Realization of an NMR analog in a microwave network with symplectic symmetry

Abstract: In a previous paper, we realized a microwave network with symplectic symmetry simulating a spin 1/2 (Rehemanjiang et al. [Phys. Rev. Lett. 117, 064101 (2016)]), following a suggestion by Joyner et al. [Europhys. Lett. 107, 50004(2014))]. The network consisted of two identical sub-units coupled by a pair of bonds with a length difference corresponding to a phase difference of $\pi$ for the waves traveling through the bonds. In such a symmetry each eigenvalue appears as a two-fold degenerate Kramers doublet. Distorting the symmetry the degeneracy is lifted which may be interpreted in terms of the Zeeman splitting of a spin 1/2 in an external magnetic field. In the present work, a microwave analog of a spin resonance is realized. To this end, two magnetic fields have to be emulated, a static and a radio-frequency one. The static one is realized by detuning the length difference from the $\pi$ condition by means of phase shifters, the radio-frequency field by modulating the length difference of another pair of bonds by means of diodes with frequencies up to 125 MHz. Features well-known from magnetic resonance such as the transition from the laboratory to the rotating frame, and Lorentzian shaped resonance curves can thus be realized.