I have read enough about entanglement that it has gotten to the point where a paper with "entanglement" in the title or abstract really needs to be special or my eyes will glaze over as I reflexively click the "next" button in my RSS reader. A couple of weeks ago, an entanglement paper got me enthused, but it has sat, unread, in a tab in my browser until earlier today.

The Physical Review Letters paper lays out experimental evidence for a very cool sort of entanglement that plays games with time and energy. Essentially, they show that if you entangle a pair of photons in a particular way and then delay (or advance) the photons in time, you change the color of the photon—or, more precisely, you can limit the available colors that the photon can assume when it is finally measured.

Lets jump to the experiment, because that gives a good idea of what is being measured and, therefore, what is entangled. The researchers took a green laser and focused it into a crystal that responds to the high intensity light in a nonlinear fashion (I am not going to explain this further, because it would require a post all on its own). The end result is that a few of the green photons get split approximately in half, creating a pair of entangled photons.

Since green light has a wavelength of 532nm, conservation of energy dictates that it gets split into two photons with a wavelength of 1064nm. There is a bit of imprecision in the process, so, one photon could be up to 16nm on either side of this ideal value. Energy conservation then dictates that the other is an equal distance from 1064nm in the other direction. This gives each photon a potential bandwidth of 32nm, and, because of that bandwidth, there will be a certain time uncertainty about exactly when the photon pair was created.

What the researchers wanted to do is manipulate how long it takes the photon to reach a detector, with the timing based on its wavelength. To do this, the researchers placed a beamsplitter so that each of the two photons travelled along separate paths. Each photon was then passed through a phase-modulator, which acts like a time delay. Following this, the photons went through a monochromator, which allows the researchers to choose exactly what wavelength they will detect.

After this, it is just a case of looking for the number of coincidental detections as the delay and detection wavelength are changed—and this is where the interesting stuff occurs.

To understand why it's interesting, it's helpful to look at what would happen with photons that aren't entangled. If the phase modulators were off, we would expect that we would only get coincident counts when both monochromators were set to the wavelength of the laser. If we set the phase modulators going in identical fashion, then we will get coincidence counts at both the wavelength of the laser and at a small offset to each side the center wavelength, which are called sidebands.

Even if the modulators switch at the same rate, but are out of phase, these sidebands will appear, positioned precisely based on the rate at which the phase modulator is switched. (This is identical in every respect to the FM signal that your radio picks up, except at optical frequencies.)

OK, back to our entangled photons. In this case, putting the phase modulators on identical settings also creates sidebands in the coincidence counts, except that these are located at twice the switching rate of the modulators. Furthermore, if the two modulators are set out of phase with each other, so that one is advancing the phase, while the other is retarding the phase, then the coincidence counts only occur at the center frequency—the sidebands are eliminated entirely.

So lets think about that for a second: by advancing one photon in time a bit, and retarding the other in time a bit, the entanglement between them only allows the photons to have identical wavelengths. Advancing both photons in time a bit only allows them to assume colors on each side of the center wavelength that differ by twice the amount expected by classical physics.

After years of playing with quantum mechanics and sitting around trying to imagine and understand it, findings like this—even when they are simply confirming an old prediction—still leave me feeling feeble-minded. Quantum mechanics: reducing self-esteem one physicist at a time.

Physical Review Letters, 2009, DOI: 10.1103/PhysRevLett.103.163601

Listing image by Patryk Buchcik