Proposal for detecting a single electron spin in a microwave resonator

We propose a method for detecting the presence of a single spin in a crystal by coupling it to a high-quality factor superconducting planar resonator. By confining the microwave field in the vicinity of a constriction of nanometric dimensions, the coupling constant can be as high as 5-10 kHz. This coupling affects the amplitude of the field reflected by the resonator and the integrated homodyne signal allows detection of a single spin with unit signal-tonoise ratio within few milliseconds. We further show that a stochastic master equation approach and a Bayesian analysis of the full time-dependent homodyne signal improves this figure by similar to 30% for typical parameters.