Abstract

Previous studies of the ruby nuclear magnetic resonance laser¹ have relied on a model of the system in which the ²⁷AI nucleus is treated as a spin-½ (two-level) system. The semiclassical model which results is reducible to two equations and so requires signal injection or modulation of a parameter to give chaotic behavior. A model involving a higher spin and more lasing levels may require a higher dimensional phase space and may, therefore, give chaotic behavior even in the free-running case. Our model is derived from a Hamiltonian for a spin-1 object in superimposed static and sinusoidally oscillating magnetic fields, incorporating also the simplest possible quadrupole interaction. The quadrupole splitting can be experimentally adjusted and is considered as a control parameter along with the excitation. With additional simplifications, a set of four equations of motion can be obtained. These reduce to the earlier two-equation model in the limit of zero quadrupole splitting. We have found period-doubling bifurcations of certain limit cycles leading to chaotic solutions. Further work is in progress, including removing some of the restrictions involved in the reduction to the four-equation system.

© 1987 Optical Society of America