Quantum entanglement is probably the most confusing and confused concept in quantum mechanics. Normally, two particles can be described using separate mathematical descriptions. But, under certain circumstances, they can become mixed in such away that only a single mathematical description can accurately predict their behavior. The consequence is that these two particles, even when separated by vast amounts of space, are linked—measurements on one particle will reveal information about the other.

Entanglement is very, very delicate. As a particle bounces off of other particles, its properties are modified in an unpredictable way, which shows up as the loss of our ability to predict both the particle's behavior and that of its partner. So, entanglement is typically found in very clean systems, where particles don't interact too much. It came as something of a surprise to find a paper describing entanglement of phonons—sound waves in crystals. This implies that the mechanical motion of some 1016 atoms was entangled, which is an impressive feat.

Why call a sound wave a phonon?

In a normal crystal, the atoms are arranged in a regular structure. If you stop somewhere in a crystal and take a picture, then if you move a particular distance and take a second picture, the two pictures will match up exactly. This regular structure introduces a periodicity to the frequencies of sound waves that travel through the crystal. This is because sound waves involve the mechanical motion of the atom.

So, imagine that we freeze a sound wave in a crystal and take a look at where the atoms are. One atom happens to sit on a point where the sound wave has shifted it as far as possible from its normal location (called an anti-node). If we travel along the frozen sound wave, we will find another atom that is also at an anti-node. That atom has to occupy the same position in the crystal lattice as the first atom.

This has consequences for the frequencies of sound that can travel through the crystal. At low frequencies, the sound waves are so long compared to the crystal structure that the wavelengths for which this condition is satisfied are very closely spaced; we don't notice any issues. At short wavelengths, however, this condition restricts sound frequencies to particular values. And, in analogy to light, we can speak of minimum quanta of sound energy, which we call phonons.

Generally speaking, because phonons propagate by moving atoms back and forth, they feel their environment very strongly. Any imperfections in a crystal will scatter the phonon, reduce its amplitude, change its phase, or change its polarization. This makes it very difficult to detect coherence and entanglement between phonons. To make matters worse, most phonons have energies that are around the equivalent of the average thermal motions of the atoms. So the atoms themselves are constantly creating and absorbing phonons. All of which makes it seem a bit hopeless.

Bring on the shiny

This is where diamond comes in to play. Diamond is very hard, which means that the atoms are tightly bound to each other and don't have much freedom to move. As a result, the upper range of phonon frequencies is very high—so high, in fact, that the thermal energy of the atoms is unable to excite or absorb these phonons. If you were to go looking for entanglement in phonons, diamond is the material of choice.

But, even so, the entanglement will not last long, so it is important to excite the phonons and test them for entanglement within a few hundred femtoseconds.

The experiment that the researchers performed was really very clever. They used lasers to excite the phonons through a process called Raman scattering. Essentially, every now and again, a photon (note the t) bumps into an atom and sets it vibrating—a phonon is generated. In doing so, the photon loses exactly one phonon worth of energy. A researcher can send in pulses of light and look at the color of the output light. If it is redder than the input color, they know that a phonon has been excited. And, because the phonon and reddened photon are generated together, they share their quantum state—that is, the phonon and the photon are entangled.

To generate phonons that may be entangled, the researcher simultaneously illuminate two diamond crystals with light pulses. The scattered light is collected and filtered so that only the light that has undergone Raman scattering is left. These two light beams are mixed in a beamsplitter and sent to two light detectors. Now, there are three possibilities: no Raman scattering occurs and the detectors don't click; a phonon is generated in one crystal and one detector clicks; and one phonon is generated in each crystal, so both detectors click.

Because both light beams pass through the beamsplitter that mixes them up, we do not know which click corresponds to which photon. This mixes the photon states. If you remember, I said that the photon state was entangled with the phonon state, so the act of entangling the two photon states should also entangle the two phonon states. Even better, because we detect these photons, we know when we should have entangled phonons.

Show me the entanglement!

So far, so good. But entangled in principle is not the same as actually entangled. To detect the entangled phonons, the researchers used Raman scattering again. For detection, the photons arrive after the first pulse, when the atoms are already in motion. When a photon bounces off an atom, it can absorb a phonon-worth of energy and emerge with a bluer color. The researchers mix the two light beams in a beam splitter, and look for simultaneous detector clicks.

In this case, however, they can also delay one light beam with respect to the other to allow them to observe a periodic variation in the occurrences of simultaneous clicks.

Essentially, the researchers send in a huge number of these double light pulses—one to generate the phonons and one to detect the coherence and entanglement of the phonons. As they do so, they delay one of the pulses used for detection by a varying amount. They then go through the data and find the subset that was acquired when they know that a phonon was generated in both crystals. This data is then compared to the delay.

If the phonons are both changing coherently with respect to each other—a sign of entanglement—then you should still see simultaneous clicks if the delay is an integral number of wavelengths. If the difference is exactly half a wavelength, you should never observe simultaneous clicks. That's what they saw, which demonstrates that the phonons are coherent.

This, by itself, doesn't conclusively show that the two phonons are entangled. To go further, the researchers closely examined the polarization combinations emitted by the blue-wavelength photons. You can use quantum mechanics to calculate the ratios of the polarization states if they're entangled, and the measurements matched those. Furthermore, they estimate that the entanglement is very nearly as good as it can get, although it decays in time as the two phonons bounce around inside the diamond crystal.

How long did the entanglement last for? I don't know, because the researchers didn't measure it. The light pulses they used were 350fs apart in time, so the entanglement lasts at least that long. However, phonons in diamond can remain coherent for several picoseconds, so, in principle, the entanglement can last for around that long. However, the fact that they didn't present data with different delays between their excitation and detection pulses implies that it probably doesn't last that long in practice. But this just makes their achievement all the more remarkable.

Science, 2011, DOI: 10.1126/science.1211914