Relationship between a nonlinear response and relaxation induced by colored noise

The nonlinear response to external disturbances of a system of interest scrA (the ‘‘atom’’) in contact with a thermal bath is studied. The central issue is the relationship between the nonlinear susceptibility and the equilibrium relaxation spectra of observables of scrA. Paralleling the results of the linear-response theory, the nth-order nonlinear susceptibility is factorized by quantum-mechanical arguments into two terms pertaining to the disturbances and the spin-bath system, respectively. The role of slow atom states, i.e., states relaxing on times T longer than the bath correlation time ${\mathrm{\tau }}_{\mathit{c}}$, is pointed out, by recurring to recent findings on their general features [Phys. Rev. A 46, 6222 (1992)]. In the frame of a stochastic picture of the bath and a multilevel scheme of the system scrA, the conditions under which the nonlinear susceptibility provides the spectrum of the slow atom states are clarified. Illustrations are drawn from magnetic resonance to demonstrate that techniques based on the nonlinear response of a spin system to multiple continuous waves compete favorably with pulsed techniques to provide information on longitudinal spin relaxation.