# Quantum Computing Candidates: Optical Lattices

Last week, I wrote about ion traps as a possible quantum computing platform, which are probably the best established of the candidate technologies. This week, I'll talk about something more speculative, but closer to my own areas of research: neutral atoms in optical lattices.

This is a newer area, which pretty much starts with a proposal in 1999. There are a bunch of different variants of the idea, and what follows will be pretty general.

What's the system? Optical lattices use the interaction between atoms and a standing wave of light to produce a periodic array of wells in which individual atoms or groups of atoms can be trapped. A one-dimensional optical lattice looks like a stack of "pancakes" of atoms, a two-dimensional lattice looks like an assortment of tubes, and a three-dimensional lattice looks like a crystal, a regular array of atoms localized at specific points in space.

These lattices can serve as a basis for quantum computing by treating each atoms in the lattice as a qubit to use in the computation.

What's the qubit? The quantum bits in this case are provided by two states of the atom. There are a whole bunch of different proposals for this, but typically, the "0" and "1" states are different sublevels of the atom. Some of the proposals use two sublevels of the same hyperfine level, others use two different hyperfine states, but as with the ion traps discussed last week, the key is just assigning two distinct atomic states as "0" and "1."

How do you manipulate the qubits? Depending on what scheme you're using, there are a couple of different ways to do this, but the basic idea is pretty similar to what you do with trapped ions: you use either lasers or microwaves to drive transitions between states in the atoms.

This issue presents one of the biggest challenges for the optical-lattice computing schemes, namely how to address specific individual bits within the lattice. The atoms in a standard optical lattice are separated by distances of something like half a wavelength of light, much smaller than can usually be resolved. You can use very long laser wavelengths to make the lattice, and ease this problem a bit, but then that poses some problems for the entangling interactions.

How do you entangle the qubits? Again, there are a bunch of proposed ways to do this, but all of them involve inducing some sort of interaction between atoms. One version is collisional-- by shifting the polarization of the beams making up the lattice, you can bring neighboring wells together into a single well. If you've chosen the "0" and "1" states properly, collisions between these two atoms can produce entanglement between the states through a "phase" added to the wavefunction. If both atoms are in the "0" state, this phase will have one value, while if both are in "1," the phase will have a different value, and that phase difference lets you produce the sort of entanglement you need for quantum computing.

Another scheme uses Rydberg states of the atoms, which are extremely highly excited states-- where we usually talk about atomic states with quantum numbers like n=1, 2, or 3, the Rydberg states have n=30-50. As a result of this high level of excitation, atoms in Rydberg states interact at much longer ranges, long enough to extend into neighboring wells of the lattice.

This lets you do entangling operations through selective excitation. The interaction between atoms in neighboring sites changes the energy needed to excite an atom to a Rydberg state, depending on the state of the atom in the next well over. You can tune your laser to a point where it ought to excite an atom from "0" to some Rydberg level, but leave atoms in "1" alone. Then you shine the same laser on the atom in the next well over. If the first atom was in "1," the second atom will be excited, but if the first atom was in "0," it's now in a Rydberg state, and the energy needed to excite the second atom is shifted, so it doesn't go anywhere. The wavefunction for the second atom picks up a phase that depends on the amount of time it spends in the Rydberg state, and as with the collisional method, this lets you produce the entanglement you need.

How do you read the result out? It's relatively easy to determine the overall state of all the atoms together, but getting the state of an individual atom in the lattice is subject to the same addressing issues mentioned in the manipulation question. The most realistic proposals for this sort of thing use long-wavelength lasers to separate the atoms by significant distances, and then image the light scattered from the atoms in the same way that the ion trap people do. It's a tricky problem, though.

Does it scale? Yes and no. It's easy to make lattices containing millions of atoms, and the operations available for entangling and manipulating those atoms in principle allow you to use all of them for computation. The problem of addressing individual bits just gets harder and harder as you add atoms, though.

What about decoherence? Given all the addressing and readout problems, you may be wondering why anybody cares about this system in the first place. The answer is decoherence. Ion traps struggle with decoherence, because ions, as charged particles, interact very strongly with any extra bits of charge nearby. Neutral atoms, on the other hand, interact only weakly with their environment, so the potential sources of decoherence aren't nearly as bad. If you choose the states involved correctly, the decoherence times involved look pretty promising, assuming the other issues can be resolved.

Summary: I have a soft spot for the lattice computation schemes, because I know and like a lot of the people involved in this work, but they're a real long shot as far as plausible systems for quantum computation go. They have some nice features, and work toward quantum information processing in these systems allows people to study a lot of really cool physics along the way, but it would require a really dramatic breakthrough to make a useful computer from this system.

If they were running for president, they would be: John Edwards. They have some nice features, and bring some interesting ideas into the discussion, but things don't quite come together the way they would need to to be a viable candidate.

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Thanks! I really appreciate these posts. I don't know much about the quantum computing field, and it's interesting to get some orientation.

Thanks again! I also really like these posts.
How many candidates are there going to be, and are there any winners?

By Jim Graber (not verified) on 29 Oct 2008 #permalink

Thank you for your detailed introduction about optical lattice according to Divincenzo's criteria. In your opinion, which kind of physical realization would be most promising for scalable quantum computation, solid state system or new kind of mechanism undiscovered??

Thanks! I really appreciate these posts. I don't know much about the quantum computing field, and it's interesting to get some orientation.