One of the less satisfying aspects of modern physics is the increasing separation between the phenomena that we measure and the experimenter. We measure almost everything today indirectly. If we operate our lab safely, we never directly detect an electron—instead, that charge creates a tiny potential difference on an amplifier. The amplifier generates a larger current that might drive a coil that is attached to a needle on a dial.

This level of indirection is the reality of modern physics. And the alternative—passing large currents through your body—is discouraged. Yet, the desire to really see what is going on is hard to resist. This has led to an interesting publication that proposes a way to detect quantum mechanical behavior directly with the human eye.

Seeing single photons

The behavior in question is entanglement. But before getting to that, let's talk about the eye. The human visual system is a pretty poor instrument as far as optics go. The eye is actually pretty good; experiments have revealed that the rods in your eye are sensitive to single photons. The brain, however, is smart; rather than try to sort out all the noise associated with every single photon detection, it tells the rods and cones not to bother it until the light reaches a certain intensity.

You can actually model the human eye pretty well by assuming that light detection requires seven or more photons and has an efficiency of about eight percent. So, if you send a stream of 100 light pulses to your eye with each light pulse containing seven photons, you will most likely be consciously aware of eight of them.

Normally, this would not be sufficient to detect an entangled photon, because, as the name suggests, it's a single photon and falls below the threshold for detection. But you can cheat: detect the photon with a detector and use that to trigger a brighter light pulse. Unfortunately by the time the light pulse reaches the observer, the entanglement is gone. You cannot be said to have detected entanglement with your own eye.

Instead of describing entanglement generally, let's focus on the specific form of entanglement used in this new approach. If you have a single photon and reflect it off a partially reflective mirror, then you have an entangled photon. The photon could have reflected off the mirror, or it could have been transmitted by the mirror. The correct description, which is required to get the physics right, is that it has done both until we detect it.

More technically, photons always exist in something called a mode—in this case, a mode is simply a description of the spatial properties of the photon (e.g., where the hell is that photon?). Now, each mode can hold an unlimited number of photons, but we only have one here. So our entangled state is the entanglement of a mode with zero photons and a mode with a single photon. Each mode has to be treated as if it has both a single photon in it and as if it were empty.

The important thing is that we want the eye to distinguish between no photons and a single photon. With a threshold of detection of seven photons, this seems like an impossible task. What this trio of physicists has proposed is a technique that might just allow this to happen. Though to be fair, the brain still doesn't detect single photons even after the researchers' magic.

The idea is based on something called a displacement operator. Imagine that you can define a photon mode by two numbers: phase and amplitude. Now, a displacement operator will modify those two numbers by a fixed amount. Essentially, this means that you can take a mode and increase the amplitude by a factor of 100. On the face of it, this corresponds to increasing the number of photons in the mode from one to 10. But the properties of this operator are a bit funny, in that a mode with a single photon will end up with about 1.4 times as many photons as the mode with no photons in it.

The authors argue that by choosing the displacement value correctly, the human eye can distinguish between the two modes and, therefore, detect entanglement. But are the two modes still entangled at that point? After all, I could just amplify the light pulses and tell the difference, right? And amplification definitely destroys the entanglement.

Is there a difference between amplification and displacement?

These amplifiers go to 11

First, let's see if amplification would work at all. Imagine that I create an amplifier that has a gain such that it will take a single photon and amplify it to the level of ten photons. This sort of hardware has noise; although the average is ten photons, the noise will be about three photons. Still, my mode with zero photons should have no photons after amplification, right?

Wrong. Spontaneous amplification will result in light pulses with anywhere between zero and 13 photons, corresponding to the case where the amplifier spontaneously emits into the mode we are interested in and the case where it doesn't. So, sometimes you could distinguish between the two modes, but not very well. If you do the experiment, you never observe entanglement.

The displacement operator is different in that it is the interference between two optical modes: that is, we interfere our single/zero photon mode with, say, 10 photons on a beamsplitter. For an empty optical mode, the beam simply splits, and we get five on each side (below threshold). But if the mode contains a photon, then the two interfere and seven photons go in one direction and three in the other (right on the threshold of detection).

There are two important points here: first, the displacement operator does not add noise. The second is that this process turns one optical mode into another optical mode with similar but not identical properties. That's important because this is entanglement between two modes—as long as you perform the same operation on both modes, the entanglement is preserved. Instead of having entanglement between an empty mode and a mode with a single photon, you have entanglement between two modes that have differing but non-zero photon numbers.

What does this actually mean in terms of physics? Not a lot really. It's just an interesting exercise in taking something that is typically invisible and making it directly visible. It is a pity that the experiment has not been performed. However, I expect that this is a rather challenging experiment, since you need all sorts of blinding between the entanglement generator (along with the equipment that tells you an entangled photon was generated) and the observer. Furthermore, you need to somehow take into account the delayed and variable reaction time of the observer relative to more reliable electronic equipment.

Still, it's a good exercise in considering how to improve detectors that are less than perfect. Hence, it might be possible to apply these results to electronic detectors as well.

Optica, 2016, DOI: 10.1364/OPTICA.3.000473