One of the requirements for quantum computing is near perfect control and coupling between the states of separate objects. This often requires that two atoms separated by large distances have an identical set of quantum states. This is very difficult to achieve, because the atoms' individual states are modified by their local environment, so, independent of a pair of atom's separation, they are very likely to be different enough to be un-useable.

A recent paper in Physical Review Letters shows how this problem can be overcome for one of the leading candidates for quantum computing: nitrogen vacancies in diamond.

I may be vacant, but I am still here

Diamond may seem an unlikely candidate for quantum experiments, but it has one redeeming feature: it's really hard. The carbon atoms are so tightly bound to each other that they cannot move around much. This means that it takes a lot of energy to set the carbon atoms in motion, so the local environment anywhere in the crystal is likely to stay relatively fixed for longer periods of times.

The advantage of being part of the crowd What the researchers are after here is something called indistinguishability. This can be a challenge because, in many quantum experiments, it is possible to tell things apart. For instance, if one nitrogen vacancy emits a photon of one color, and another of a different color, I can distinguish both the photons and their source. However, if the photons are identical in every respect, I cannot tell them apart, nor can I tell where they come from. This property, called indistinguishability, is a key requirement for creating and transferring [ars_old_tp entry_id="49540"]entangled states.[/ars_old_tp] And indistinguishable photons have a very cool property that is easiest to understand using a mirror. If a stream of single photons are aimed at a partially reflective mirror, half of the time they will pass through and half of the time they be reflected. If I set up detectors on either side of the mirror, only one detector will click at any given time—they should never click together. Now, if I bring in a second source of single photons that are different (say a different polarization), the two photon streams behave as if they don't know about each other. I will get coincidental clicks about a quarter of the time. But, if the two photon sources produce indistinguishable photons, then they interfere with each other. If the two photons choose different paths (i.e., one is reflected and the other is transmitted), then the interference is destructive; if they choose the same path, then the interference is constructive. This means that both photons can be reflected or both photons can be transmitted, but, whatever they do, they do it together. The result: only one detector clicks at a given time.

Nitrogen is a common, and often accidental, inclusion in diamond—it gives the diamond a brown color. Jewelers might not like it, but physicists love it. Carbon likes to be surrounded by four other carbon atoms, but nitrogen can't handle that many partners at once, preferring to be surrounded by three other atoms. If you replace a carbon atom with nitrogen in diamond, then the nitrogen snubs one of the surrounding carbon atoms, leaving the carbon atom with a spare electron.

The result is a kind of pseudo atom, where the spare electron is confined on all sides by carbon and nitrogen atoms, but is wanted by none of them. The confinement gives it a set of well-defined energy levels. Because diamond is so hard, those energy levels don't get washed out by all the background motion of the crystal.

The result is that you have a set of relatively long-lived and coherent quantum states that are accessible using light fields: perfect for quantum computing.

That's very useful, but there is always a but. In this case, each nitrogen vacancy is different from its neighbors, which means that two of them don't have the same quantum states. Until now, it has been a matter of luck to find two nitrogen vacancies with the right energy levels to allow them to produce indistinguishable photons.

If we all had electrodes, we could be vacant together

The researchers recognized that the energy levels of nitrogen vacancies could be modified by applying a voltage in their vicinity. The problem was that the voltage would effect many different vacancies, so, a little bit of finesse was required.

To achieve a localized change in the energy level spacing, the researchers milled the diamond crystal so that it contained two tiny lenses, allowing them to send light to, and receive light from, two nitrogen vacancies separately. They then deposited a set of electrodes leading up to the lenses. These electrodes might influence the behavior of many vacancies, but the lenses ensured that only one of those would be visible. In effect, the researchers could apply different voltages to two different nitrogen vacancies.

To test if their nitrogen vacancies were emitting indistinguishable photons (see side bar), the researchers send the photons emitted from each vacancy on a beam splitter (think partially reflective mirror) to see if the photons always went in the same direction. This is the gold standard for proving that photons are indistinguishable.

First, they performed the experiment using photons with different polarizations. No matter what voltage was applied to the electrodes, the photons would be distinguishable. As expected, this resulted in a photon striking detectors on both sides of the beam splitter about a quarter of the time. (In other words, the two photons had independent probabilities of being reflected by the beam splitter.)

Then they chose identical polarizations and carefully set the voltage so that, as far as they could tell, the emitted photons were indistinguishable. The coincidence tests showed that this was, indeed so—only one of the two detectors would go off when a pair of photons hit the splitter. The final test was to tune to the electrode voltage and see if the coincidence counts fell off for a particular voltage

I have to say that the results of these experiments are pretty noisy. Indeed, the last experiment, especially, is just barely on the right side of the statistically significant border. You can also get a hint as to how difficult this experiment was from the scales on the graphs: they accumulated just 50-100 coincident detections in six hours.

This is always the way, though. The first experiment only just works. In a few years, this will be a routine part of experimental work, and researchers will be able to address vacancies with an identical set of quantum states at higher efficiencies and with a very clean signal. Assuming that occurs, this will become a very important tool in laboratories in the near future.

Physical Review Letters, 2012, DOI: 10.1103/PhysRevLett.108.043604