Spin resonance without a spin: A microwave analog

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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mi>π</a:mi> </a:math> for the waves traveling through the bonds. As a consequence, all eigenvalues appear as Kramers doublets. Detuning the length difference from the <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mi>π</b:mi> </b:math> condition Kramers degeneracy is lifted, which may be interpreted as a Zeeman splitting of a spin <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mfrac> <c:mn>1</c:mn> <c:mn>2</c:mn> </c:mfrac> </c:math> 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 radio-frequency field. This setup enables the realization of well-known NMR phenomena, such as the transformation from the laboratory to the rotating frame and the observation of Lorentzian-shaped resonance lines.