When modeling experimental 2D spectra, the effects of finite pulse durations are usually neglected to optimize computational costs. We present an analytic treatment of finite pulse duration effects on electronic 2D spectra. While the photon echo signal is more robust, the double quantum signal shows unexpected dependencies, based on mixing of absorptive and dispersive components. In the limit of Lorentzian pulse shapes, we compare the exact results of our analytically solvable approach to standard approximations made for finite pulse effects. We show how these approximations fail to reproduce the correct phase and amplitudes of vibrational oscillations.
When modeling experimental 2D spectra, the effects of finite pulse durations are usually neglected to optimize computational costs. We present an analytic treatment of finite pulse duration effects on electronic 2D spectra. While the photon echo signal is more robust, the double quantum signal shows unexpected dependencies, based on mixing of absorptive and dispersive components. In the limit of Lorentzian pulse shapes, we compare the exact results of our analytically solvable approach to standard approximations made for finite pulse effects. We show how these approximations fail to reproduce the correct phase and amplitudes of vibrational oscillations.
Summary form only given. A very high temporal resolution and a broad bandwidth are but two advantages provided by the use of extremely short sub-5-fs pulses in a nonlinear spectroscopic experiment. However, the applicability of the standard theoretical description becomes questionable for the pulses that consist merely of a couple of optical oscillations. Far instance, the conventionally employed slowly varying envelope approximation, implying that the change of the pulse amplitude on the duration of an optical cycle is negligible compared to the magnitude of the amplitude itself, can no longer be maintained. Furthermore, the phase-matching bandwidth that is limited due to dispersion in the nonlinear medium rapidly gains importance with the increase of the spectral width of the pulse. Another point of serious concern is the frequency-dependent variation in the sensitivity of signal photodetectors. In combination, these features result in what is known as a spectral-filter effect. Finally, artificial lengthening of the experimental transients is a direct consequence of the noncollinear geometry employed in spectroscopic experiments. We present a theoretical analysis which thoroughly reexamines the formalism of ultrafast photon echo spectroscopy. We obtain a general expression for the echo signal, which is valid even for single-cycle-pulse applications. The derived formalism is applied to photon-echo spectroscopy on the hydrated electron with 5-fs pulses.
Two-dimensional (2D) spectroscopy is a powerful pump-pump-probe technique for revealing couplings between quantum states and disentangling the different contributions to the optical response of a system. We present an efficient method for 2D spectroscopy simulations in the Markovian limit for the environment, capable of handling arbitrary pulse shapes and reproducing time-ordering and overlapping pulse effects, while maintaining a computational cost that scales linearly with the number of sampling points. We leverage this framework to investigate how 2D spectra are affected by spectral phase distortions and highly non-Gaussian pulse shapes, such as those produced experimentally by hollow-core fibers or non-collinear optical amplifiers. We show that realistic pulses can induce the appearance of additional spectral features, lineshape distortions and oscillating contributions in the system's dynamics. Notably, even weak temporal pulse tails arising from uncorrected high-order spectral phase terms cause visible changes in the 2D spectra. We also find that homodyne detection schemes employed in experiments can mitigate the presence of such pulse effects. These results emphasize the importance of including realistic pulses in 2D spectroscopy simulations to identify pulse-induced effects and minimize ambiguities in the interpretation of experimental data.
We present perturbative analytical solutions to the optical Bloch equations at third order, with finite duration Gaussian pulse envelopes. We find that a given double-sided Feynman diagram in this approximation can be conveniently described in the frequency domain as a product of the expression in the impulsive limit and a finite-pulse factor. Finite-pulse effects are Feynman-diagram-dependent, however, and include nontrivial phase corrections that can occur even in the case of transform-limited pulses. The results constitute a practical framework for modeling phenomena in multidimensional coherent spectroscopy that cannot easily be captured in the impulsive limit, including the roles of bandwidth, resonance, and pulse chirp.
