Nonlinear Spectroscopy:Characterizing Fluctuations Andrei Tokmakoff MIT Department of Chemistry 2009
System-Bath Interactions • System: Spectroscopically Bright States • Bath: Dark States • → Energy Gap Fluctuations • In spectroscopy … (Condon Approx.)
Energy Gap Fluctuations • Energy Gap Correlation Function • Dipole Correlation Function → Absorption lineshape • Second Cumulant approx.
A bath of arbitrary form • Spectral Density • Brownian Oscillator Model
Nonlinear response for fluctuating system • Following earlier approach: • Cumulant approximation:
Two pulse echo ~1/D
Correlated Energy Fluctuations Frequency Auto- and Cross-Correlation Functions: