Indirect Excitation Control: Ultrafast Quantum Gates for Single Atomic Qubits

Last week, John Baez posted a report on a seminar by Dzimitry Matsukevich on ion trap quantum information issues. In the middle of this, he writes:

Once our molecular ions are cold, how can we get them into specific desired states? Use a mode locked pulsed laser to drive stimulated Raman transitions.

Huh? As far as I can tell, this means “blast our molecular ion with an extremely brief pulse of light: it can then absorb a photon and emit a photon of a different energy, while itself jumping to a state of higher or lower energy.”

I saw this, and said “Hey, that’s a good topic for a blog post.” And on Friday, the new issue of Physical Review Letters included a new paper on just this topic (arxiv version for those without subscription access), making it a good topic for a ResearchBlogging post. So,

So, what’s this all about? The paper reports on a new way of moving atoms from one state to another much faster than is possible with more typical methods. This is potentially useful for speeding up the operation of a quantum computer.

Transition speeds are critically important for quantum computing, because all quantum information processing systems are subject to some interactions with the environment that will eventually destroy the quantum character of the information through the process known as “decoherence.” If you do a really good job, you can get decoherence times that are measured in seconds, which sets an upper limit on the number of operations you can do with a simple system before decoherence kills you (you can do quantum error correction to extend that, but then things start to get complicated). If you can do your state-change operations in 50 picoseconds rather than tens or hundred of microseconds, you can pack a lot more computing into that same amount of time.

And this works by making atoms absorb photons and then emit them? Right. The sort of transition they use to do these operations is called a “Raman transition” after the Indian physicist and Nobel laureate C. V. Raman who worked out some of the quantum properties of the interaction between light and atoms. A Raman transition makes use of the fact that there are three different ways for atoms to interact with photons and change states.

There are? Yes, there are. An atom in a low-energy state can absorb a photon of the appropriate energy, and use that energy to move to a higher energy state, which is just called “absorption.” An atom placed in a high-energy state will eventually drop down to a lower energy of its own accord, in the process of “spontaneous emission.” And an atom in a high energy state that encounters a photon of the appropriate energy can be induced to emit a second photon of the same energy, and drop down to a lower energy level. This last process is called “Stimulated Emission,” and accounts for the “SE” in the word “laser”, which started life as an acronym for “Light Amplification by Stimulated Emission of Radiation.”

Isn’t that kind of weird? Not really. It seems less obvious than the others to the casual observer, but it’s actually very easy to explain mathematically. You get stimulated emission very naturally from even a semi-classical model of light and atoms. Spontaneous emission is the difficult one to explain, though that’s a topic for another post.

OK, so these Raman transitions, what are they? The specific case of interest is a “stimulated Raman transition,” which is a subset of Raman transitions in general, as illustrated in this figure:

Horizontal lines indicate different states of an atom or molecule, with the energy increasing as you move up. The vertical lines indicate absorption or emission of photons. A Raman transition is one in which the atom absorbs a photon of one energy, and emits a photon of another energy, ending up in a different low-energy state than it started in.

A stimulated Raman transition is one where the downward step takes place through stimulated emission– that is, after the atom has absorbed one photon, a second photon of a slightly different frequency comes along and stimulates it to emit an identical photon, and move down to a lower energy state. You can end up in a higher state than you started by absorbing a photon of one energy, and emitting a slightly lower energy, or you can end up in a lower energy state by absorbing at one energy, and emitting at slightly higher energy. These are called “Stokes” and “anti-Stokes” processes for historical reasons that don’t really matter.

So you excite the atoms with one pulse of light, then send in a second pulse of light, and knock them back down? That’s the basic idea. It’s a little more complicated than that, though, because if you do it right, you never put the atoms in the excited state– they go up, and immediately come back down. That’s why the upper states are labeled “Virtual Energy States” in the figure– you detune the lasers so they don’t quite have enough energy to reach the excited state, but the two photons connect to the same “virtual” state at a lower energy.

You can do that? It lowers the rate at which the process happens quite a bit, but you can compensate for it by cranking up the intensity. If you use a strong enough light pulse, and a big enough detuning, you can move all the atoms from one low-energy state to another without ever occupying the excited state.

And you do this, why? Because if the atoms are ever in the excited state, there’s a probability that they can decay spontaneously, which is disastrous if you’re trying to do quantum information processing, because you have no control over where the atoms ends up in spontaneous decay.

No, I mean, why not just go directly from one low-energy state to the other? Why mess around with the upper state at all? Ah. The answer there is speed. It’s much faster to use a Raman transition in the visible or ultraviolet than to do any kind of direct excitation.

Why is that? Well, a couple of reasons. First of all, depending on the low-energy states you’re using, the transition may be “forbidden” by one rule or another– it might require a change in the angular momentum or other properties that can’t be managed with simple absorption. This means you need either really massive amounts of power, or a long time to move from one to the other.

Another reason is that the absorption process necessarily requires a time that is longer than the time for the light associated with the transition to oscillate. If you’re dealing with low-energy states like hyperfine ground states, these frequencies are in the radio frequency range, which limits you to transition times in the microseconds or many nanoseconds range. Optical frequencies are something like six orders of magnitude faster, which would let you do transitions in picoseconds.

Which is what they do here? Exactly. They take a trapped Ytterbium ion, and blast it with a picosecond pulse from a laser tuned near the transition frequency between the ground state and one of the excited states. When they arrange the frequency and polarization properly (splitting the pulse in two, and rotating the polarization of one before sending it onto the ion), they can transfer the atom from one ground state to the other (separated by 12 GHz) with a single 50 ps pulse.

That’s pretty fast. Yes, yes it is. Of course, this doesn’t mean you’ll be building a 20 GHz quantum computer any time soon– there’s a lot of other stuff that goes into a quantum computer that would require some additional time– but this shows that, in principle at least, you can do the necessary state changes extremely quickly. Which is nothing to sneeze at.

Campbell, W., Mizrahi, J., Quraishi, Q., Senko, C., Hayes, D., Hucul, D., Matsukevich, D., Maunz, P., & Monroe, C. (2010). Ultrafast Gates for Single Atomic Qubits Physical Review Letters, 105 (9) DOI: 10.1103/PhysRevLett.105.090502