A Fully Quantum Mechanical Theory of Radiation Damping and the Free-Induction Decay in Magnetic Resonance

For most of its history, magnetic resonance has been described semiclassically, with spins treated by quantum mechanics and magnetic fields by classical physics. Here, we use the formalism of cavity quantum electrodynamics to give a fully quantum mechanical theory. We do not quantize the RF field directly but, instead, couple the spins to a quantized harmonic oscillator, representing the probe. This enables accurate numerical estimates of the rate of radiation damping in NMR. To facilitate these calculations, we also present a new semiclassical theory of radiation damping, rewritten using the reciprocity theory to eliminate the filling factor. Throughout we emphasize that radiation damping, usually considered a nuisance by practitioners, forms the basis for signal reception and occurs in every magnetic resonance experiment. Keywords: cavity quantum electrodynamics; quantized LC oscillator; quantum Bloch vector; photons; coherence