Electric NMR

Electric Dipole Echoes in Rydberg Atoms

S. Yoshida, et al.

PRL 98, 203004 (2007)

URL: http://link.aps.org/abstract/PRL/v98/e203004


This group from Rice has demonstrated the electric analog of spin echoes.

In NMR, spins precess around an applied magnetic field. Due to local variations in the magnetic field, not all spins precess at the same rate. However, one can apply a pulse that flips every spin in the sample, and all the spins basically reverse their motion. If the spins start precessing at t=0 and the flipping pulse (a pi-pulse) is applied at t=T, then at t=2T, all the spins will be right back where they started, even though they were precessing at different rates! The large magnetic moment of the sample at t=2T is called a spin echo. Effects like collisions, diffusion, thermal excitations, and other interactions prevent the system from returning to its exact initial configuration, but the echo can be detected after rather long delays.

So what does this have to do with electric dipoles? I learned that to first order in the applied field, the equation of motion for the electric dipole also describes precession. That's not exactly true --- the thing that actually precesses is a pseudospin comprised of the orbital angular momentum and something called the Runge-Lenz vector, which is proportional to the electric dipole moment. The difference of two pseudospins gives the Runge-Lenz vector. The authors say this is true of a classical dipole as well as the quantum theory.

One major difference between NMR and the experiment described here is that electric dipoles oscillate much more rapidly than magnetic dipoles. To make the relevant time scale as long as possible, the use Rydberg atoms --- potassium atoms in the n=350 level.

When they performed the experiment, the authors observed a marked increase of the survival probability when a flipping pulse was applied, in contrast with the exponential decay observed without the flipping pulse.

Another difficulty of this experiment versus NMR is the effect of the environment. Couplings to and interactions with spurious electric fields in the environment lead to much more rapid decoherence in the Rydberg gas than in a typical NMR sample. The authors point out that this is not necessarily a bad thing: dipole echoes could prove to be a useful tool in studying decoherence.