In this thesis we discuss a theoretical description of ultrafast and non-linear spectroscopy. Due to the high intensities and ultrashort pulse durations involved in such experiments, it is necessary to use an explicitly time-dependent formalism. In addition, many of the systems we have considered exhibit strong interactions between the constituent particles, such as electron-electron, electron-nuclear and electron-photon interactions. To properly account for such interactions we have made extensive use of effective models, designed to capture the qualitative aspects of the systems.The thesis is based on six papers, that can be broadly categorized as follows: In Papers III and VI we study the non-linear interaction of light and matter. In Paper III we look at the multi-photon photo-emission from InAs nanowires, and in particular at the polarization dependence of the photo-emission signal on the crystal structure. In Paper VI we discuss second harmonic generation in a two-level system, and compare the fluorescence spectra from a quantum and semi-classical treatment of radiation.The remaining four papers are concerned with ultrafast dynamical processes: In Papers I and II we study atomic desorption from a surface, resulting from strong electron-nuclear interactions. To account for these interactions we consider a finite system that can be solved using exact diagonalization. We show that the desorption yield can be controlled by using a protocol with two ultrashort pulses and varying their delay. To assess finite size effects we compare the exact solution of the finite system to an approximate solution of a semi-infinite system based on non-equilibrium Green's functions and Ehrenfest dynamics. In Paper V we study Auger decay in a real-time description, and propose a protocol to induce the quantum Zeno effect by driving the system during decay. The Zeno effect leads to an increase in the Auger lifetime, that is experimentally measurable and can be controlled by varying the intensity of the driving field. In Paper IV we discuss the role of electron-electron interactions for charge-separation in donor-acceptor systems. We identify a regime where the charge-separation is driven solely by electronic correlations, that are captured by treating interactions to first order beyond a mean-field description.
We calculate the photon echo decay for a strongly coupled electron–phonon system, without making unrealistic assumptions about excitation pulse durations. We find that asymptotically, the photon echo decay is exponential, and we provide a formal expression for the decay rate 1/T2 which is independent of pulse duration. In contrast to the usual results, our expression for 1/T2 is nonperturbative in the electron–phonon interaction. We calculate the dependences of the echo amplitude on pulse power and duration, finding that the strong electron–phonon coupling modifies the simple two level system result. We also focus on the relationship between the zero phonon line shape in the homogeneous optical absorption spectrum, and the photon echo decay rate. We find that the zero phonon line shape is Lorentzian, with width 1/πT2. We show that the usual optical Bloch equation approach to analyzing time-domain experiments, which normally is only applicable if the electron–phonon coupling is weak, can be extended to the case of strong coupling. These strong coupling Bloch equations are adequate for analyzing the time dependence, but not the pulse power and duration dependences, of time-domain experiments. Our results indicate that within the Condon approximation, electron–phonon coupling cannot explain the very low temperature anomaly of recent photon echo experiments on impurities in molecular crystals.
The nonperturbative approach to the calculation of nonlinear optical spectra of Seidner et al. [J. Chem. Phys. 103, 3998 (1995)] is extended to describe four-wave mixing experiments. The system-field interaction is treated nonperturbatively in the semiclassical dipole approximation, enabling a calculation of third order nonlinear spectroscopic signals directly from molecular dynamics and an efficient modeling of multilevel systems exhibiting relaxation and transfer phenomena. The method, coupled with the treatment of dynamics within the Bloch model, is illustrated by calculations of the two-dimensional three-pulse photon echo spectra of a simple model system-a two-electronic-level molecule. The nonperturbative calculations reproduce well-known results obtained by perturbative methods. Technical limitations of the nonperturbative approach in dealing with a dynamic inhomogeneity are discussed, and possible solutions are suggested. An application of the approach to an excitonically coupled dimer system with emphasis on the manifestation of complex exciton dynamics in two-dimensional optical spectra is presented in paper II Pisliakov et al. [J. Chem. Phys. 124, 234505 (2006), following paper].