The recently published December 21, 2007 issue of Science included a paper reporting the first experiment to observe a geometric operation on a solid state quantum bit ('qubit').
An illustrative example of how geometry induces transformation is the following. Raise your right arm above your head, with your thumb pointing left. Now bring your hand down so that it is in front of you, and then move your arm out to the right, without twisting it. Now raise your arm back above your head, and you will find that your thumb now points in a different direction, namely to the front.
During the whole process,your arm did not twist, and yet it ends up rotated! Formally speaking this little experiment deals with a vector living on the surface of a sphere and changing its position without locally changing its direction. When the vector reaches its initial position again it ends up rotated by a certain angle due to a global property of the surface that is its curvature.
For the case of a sphere, this angle turns out to be just proportional to the area enclosed by the path on the surface. Such intrinsic transformations induced by following paths through a geometric landscape are called holonomies. Corresponding effects are widespread in science with particularly important cases occurring in quantum physics, something that was first clearly pointed out by Berry only in the 1980's where the geometry dependent path reveals itself in the phase of the quantum state.
In this experiment, we observed this for the first time on a solid state qubit. This qubit is made from approximately 1 billion aluminum atoms acting in concert like a single atom and the precise control of its Hamiltonian was achieved using microwave photons. This type of qubit has also lead to the observation of the energy statistics of the microwave field, generation of single microwave photons,and coupling of two qubit by a microwave resonator.
Authors: P.J. Leek, J.M. Fink, A. Blais, R. Bianchetti, M. Göppl, J.M. Gambetta, D.I. Schuster, L. Frunzio, R.J. Schoelkopf, and A. Wallraff