Spin resonance without a spin: A microwave analog

TL;DR

This paper demonstrates a microwave network that mimics nuclear magnetic resonance phenomena, including eigenvalue degeneracies and resonance behaviors, using symplectic symmetry and bond length modulations.

Contribution

It introduces a novel microwave analog of NMR that reproduces key quantum effects through classical wave interference and network design.

Findings

Eigenvalues appear as Kramers doublets due to symplectic symmetry.

Detuning lifts degeneracy, analogous to Zeeman splitting.

Periodic modulation emulates magnetic radiofrequency fields.

Abstract

An analog of nuclear magnetic resonance is realized in a microwave network with symplectic symmetry. The network consists of two identical subgraphs coupled by a pair of bonds with a length difference corresponding to a phase difference of $\pi$ for the waves traveling through the bonds. As a consequence all eigenvalues appear as Kramers doublets. Detuning the length difference from the $\pi$ condition Kramers degeneracy is lifted, which may be interpreted as a Zeeman splitting of a spin 1/2 in a magnetic field. The lengths of another pair of bonds are modulated periodically with frequencies of some 10 MHz by means of diodes, thus emulating a magnetic radiofrequency field. Features well-known from NMR such as the transition from the laboratory to the rotating frame, and Lorentzian shaped resonance curves can thus be realized.