Linear and nonlinear susceptibilities of a decoherent two-level system

Abstract

The linear and nonlinear dynamical susceptibilities of a two level system are calculated as it undergoes a transition to a decoherent state. Analogously to the Glover-Tinkham-Ferrell sum rule of superconductivity, spectral weight in the linear susceptibility is continuously transferred from a finite frequency resonance to nearly zero frequency, corresponding to a broken symmetry in the thermodynamic limit. For this reason, the behavior of the present model (the Mermin model) differs significantly from the spin-boson model. The third order nonlinear susceptibility, corresponding to two-photon absorption, has an unexpected non-monotonic behavior as a function of the environmental coupling, reaching a maximum within the decoherent phase of the model. Both linear and nonlinear susceptibilities may be expressed in a universal form.