Ruby NMR laser: A phenomenon of spontaneous self-organization of a nuclear spin system

Abstract

Radio wave amplification by stimulated emission of radiation (NMR laser) was observed in ${\mathrm{Al}}_2$ ${\mathrm{O}}_3$: ${\mathrm{Cr}}^{3+}$ (ruby) with the ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$ spin system pumped to an inverted Zeeman state by means of dynamic nuclear polarization (DNP) and with an LC circuit tuned to the NMR transitions. A theory is developed which combines standard Bloch equations with the dynamic equations of a heat-reservoir model for the spin dynamics. Experimental data concerning the relaxation and polarization mechanisms in the nonradiant state are presented, and the parameters of the reservoir model are determined. In accord with these results, dynamic NMR laser equations for different modes of operation (continuous or pulsed) are derived from which the threshold of the NMR laser, its critical behavior near threshold, and its transient response after $Q$-switch tuning can be calculated. The agreement between theory and experiments in the superradiant state reflects unambiguously the interplay between nuclear-spin relaxation, DNP, spin fluctuations, and the self-induced ordering of the ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$ spins perpendicular to the applied field. In particular, the results highlight the decisive role of the electronic dipole-dipole system in the spin and NMR laser dynamics of ruby. Special emphasis is placed on the close relationship between the NMR laser, as a system far from thermal equilibrium which shows the phenomenon of cooperative self-organization, and a system at thermal equilibrium which undergoes a second-order phase transition. Thus, the rotating nuclear-spin magnetization is treated as an order parameter.