  In NMR experiments, interaction of quantized radio-frequency (rf) field leads
to entanglement of nuclear spin with the electromagnetic field. In an entangled
state, the nuclear spins are depolarized with no net magnetization, which
cannot give a detectable signal in inductive detection. We show that when the
electromagnetic field is in coherent state, inductive detection is just true.
We develop the mathematics to study the evolution of a coherent rf-field with a
sample of all polarized spins. We show that evolution can be solved in closed
form as a separable state of rf-field and spin ensemble, where spin ensemble
evolves according to Bloch equations in an rf field. We extend the analysis and
results to a spin ensemble with Boltzmann polarization. The rabi frequency and
coupling strength of spins to rf-field depends on number state of the rf-field.
We show that in interaction with a coherent rf-field, this variation in
coupling strength, introduces negligible error.
