once a year, everyone at the MESA+ Institute, where I work, gets together to celebrate the achievements of the past 365 days. Everyone listens to talks by students, post docs, and learned professors. If something catches my interest, I grab the publications and have a closer look. This year was no different.

In one of the optics sessions, a soon-to-be-minted PhD presented one of his key findings: a funny kind of optical hardware that offers unique opportunities for researchers doing quantum experiments. Although simple and boring on the surface (it's a beamsplitter, nothing more than a partially reflective mirror), his simple component is exactly what makes optical quantum computing possible. I promise his results are exciting and unexpected.

An ode to the beamsplitter

A beamsplitter is just a partially reflective mirror. In a standard optics text-book, a beamsplitter is a plate of glass that reflects exactly half the light that strikes it and allows the other half to pass unimpeded (so no light is absorbed). But a light wave has more than just an amplitude (how bright it is)—it also has a phase. The phase of the transmitted and reflected light beams are not the same. Essentially, when light crosses and/or reflects from a surface, the electric field has to obey certain rules of continuity (just like movie fans, nature abhors discontinuities). So, for instance, the electric field is not allowed to suddenly jump from one value to another as it crosses the interface. The only way that this can be satisfied is if the reflected light and the transmitted light have a phase difference of 180 degrees.

This means that if we were to lay the reflected and transmitted waves next to each other, the peaks of the electric field would not line up. Instead, the peaks and the troughs would line up. Normally, this wouldn't matter, but it has strange consequences once you look deeper.

Let's imagine we have a beamsplitter—a partially reflective plate of glass—set up at a diagonal to a beam of light. The light beam comes in from the left. The light is partially transmitted to exit stage right and partially reflected to vanish through the floor. I can add a second beam, though, that approaches the beamsplitter from above. This beam will be partially reflected to exit stage right and partially transmitted to vanish through the floor. Now, the light exiting to the right will be a mix of some light that has been transmitted by the beamsplitter and light that has been reflected. So one beam (the reflected beam) has undergone a phase shift, while the other has not.

Now let's turn down the brightness of the light so that there is only one photon from each beam hitting the beamsplitter at a time. If the two photons arrive separately, then each can be reflected or transmitted and nothing special happens. But, if they arrive together, that phase change matters. If one photon tries to go right and one tries to go down, then their electric fields will add to zero at the interface, so no light will exit the beamsplitter. That means the beamsplitter somehow absorbed both photons—which it can't do, because it is made from a non-absorbing material. Since we need to conserve energy, the photons never take different paths.

Instead, both photons have to go right, or both photons have to go down. The chance of going in either direction is still 50/50, but whatever the dice roll, both photons stick together. This is called photon bunching, and all ordinary beamsplitters do this. Indeed, photon bunching is used in certain quantum computing operations.

But sometimes doing the opposite would also be good: to anti-bunch photons and to have control over the degree of bunching/anti-bunching. Until now, this was difficult.

That beamsplitter is... not right

What do you need to create a beamsplitter that allows both bunching and anti-bunching? White paint. Oh, and a few other small pieces of technical equipment.

White paint is white because it scatters light. Think of it like sugar. If you examine a single crystal of sugar, it appears transparent, but it glints. The glint comes from a small amount of light that is reflected from the sugar's crystal facets. A pile of sugar appears white because all those tiny reflections add up to all the light being reflected in a very disordered way.

The same is true for a thin layer of paint, except that some light makes it through. The light that goes through is typically reflected along the way, so you basically get a halo with randomly positioned bright and dark spots. The bright spots correspond to where different paths through the paint add up in phase.

That knowledge is what drives the bit of research that we're looking at. We can control which paths the light takes through the paint by controlling the phase of the light at each point where it enters the paint. The phase determines which path the light takes, and the phase determines whether the different paths add up at a location on the other side.

By controlling the phase of the light in a spatially dependent manner, we can choose to focus light to a point through a layer of paint. But this technique has far more flexibility. Instead of focusing to a point, you can also focus to two points with equal brightness. The paint acts like a beamsplitter.

To achieve this trick, the light goes through an LCD screen. The liquid crystal in an LCD display changes the apparent distance through which light must pass, depending on the voltage applied to the pixel. This allows the researchers to tune the relative phase of the light beam in space so each little patch of light has a slightly different phase from the patches that surround it.

Now, we don't know which paths the light is going to take through the paint, so we can't know in advance which phase to apply at each LCD pixel. Instead, you choose two locations that you want a focus. Then you vary the voltage on each pixel sequentially to maximize the brightness of the light at each location.

Making a beamsplitter is more complex: you have to do the same trick twice because a beamsplitter has two inputs and two outputs. So one light beam goes through half the LCD screen and is focused through the layer of paint to two locations, while a second light beam goes through the other half of the LCD screen and is focused on the same two locations. In each case, you have to try and balance everything so that both beams contribute equally to both spots. After spending a while doing trial and error, you have a beamsplitter.

Sometimes worst is best

From a purely practical point of view, this is a terrible beamsplitter. Sure, you get equal intensities in each spot, but each spot is thousands of times less bright than the light that was input. In other words, this is a beamsplitter that loses most of its light. This is important.

Even though our simple beamsplitter loses so much light, you can still send single photons into it. Getting a readout just takes a while. In the end, you will observe that if you put a single photon into each beam at the same time, you either get two photons in one spot or the other, but not one in each spot. Exactly as predicted by a normal beamsplitter.

But, now we have some additional freedom. By changing the global phase of one beam—that is, you apply a phase shift to one beam relative to the other over the entire beam—you separate the photons. Instead of always seeing two photons at one focus or the other, you always see one photon at each focus. This cannot be done with an ordinary beamsplitter, even if you modify the relative phase of one beam relative to the other.

Simply put, if you apply a global phase change to one beam relative to another when incident on an ordinary beamsplitter, it will change the time of arrival of the photon. Once you account for that, you still end up with bunching, or with each photon arriving separately. Here, however, the photons are detected at the same time, and they preferentially go in separate directions.

Now, you might think that this is a trick. We don't know the path that the light takes in the layer of paint, so maybe this is not really a beamsplitter. However, the fact that we observe bunching means that the two inputs overlap spatially and interfere with each other. Furthermore, a global phase change doesn't change the path of the light through the paint, so the two inputs still overlap. So this really is a beamsplitter—just a beamsplitter unlike any other.

This is brought home by the theory that describes it. In calculations, the researchers showed that a perfect beamsplitter—i.e. one that doesn't lose any light—cannot do this. It is the very imperfections in the beamsplitter that allow the possibility of anti-bunching. Let's go beyond that though. One could imagine using colored glass as a beamsplitter, which would also absorb some light, but this wouldn't work. While losses allow the possibility, those losses have to be randomized over a wide range of different light paths to allow anti-bunching.

That was a revelation to me.

Of course, the losses also limit how and where this sort of beamsplitter might be used. It is critical that nothing moves during the experiment, so it really only works in lab. I think this kind of beamsplitter can be used for cool demonstrations of linear optical quantum computing. But I doubt that it will ever leave the lab (please note that all such statements are a guarantee that a commercial demonstration is less than one month away).

Physical Review A, 2016, DOI: 10.1103/PhysRevA.93.053817
Optics Express, 2016, DOI: 10.1364/OE.24.016440
*I used to work in the research group where part of this work was carried out.