Phase-stabilized two-dimensional electronic spectroscopy.

Two-dimensional (2D) spectroscopy is a powerful technique to study nuclear and electronic correlations between different transitions or initial and final states. Here we describe in detail our development of inherently phase-stabilized 2D Fourier-transform spectroscopy for electronic transitions. A diffractive-optic setup is used to realize heterodyne-detected femtosecond four-wave mixing in a phase-matched box geometry. Wavelength tunability in the visible range is accomplished by means of a 3 kHz repetition-rate laser system and optical parametric amplification. Nonlinear signals are fully characterized by spectral interferometry. Starting from fundamental principles, we discuss the origin of phase stability and the precise calibration of excitation-pulse time delays using movable glass wedges. Automated subtraction of undesired scattering terms removes experimental artifacts. On the theoretical side, the response-function formalism is extended to describe molecules with three electronic levels, and the shape of 2D spectral features is discussed. As an example for this technique, experimental 2D spectra are shown for the dye molecule Nile Blue in acetonitrile at 595 nm, recorded for a series of population times. Simulations explore the influence of different model parameters and qualitatively reproduce the experimental results. We show that correlations between different electronically excited states can be determined from the spectra. The technique described here can be used to measure the third-order response function of complex systems covering several electronic transitions.