1. Nonlinear Spectroscopy: Characterizing Fluctuations Andrei Tokmakoff MIT Department of Chemistry 2009

2. Fluctuations in lineshapes

3. System-Bath Interactions System: Spectroscopically Bright States Bath: Dark States → Energy Gap Fluctuations In spectroscopy … (Condon Approx.)

4. Energy Gap Fluctuations Energy Gap Correlation Function Dipole Correlation Function → Absorption lineshape Second Cumulant approx.

6. A bath of arbitrary form Spectral Density Brownian Oscillator Model

7. Nonlinear response for fluctuating system Following earlier approach: Cumulant approximation:

8. Two pulse echo ~1/ 

9. Two pulse echo

10. Lens analogy

11. Three pulse echoes: Peak shift

12. 2D Lineshapes

13. Spectral Diffusion and Waiting Time

14. Time-domain 2D Spectroscopy

15. Time-Domain: Echo shape

16. 2D IR Relaxation Experiment Probes Spectral Diffusion

17. Ellipticity

18. Correlation of Spectral Broadening

19. Correlation Effects in 2D IR Spectra

20. Correlated Energy Fluctuations Frequency Auto- and Cross-Correlation Functions: