This paper contains the major results of my graduate research so far, compressed into four pages. Instead of the abstract I’m posting something closer to a layman’s explanation, which is below the fold since it got a bit long.
Flux qubits and readout device with two independent flux lines
B. L. T. Plourde, T. L. Robertson, P. A. Reichardt, T. Hime, S. Linzen, C.-E. Wu, and John Clarke
Phys. Rev. B 72, 060506(R) (2005)
Sort-of non-technical explanation: Many of the weirder effects of quantum mechanics don’t show up in macroscopic objects due to a kind of averaging out that occurs when large numbers of atoms are involved. One of these, known as coherent superposition, is the effect described in the famous Schrödinger’s Cat thought experiment. If a physical system has several possible states, mathematical combinations of these states are also available to it: so in the case of Schrödinger’s cat, the states “alive” and “dead” can be combined into coherent superpositions such as “alive” + “dead” and “alive” – “dead”, in which the cat is simultaneously alive and dead. In the case of an actual cat, however, the superposition state would disappear due to the averaging-out process I mentioned, which is referred to as decoherence. The time required for decoherence to take place for a system like a Schrödinger’s cat would be vastly shorter than any observable time.
What we did in our experiments was to build a macroscopic electrical circuit that behaved like a quantum object, with decoherence times long enough that we were able to see quantum effects. The circuit in question was a loop of aluminum, broken in three places by thin layers of aluminum oxide (which in crystal form is sapphire). The circuit was cooled to a temperature 0.04 degrees Kelvin above absolute zero, which is well below the temperature at which aluminum becomes superconducting, losing all resistance to the flow of electricity. One of the wonderful things about superconductors is that electrons condense into a single quantum state, so it becomes a much simpler system with the potential for long decoherence times. The three breaks in the aluminum loop form Josephson junctions in the superconductor, which allow us to control the electrical properties of the circuit.
In order to prove that this was really acting like a quantum object, we had to show that we could make coherent superposition states. Two basic states of the circuit are currents travelling around the loop, either clockwise or counterclockwise. By adjusting the magnetic field applied to the loop (when the field is summed over the loop this is referred to as the flux in the loop), we can make one type of current flow energetically favorable, so that currents flow in just one direction. But we can also balance the flux so that clockwise and counterclockwise currents have the same energy (this is called the degeneracy point). In that case, the system will naturally form coherent superposition states like CW + CCW and CW – CCW. It turns out that, while the CW and CCW states have the same energy, the combinations have different energies depending on whether they are added or subtracted from each other. This allows us to detect the superposition by applying microwave radiation with energy equal to the energy difference between the two states; when the circuit is in the lower energy state it will absorb the radiation and switch to the higher energy. We looked at the radiation absorbed by the circuit as the magnetic flux was varied across the degeneracy point: on a plot of radiation frequency vs. magnetic flux, an incoherent system will show straight lines going down to zero when the current flows are balanced, but a coherent system will bend away from zero frequency as it forms superposition states. Here’s what we saw:
Not only did we see the bending of the curve away from zero, we were able to measure the energy difference between the two coherent superposition states, based on the observation that the lowest radiation absorbed was at a frequency of 4 GHz. The next step was to show that we could create coherent superpositions even at points when they aren’t energetically favorable. This is done by sending short pulses of radiation, which cause the circuit to oscillate between CW and CCW current states, passing through superpositions of the two states as it does so. These are known as Rabi oscillations, and they fade away as the system loses its coherence, so this also gives us a measurement of the decoherence time. This is one of our Rabi oscillation measurements:
As you can see the oscillations
disappear in are significantly smaller after about 80 nanoseconds. We’d like this time to be a lot longer, which brings me to the question of what the purpose of all this is. This connects to quantum computing, a hot topic in physics based on the idea that computers can do certain calculations much faster if they can manipulate quantum superpositions of numbers. The basic element of a quantum computer would be a quantum bit, or “qubit”, which like a classical bit would have “0” and “1” states but could also form superpositions of these states. The circuit I’ve described here is an example of a qubit, known as a flux qubit since it uses the magnetic flux in the loop. There are a number of different approaches being investigated for quantum computing, but one advantage of using superconductors is that the qubits can be produced on a chip using existing semiconductor technology, and scaled to a system with many qubits relatively easily. Several groups around the world are currently working on flux qubits, and we are not the first to achieve results like these. Our qubit is distinct from the others in a few ways: it is quite a bit larger than other implementations, and the magnetic field is applied to it from a coil integrated onto the chip, which is important for scalability. Whether this route will be practical for quantum computation has yet to be determined, of course, but that’s more of a problem for the engineers. (Feynman would say that we are already doing engineering…)
Anyway, I hope this explanation was illuminating and/or interesting. In the past I’ve just posted the abstract, which tends to be a bunch of meaningless jargon to those outside the field.
UPDATE: I have posted a follow-up on decoherence issues here.