Probing and manipulating quantum states near an avoided level crossing in an isolated spin system.

We propose to use radio frequency manipulation to excite and manipulate the state population at an avoided level crossing. We can measure the isolated susceptibility in LiHo1-xYxF4 using transverse field diamagnetic muons, where the isolated susceptibility is a superposed quantum state of the Ho spin state at an avoided level crossing. Subsequently we will use diamagnetic muons to measure directly the decoherence of this quantum state. This will demonstrate that diamagnetic muons combined with state manipulation can identify and measure quantum coherent states in bulk systems.