Spin versus Boson Baths in Nonlinear Spectroscopy

The third-order optical response function of a chromophore coupled to a bath consisting of noninteracting two-level systems (TLSs) undergoing stochastic jumps is calculated. The results can be applied to a broad class of nonlinear optical techniques in single-molecule spectroscopy and bulk measurements in glasses, polymers, and mixed crystals. In the limit of many TLSs weakly coupled to the chromophore, the response can be obtained using the second-order cumulant expansion and resembles that of the Brownian oscillator model. Quantum corrections to the spectral density which accounts for the Stokes shift can be included in this limit using the fluctuation-dissipation theorem. However, the temperature dependence predicted by the two models is very different. Corrections to the cumulant expansion to fourth order in coupling strength are derived.