It’s been a while since we’ve had any good, solid physics content here, and I feel a little guilty about that. So here’s some high-quality (I hope) physics blogging, dealing with two recent(ish) papers from Chris Monroe’s group at the University of Maryland. The first is titled “Bell Inequality Violation with Two Remote Atomic Qubits” (and a free version can be found on the Arxiv); the second is “Quantum Teleportation Between Distant Matter Qubits” (and isn’t available on the arxiv because it’s in Science, but you can get it from their web site). Both of these deal with the physics of entanglement, the “spooky action at a distance” of the famous Einstein, Podolsky, and Rosen paper.

The idea of entanglement is that two quantum systems can have their states correlated in ways that no classical system can match. If you prepare two atoms in an entangled quantum state, measuring the state of one of them instantaneously and absolutely determines the state of the other. The state of either atom prior to the measurement is indeterminate– it can be in one of two states, but is not definitely in either– but the states of the two together are correlated– if one atoms is found to be in State 1, the other will always be found in State 2, and vice versa.

Once you have that, you can use the entangled state to show conclusively that quantum mechanics is a non-local theory (that’s the “Bell Inequality” paper), or you can use the fact that the two states are entangled to transfer quantum information from one to the other, through “quantum teleportation” (the second paper). These two papers showcase the aspects of entanglement that make it just about the coolest thing in modern physics: first, the utter weirdness of non-local quantum states, and second, the fact that these non-local states can be used to do useful tricks.

Of course, before you can do either a Bell inequality experiment or a quantum teleportation experiment, you need to somehow entangle the states of two atoms. That turns out to be a tricky business, and is the main reason why we don’t see these sorts of effects all the time. The Monroe group has used a neat trick from quantum optics to entangle the states of two different ytterbium ions held in two different vacuum chambers essentially by accident. They just coax the ions into emitting photons, direct those photons onto a beamsplitter (as shown below), and 25% of the time, the ions end up with their states entangled.

The figure above is taken from Fig. 1 of the first paper linked above, and shows the two different correlation experiments that they do to demonstrate the entanglement. The left-hand part, part a), shows how they establish that the state of the ion is correlated with the light that it emits, by collecting an emitted photon into an optical fiber, measuring its polarization, and then measuring the state that the ion is in.

The key to this trick is that the basic principle of atomic physics (ions are just atoms stripped of one of their electrons) establish certain “selection rules” determining what sort of transitions those atoms can undergo, and what sort of light they absorb or emit along the way. The details are kind of technical, but the essential idea is that an atom or ion placed in a high-energy state can drop down to one of two different lower-energy states, emitting a photon in the process. Which state the atom ends up in depends on the polarization of the light emitted, so if you measure the light to have, say, vertical polarization, you know that the atom ended up in State 1, and if you measure horizontal polarization, you know that the atom ended up in State 2.

Of course, quantum mechanics complicates everything, and it turns out that prior to a measurement of the photon polarization or the atomic state, neither of those things is defined. The atom is equally likely to be in State 1 or State 2, and the photon is equally likely to be either horizontal or vertical. Until you measure one or the other, both are in an indeterminate state of both possible outcomes at the same time. When you finally measure them, they’ll always end up correlated, but until you measure them, they don’t have well-defined values.

That allows you to establish entanglement between the polarization of one photon and the state of the ion that emitted it. How does this help you establish entanglement between two different ions, though? that’s the right-hand side of the figure, part b). The trick is simple: you take two ions in two traps, collect the light from each, and direct those two photons not onto a detector, but onto a 50-50 beamsplitter that is equally likely to transmit or reflect the photons. You line the beamsplitter up so that the transmitted photons from one ion follow the same path as the reflected photons from the other (and vice versa). Then you put one detector in each of the output ports of the beamsplitter, and look for photons (without measuring their polarization).

How does this help? Well, to understand how this leads to entanglement, you need to think carefully about what happens when two photons arrive at the beamsplitter at the same time. There are four possible outcomes: both photons can go to Detector 1; both photons can go to Detector 2; both photons can reflect off the beamsplitter, giving one photon at each detector; or both photons can be transmitted through the beamsplitter, again giving one photon at each detector. You might think that these four would be equally likely, so there would be a 50% chance of detecting two photons at the same detector and a 50% chance of detecting one photon at each detector, but you’d be wrong. In fact, there’s only a 25% chance of finding one photon at each detector, and a 75% chance of finding two photons at the same detector.

