Coherence and Stimulated Emission in the Tavis-Cummings Model: A Quantum Description of the Free Induction Signal and Radiation Damping in Magnetic Resonance

TL;DR

This paper provides a quantum mechanical analysis of radiation damping and free induction signals in magnetic resonance using the Tavis-Cummings model, linking microscopic quantum dynamics to macroscopic NMR phenomena.

Contribution

It introduces a numerical quantum approach to model radiation damping and free induction signals, connecting quantum Rabi frequencies with classical damping constants in magnetic resonance.

Findings

Quantum description relates Rabi frequency to radiation damping constant.

Cavity losses can be incorporated via a master equation.

Numerical solutions support the quantum picture of NMR signals.

Abstract

We numerically solve the Liouville equation for the Tavis Cummings model of multiple spins coupled to a lossless single mode cavity, starting from an initial condition with small numbers of fully polarized spins tipped by a specified angle, and the cavity in its ground Fock state. Time evolution of the magnetizations and cavity states, following small to medium nutation by a classical field, yields a microscopic quantum mechanical picture of radiation damping in magnetic resonance, and the formation of the free induction signal, that is, the transfer of Zeeman energy, via spin coherence, to cavity coherence. Although the motion of the Bloch vector is nonclassical, our quantum description is related to the macroscopic picture of NMR reception, by showing the close relationship between the usual radiation damping constant, and the quantum mechanical Rabi nutation frequency (as enhanced by cavity coupling and stimulated emission.) That is, each is the product, of a nutation rate per oscillator current, and a current. Although the current in the damping constant is explicitly limited by cavity losses, which do not enter the formula for the Rabi frequency, we nonetheless show (in an appendix) how these losses can be introduced into our problem by means of a master equation. Numerical solution of the classical Bloch-Kirchhoff equations reinforces the conclusion that the strength of the free induction