I’m a big fan of review articles. For those not in academic science, “review article” means a long (tens of pages) paper collecting together the important results of some field of science, and presenting an overview of the whole thing. These vary somewhat in just how specific they are– some deal with both experiment and theory, others just theoretical approaches– and some are more readable than others, but typically, they’re written in a way that somebody from outside the field can understand.
These are a great boon to lazy authors, or authors facing tight page limits (“Ref.  and references therein” takes up a lot less space than individual citations for the ten most important historical papers), and also to people who would like to get a technical introduction to a new field. They have a slight tendency to overemphasize the particular interests or results of the people writing the review, but that’s not too big a distortion, provided the authors are chosen well.
The journal Reviews of Modern Physics is primarily review articles of this type, and a recent paper there caught my eye as something worth talking about on the blog. Hence this post.
Waitaminute– do you seriously expect us to wade through 51 pages of a physics article? No, not really. Not unless you really want a thorough overview of the field. It’s more that this is an area of work that is generating some interest these days, and this article is a convenient collection of the important results. You don’t need to read the whole thing, though– you can just skim it for the good parts if you like.
All right, then. So, what do loathsome bipedal crustaceans have to do with quantum information? That’s a Zoidberg, not a Rydberg. A “Rydberg atom” is an atom in a highly excited state, very close to the ionization limit– technically, it probably ought to be “quantum information with atoms in Rydberg states,” but “Rydberg atom” is well established jargon and there’s nothing to be done about it now.
The name comes from the Rydberg formula, which was the first really good description of the emission spectrum of hydrogen, which Niels Bohr eventually showed could be interpreted as describing transitions between discrete electronic states of the atom. The Rydberg formula only works well for the low-lying states of hydrogen, because interactions between the electrons in more complicated atoms (i.e., everything else) shift all the energy states. If you take one electron and excite it to a very high level, though, the states up there start to follow something like the Rydberg formula again.
What do you mean, “very high level?” Well, the transitions in hydrogen that produce visible light are between levels with a quantum number of 3, 4, 5, or 6 and a level with a quantum number of 2. Rydberg states in other atoms have quantum numbers of 30 or more, sometimes as high as a couple hundred.
OK, that’s pretty high. What do these have to do with quantum information? Well, the idea of using Rydberg states in quantum information is to try to find a way around the somewhat contradictory requirements for a quantum computer. If you want to do quantum information processing with a reasonable number of “qubits,” you need a system that on the one hand is well insulated from the environment, so your bits don’t flip randomly, but on the other hand, you need to be able to couple the bits together strongly so that you can entangle the states of different bits. Finding systems that will give you the right balance between these two requirements is a big part of research in quantum computing.
Ground-state neutral atoms in optical lattices are one possible system, and they offer good insulation from the environment– it takes a substantial amount of energy to excite an atom from the ground state, and by definition, they don’t have anywhere to decay to, so they can have very long lifetimes. Their interactions are extremely weak, though, so it’s tricky to do entangling operations between them. You can set up situations where you can entangle the states of neighboring atoms, but this tends to be slow, and the atoms involved are generally very close together, which makes it difficult to address them individually, which is another key element of a quantum computer.
So how can exciting them to very high states help? Doesn’t that just give them lots of places to decay to? Yes and no. You do get a lot of possible decay paths, but it turns out that the lifetime of a Rydberg atom increases as you increase the quantum number– it scales like the quantum number n cubed, so if you go to high Rydberg states, the atoms will stay there a good while. More importantly, the interactions between them scale like n to the fourth power, so two atoms in Rydberg states will interact strongly while they’re separated by distances so large that neutral atoms wouldn’t notice each other at all.
Yeah, but doesn’t that just make them fall apart really quickly? It could, but the key to most of these schemes is to keep the atoms in the Rydberg state for only a short time. Basically, you use two ground states as the “0″ and “1″ states for your qubit, and use excitation to the Rydberg state as a means of entangling two nearby atoms.
How does that work? There are two main ways to do it. The simplest uses “Rydberg blockade,” which stops atoms from being excited if there’s another atom already in the Rydberg state. The interaction can be strong enough that if you have one atom already excited to the Rydberg state, and try to excite another one, the interaction between the already-existing Rydberg and the one you’re trying to create is so strong that it changes the laser frequency you would need to use, and blocks the excitation.
You can use this to do an entangling operation between a “control” qubit and a “target” qubit. First, you hit the atom serving as your control qubit with a laser that excites the “1″ state to a Rydberg level, but leaves the “0″ state alone. Then you hit the target atom with a laser pulse that should excite the “1″ state to the Rydberg level, then drive it back to the “1″ state.
If your control qubit is in the “0″ state, nothing interesting happens. If the control qubit starts out in the “1″ state, though, this stops the target from being excited, which gives the resulting wavefunction a different phase than it would’ve had otherwise. That control-dependent phase shift allows you to construct a quantum gate that entangles the states of the control and target qubits, and it turns out you can use these gates to do all of the operations you would need to do for a quantum computer.
So you entangle the two by not exciting one. That’s kinda cool. Yeah. The other method is to actually excite both, and let the interaction between them in the Rydberg state provide the entangling phase shift. This doesn’t need as strong an interaction as the blockade mechanism, but it involves more time spent in the Rydberg state, which slightly increases the chance of errors.
So, this actually works? They’re in a very early stage, but the basic idea is sound. The review article includes a nice summary of the current state of the experiments, including demonstrations of the state changes that you need to make for the quantum computing operations, and also some demonstrations of the blockade effect. The operation fidelities are nowhere near what they’d need to be for a real quantum computer– some of their key steps work about 80% of the time, rather than the 99%+ you would need to build a useful computer– but it’s an early stage, and these are cool experiments in their own right.
So, be honest now, is this going to be the killer technology needed to make a quantum computer? I wouldn’t put money on this, no. But it’s good, solid physics, and the process of doing these experiments will teach us a lot about the manipulation of atomic states and quantum information, and that’s always a good thing. There may even be particular problems for which this is the right quantum simulation approach– we’ll have to wait and see.
If you want to know what the current state of the subfield is, though, this review is a good place to look.
Saffman, M., Walker, T., & Mølmer, K. (2010). Quantum information with Rydberg atoms Reviews of Modern Physics, 82 (3), 2313-2363 DOI: 10.1103/RevModPhys.82.2313