Coherent states in Magnetic Resonance

TL;DR

This paper demonstrates that using a coherent state for the electromagnetic field in NMR experiments allows for detectable signals despite entanglement, and develops a mathematical framework for this interaction.

Contribution

It introduces a mathematical model for the evolution of a coherent rf-field with polarized spins, showing that the system remains separable and solvable in closed form.

Findings

Coherent rf-field enables detectable NMR signals despite entanglement.

The evolution of the system can be described by Bloch equations in a separable state.

Variation in coupling strength due to coherent states introduces negligible error.

Abstract

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.