Since an electron is a tiny magnet, every two electrons should exert torques on one another - as magnets do.
This fundamental interaction, however, was not observed at the atomic scale, since there it is overwhelmed by the much stronger Coloumb exchange forces. At distances greater than the atomic scale, the energy, scaling as 1/r^3, is typically smaller than the effect of magnetic field noise fluctuations.
By co-trapping two Sr^+ ions, we were able to measure the magnetic spin-spin interaction between their valence electrons. The ions were separated by 2-3 microns, resulting in a ~ milihertz interaction. Each experiment was ~15 seconds long, during which spin-spin entanglement was measured. By varying the distance between the ions, we were able to recover the 1/r^3 dependence of the interaction.
The experiment was made possible by a set of capabilities/understandings we developed in the past 3 years :
1) Measurement of a signal within a Decoherence Free Subspace.
2) Quantum Lock-in of weak signals.
3) Improved detection for long (>10 sec) experiments.
4) Single ion preparation and manipulation.
I will try to give an overview of these efforts as well as discuss the fundamental aspects of e-e measurement.