This happens because of the quantum character of photons when you include the polarization. Photons are in the class of particles known as bosons, which for our purposes just means that they like to be in the same state– that is, with the same polarization, traveling in the same direction. When two photons of the same polarization hit a beamsplitter at the same instant, they will always leave together– one will be reflected, and the other transmitted. In the ion experiments done in the Monroe group, this happens half of the time.

When the two photons arriving at the beamsplitter have different polarizations, they don’t have any effect on each other, in terms of how they depart. Each photon is equally likely to be reflected or transmitted, meaning that half of the pairs of photons with different polarization will end up leaving together, while the other half split. But the photons only arrive with opposite polarizations half of the time, and the pairs with the same polarization always leave together, meaning that only one half of one half of the incoming pairs of photons will leave and fall on separate detectors.

Notice, though, that I didn’t say what the polarizations were, just that they were the same or different. The polarization might be vertical, or it might be horizontal– there’s no way to tell without measuring it, and we didn’t do anything to determine the polarization of the photons. That means that the polarization is still indeterminate– when we detect one photon at each detector, we don’t know if the photons were horizontal or vertical, but we know that the operation of the beamsplitter guarantees that they were opposite– if we had measured one to be vertical, the other would be horizontal, and vice versa. That’s an entangled state– the photons are neither definitely horizontal nor definitely vertical, but we know that they’re different.

If we back up a step, though, we know that the sources of those photons were ions, and that the state of the ions was entangled with the state of the photons– that is, if we measured Ion 1 to be in State 1, we know that the photon it emitted was vertically polarized. So the ions were entangled with the photons, and the beamsplitter entangled the two photons with each other.

This means that now the ions are entangled with each other. If we measure Ion 1 to be in State 1, we know that the photon it emitted must have been vertically polarized. But we know that the photon emitted by Ion 2 must have had the opposite polarization, which in turn means that Ion 2 must be in State 2.

So, by collecting the light emitted by two trapped ions in two different traps separated by about a meter, and letting that fall on a beamsplitter, the Monroe group can establish a quantum correlation between the state of the two ions, without the ions themselves coming in contact with one another, or exchanging photons directly. And this happens more or less by accident– they set up the experiment, let the photons fall where they may, and 25% of the time, they get entangled ions. And, more importantly, they *know* that they have entangled the two ions– when both photon detectors record a photon, they know that the ions are in opposite states, even though the exact states of the ions remain indeterminate.

This entanglement allows them to demonstrate fundamental quantum effects, first showing that the correlation between the states of the ions is stronger than can be achieved with photons of definite states (the Bell inequality measurement). The experiment is essentially the same as the Aspect experiments (described with bonus bloggy infighting!), and shows a respectable three-and-a-bit standard deviation difference from the classical prediction. They can also use this system to do quantum teleportation by preparing Ion 1 in a particular state, and then moving that state to Ion 2 using the entanglement as a resource. They successfully “teleport” the state 90% of the time, exceeding the classical limit of 2/3 by a large margin.

Of course, you may be saying to yourself “Sure, it’s cool that they can do all this with no real effort, but isn’t this accidental entanglement an awfully inefficient way to do things?” You’d be right– they only collect a small fraction of the emitted photons, and when they do get both photons, they only get the right entangled state 25% of the time, and then there are transmission losses and detector efficiencies, and all sorts of other factors. In the Bell inequality paper, they manage to produce an entangled pair once every 39 seconds or so, while in the teleportation experiment, they accomplish the teleportation about once every 12 minutes (the teleportation scheme is a lot more complicated, making the efficiency worse). They’re not exactly going to realize the full promise of quantum information processing with a millibit-per-second data transfer rate.

There are a few tricks they can pull to increase the success rate, and make the overall system more efficient. For now, though, this is just good enough for demonstrating and exploring the weirdness of quantum physics. But really, isn’t that cool enough?

(Looking at the Monroe group’s web page, I see that there’s a third paper using the same system, this one demonstrating quantum gate operations. I haven’t have a chance to read it, though. Maybe that’ll be the next ResearchBlogging post…)

Matsukevich, D., Maunz, P., Moehring, D., Olmschenk, S., & Monroe, C. (2008). Bell Inequality Violation with Two Remote Atomic Qubits Physical Review Letters, 100 (15) DOI: 10.1103/PhysRevLett.100.150404

Kim, M., & Cho, J. (2009). PHYSICS: Teleporting a Quantum State to Distant Matter Science, 323 (5913), 469-470 DOI: 10.1126/science.1169279