A solution to Maxwell's equations in the three-dimensional frequency domain is used to calculate rephasing two-dimensional Fourier transform (2DFT) spectra of the D2 line of atomic rubidium vapor in argon buffer gas. Experimental distortions from the spatial propagation of pulses through the sample are simulated in 2DFT spectra calculated for the homogeneous Bloch line shape model. Spectral features that appear at optical densities of up to 3 are investigated. As optical density increases, absorptive and dispersive distortions start with peak shape broadening, progress to peak splitting, and ultimately result in a previously unexplored coherent transient twisting of the split peaks. In contrast to the low optical density limit, where the 2D peak shape for the Bloch model depends only on the total dephasing time, these distortions of the 2D peak shape at finite optical density vary with the waiting time and the excited state lifetime through coherent transient effects. Experiment-specific conditions are explored, demonstrating the effects of varying beam overlap within the sample and of pseudo-time domain filtering. For beam overlap starting at the sample entrance, decreasing the length of beam overlap reduces the line width along the ωτ axis but also reduces signal intensity. A pseudo-time domain filter, where signal prior to the center of the last excitation pulse is excluded from the FID-referenced 2D signal, reduces propagation distortions along the ωt axis. It is demonstrated that 2DFT rephasing spectra cannot take advantage of an excitation-detection transformation that can eliminate propagation distortions in 2DFT relaxation spectra. Finally, the high optical density experimental 2DFT spectrum of rubidium vapor in argon buffer gas [J. Phys. Chem. A 2013, 117, 6279-6287] is quantitatively compared, in line width, in depth of peak splitting, and in coherent transient peak twisting, to a simulation with optical density higher than that reported.
Optical two-dimensional coherent spectroscopy (2DCS) has become a powerful tool for studying energy-level structure, dynamics, and coupling in many systems including atomic ensembles. Various types of two-dimensional (2D) spectra, including the so-called single-quantum, zero-quantum, and double-quantum 2D spectra, of both
D lines (
D1 and
D2 transitions) of potassium (K) atoms have been reported previously. For rubidium (Rb), a major difference is that the
D lines are about 15 nm apart as opposed to only about 3 nm for K. Simultaneously exciting both
D lines of Rb atoms requires a broader laser bandwidth for the experiment. Here, we report a broadband optical 2DCS experiment in a Rb atomic vapor. A complete set of single-quantum, zero-quantum, and double-quantum 2D spectra including both
D lines of Rb atoms were obtained. The experimental spectra were reproduced by simulated 2D spectra based on the perturbation solutions to the optical Bloch equations. This work in Rb atoms complements previous 2DCS studies of K and Rb with a narrower bandwidth that covers two
D lines of K or only a single
D line of Rb. The broadband excitation enables the capability to perform double-quantum and multiquantum 2DCS of both
D lines of Rb to study many-body interactions and correlations in comparison with K atoms.
Two-dimensional Fourier-transform (2DFT) spectra of the D2 line of rubidium vapor in argon buffer gas are simulated using a three-dimensional frequency domain solution of Maxwell's equations that treats linear propagation distortions exactly. Simulations for the homogeneous optical Bloch model at optical densities of up to 3 are compared to measured rephasing 2DFT spectra. Experimentally observed propagation distortions are qualitatively reproduced in calculated 2DFT spectra, including peak broadening, peak splitting, and peak twisting. Varying beam overlap through the sample is crudely modeled in simulations, demonstrating that reduced beam overlap causes narrowing of the peak shape in the excitation dimension and an overall reduction in signal size. Propagation distortions, including peak splitting depth and peak twist, are found to vary with waiting time and with the excited state lifetime at a fixed total dephasing time, suggesting a coherent mechanism.\nA new method for reducing repetitive excitation of the sample by scanning beams with respect to a stationary sample cell using a fast steering mirror is described. This apparatus extends the average time between excitations at any point in the sample to >0.3 s and accommodates a wide variety of sample cell formats, including cryostats, air-tight cuvettes, and flow cells.\nColloidal indium arsenide (InAs) quantum dots (QDs) are interrogated by degenerate pump{ probe transient absorption spectroscopy at a photon energy of approximately 1.5 times the band gap using spatially-averaged excitation probabilities lower than in previously reported studies. Signatures of Auger recombination appear with a timescale of 26 +/- 5 ps. Carrier cooling and recombination pathways are explored, revealing new dynamics not observed in studies that probe the band edge.
Optical two-dimensional Fourier transform (2DFT) spectroscopy has been developed over the last decade as a powerful tool for studying a variety of physical systems, ranging from atoms to molecules to solids. This review covers our use of 2DFT spectroscopy to study exciton dynamics in semiconductor nanostructures. In quantum wells, 2DFT spectroscopy confirms the importance of many-body contributions to the coherent optical response and reveals nonradiative double-quantum and Raman coherences. For natural quantum dots, 2DFT spectroscopy enables ensemble measurements of the homogeneous linewidth, including the temperature and density dependence. Relaxation from quantum well states into the quantum dots can also be studied using 2DFT spectroscopy.