I have completely lost count of how many times I have read phrases like, "Consider a light source that emits photon pairs that are indistinguishable." This indistinguishability, along with the ability of these pairs to be correlated, plays a central role in the games that we play with quantum mechanics.

This isn't only a matter of games for academics—there are also security and computational applications that depend on photons that are (theoretically, at least) indistinguishable. But real experiments use real equipment that is never quite ideal. In some ways this is a benefit, because an ideal pair of detectors would detect differences in our slightly-less-than-ideal photons, destroying experiments and generating cynical graduate students.

Now, some new research from ETH Zurich and Aalto University in Finland explores how imperfect indistinguishability alters the appearance of quantum effects.

Controlling wavelength

The basic idea of the experiment is simple. Take two objects that emit single photons that are identical to each other. Detect these photons after they have been mixed together using a beam splitter. If they are identical, both photons will appear on the same output port of the beam splitter and set off the same detector. If they are different, they can appear on different output ports and set off different detectors.

As the wavelength difference between the two photons varies, the statistics logged by the detectors reveal whether the photons can be usefully considered "distinguishable."

The researchers built independent but identical photon sources by mixing dye molecules into a polymer matrix, which was then cooled to near absolute zero. The emission wavelength of the dye molecules is very sharply defined thanks to the low temperature, but each dye molecule has a different local environment—the polymers are randomly arranged, so each dye molecule sits in a local electric field that has its own orientation and strength. As a result, each dye molecule has a unique color.

To get two single photon emitters, the researchers used two microscopes to collect light from a very small region of the dye—so small, in fact, that only a single dye molecule was responsible for the photons collected by the microscope. This makes the system a single photon emitter, because a dye molecule can only emit a single photon after it has been excited. To emit a second photon, it must be re-excited; since excitation is done by an external laser pulse, this is easy to control.

Of course, the photons are distinguishable because they emit different colors. The researchers use the source of this natural difference—the local electric field—as a knob that changes the dye molecule's emitted wavelength. An externally applied field can change the emission wavelength; the researchers did this using a pair of tiny electrodes positioned in close proximity to one of the microscope objectives.

Controlling arrival time

Now they had two independent sources of photons with emission wavelengths that could be continuously varied from indistinguishable to distinguishable. The second variable in the experiment is the time of arrival of the photons at the beam splitter. A typical experimental result was to set the emission wavelength and then tune the arrival time of the photons. When they are identical in both wavelength and arrival time, only one photodetector should detect light; when either the color or the arrival time are different, both detectors can click.

In practice, though, noise gets in the way. As a result, even when the photons are experimentally as indistinguishable as possible, the researchers only got something like 60-70 percent of the clicks from a single detector.

Detuning the color of one photon from another by about 300MHz—this is a huge amount in terms of what is usually done to ensure photons are indistinguishable—resulted in performance that was pretty much as good as the perfect case, but the timing of the photons had to be more accurate.

Overall, the results are surprising, in that the amount of detuning that could be tolerated was huge. But in another way, it was also not surprising because, as the photons become more distinguishable, the data indicates less than perfect indistinguishability.

You'd also expect that the timing constraints were tighter for photons with slightly different emission wavelengths, because the two are related—wavelength and frequency are inversely proportional, and frequency is the inverse of time. I would, therefore, expect the quantum interference would be completely gone if the arrival difference was 3ns or better, which is exactly what the researchers found.

This is quite significant, because 200-300MHz puts indistinguishable photons in the range of "pretty crappy " (and hence, relatively cheap) single photon sources. So this finding, which provides constraints on how bad the emitters can be, might come as a relief to those whose job it is to develop commercial single photon sources.

For those of you wondering why this lovely dye source can't be used more often: dye molecules fall apart after a few thousand excitations, meaning that the photon source is essentially a disposable one.

Physical Review Letters, 2010, DOI: 10.1103/PhysRevLett.104.123605