We report on studies of state-populations during the two-photon absorption process using intense X-ray pulses. The calculations were performed in a time-dependent manner using a simple three-level model expressed by coupled rate equations. We show that the proposed approach describes well the measured rates of X-rays excited in the one-photon and two-photon absorption processes, and allows detailed investigation of the state population dynamics during the course of the incident X-ray pulse. Finally, we demonstrate that the nonlinear interaction of X-ray pulses with atoms leads to a time-narrowing of state populations. This narrowing-effect is attributed to a quadratic incidence X-ray intensity dependence characteristic for nonlinear interactions of photons with matter.
We report on studies of state-populations during the two-photon absorption process using intense X-ray pulses. The calculations were performed in a time-dependent manner using a simple three-level model expressed by coupled rate equations. We show that the proposed approach describes well the measured rates of X-rays excited in the one-photon and two-photon absorption processes, and allows detailed investigation of the state population dynamics during the course of the incident X-ray pulse. Finally, we demonstrate that the nonlinear interaction of X-ray pulses with atoms leads to a time-narrowing of state populations. This narrowing-effect is attributed to a quadratic incidence X-ray intensity dependence characteristic for nonlinear interactions of photons with matter.
Based on five-level rate-equation theory, we develop the laser-pulse-duration dependence of two-photon-absorption-induced singlet and triplet excited-state absorptions (ESAs). We present analytical expressions for the effective three-photon absorption coefficients caused by both singlet and triplet ESAs under the pulsed excitation on time scales from femtoseconds to microseconds. We demonstrate that the triplet ESA is predominant with longer laser pulses (microseconds to tens of nanoseconds) and that the resultant nonlinear absorption (NLA) can be adequately interpreted by a simplified four-level model. Under the excitation of picosecond laser pulses, generally speaking, the competition between singlet and triplet ESAs is observable. In this instance, the photodynamics of the system can be understood by a five-level model. In the femtosecond regime, however, a three-level model is validated in the prediction of NLA, because the triplet ESA becomes negligible.
New generations of ultrashort and intense laser pulses as well ashigh power synchrotron radiation sources and x-ray free electronlasers have promoted fast developments in nonlinear optics andx-ray spectroscopy.The new experimental achievements and the appearance of varieties of novelnonlinear phenomena call for further development of theories. The objective of this thesis is to develop and apply thetheories to explain existing experimental data and to suggest new experiments. The first part of the thesis is devoted to nonlinear propagation of optical pulses. It is shown that the vibrational levels can be selectively populated by varying the duration, shape and intensity of the pump pulse. We obtained a strict analytical solution for the resonant two-photon interaction in a multilevel system beyond rotating wave approximation. Simulations show that the polarization anisotropy of the two-photon excitation affects strongly the anisotropy of photobleaching.The two-photon area theorem is reformulated with taking into account the dynamical Stark shift and the contribution from the permanent dipole moments. In general the dynamical Stark shift does not allow complete population of the excited state, but it can be compensated by detunings in atoms. A dynamical theory of the sequential two-photon absorption of microsecond pulses is developed to explore the role of transverse inhomogeneity of the light beam on optical limiting properties. The propagation of ultrashort laser pulses in nondipolar and dipolar media is investigated with special attention to the generation of superfluorescence and supercontinuum and the formation of attosecond pulses. The second part of the thesis addresses the interaction of molecules with x-ray radiation. We explore here the role of nuclear dynamics in resonant Auger scattering. Multimode simulations of the Auger spectra of ethylene molecule explain the main spectral features of the experimental spectra and show that the spectral profiles are formed mainly due to six vibrational modes. We predict the Doppler splitting of the atomic peak in resonant Auger scattering from SF6 molecule for circularly polarized x-rays. This effect is confirmed by the recent experiment. A new scheme of x-ray pump-probe spectroscopy, namely, resonant inelastic x-ray scattering accompanied by core-hole hopping induced by strong laser fields is suggested. The laser-induced promotion of core holes opens the symmetry forbidden scattering channels and gives rise to new spectral lines in the x-ray scattering spectrum. The strength of the symmetry forbidden lines becomes strong when the time of Rabi flopping is shorter than the lifetime of the core-excited state. We study the role of propagation of femtosecond x-ray free-electron pulses on the Auger process. Simulations show that there exists a strong competition between Auger decay and stimulated emission. The Auger yield and Auger branching ratio are strongly suppressed in the course of pulse propagation.
We present a detailed quantum theory and simulations of few-photon Fock state pulses interacting with a two-level system (TLS) in an open waveguide-QED system. For a rectangular pulse shape, we present an exact temporal scattering theory to derive analytical expressions for the TLS population, using one-photon and two-photon pulses, for both chiral and symmetric emitters. We also derive the stationary (long-time) and time-dependent spectra for one-photon excitation, and show how these differ at a fundamental level when considering TLS population effects. Numerically, we also present matrix product state (MPS) simulations, which allow us to compute more general photon correlation functions for arbitrary quantum pulses, and we use this approach to also show results for Gaussian quantum pulses and to confirm the accuracy of our analytical solutions. In the case of a chiral TLS, we show how a one-photon pulse, of any temporal shape, yields a transmitted long-time spectrum that is identical to the input pulse, despite significant TLS population effects. However, the dynamical spectra and spectral intensity show rich population effects, allowing for their detection in spectroscopic experiments. We also show the striking differences between one-photon and two-photon excitation, where the latter shows clear signatures of nonlinear saturation effects. In addition, we demonstrate how significant population TLS dynamics also occur for pulses that are relatively long compared to the radiative decay time (showing that a weak excitation approximation, which neglects finite TLS population effects, cannot be made) and investigate the population signatures, nonlinear features and dynamical behavior as a function of quantum pulse length.
I classify multiphoton absorption into separable, linked, and simultaneous processes. The first and second types can be distinguished when the rate-equation approximation is valid whereas the third type refers to the case when the full description of multiphoton absorption is essential. For this purpose, rate equations are solved analytically without decay processes which shows that even if many photons are absorbed the interaction with the light field is linear and one has the case of separable multiphoton absorption. Next a short-pulse approximation is investigated in which I first solve the rate equations without decay processes and then solve only rate equations for the ensuing decay. Finally, the full rate equations are examined and a successive approximation of the underlying Volterra integral equation of the second kind is derived leading to linked multiphoton absorption by the involved decay widths. The three methods are applied to a nitrogen atom in intense and ultrafast x rays from free-electron lasers (FELs). The linearity theorem barely approximates the results in the presence of decay processes which is also not satisfactorily corrected for by the short-pulse approximation. The successive approximation gives excellent agreement with the numerically-exact solution of the rate equations.
We have considered an analytical control of two-photon absorption process of atoms in the strong-field interaction regime. The experiment was performed on gaseous cesium atoms strongly interacting with a shaped laser-pulse from a femtosecond laser amplifier and a programmable pulse-shaper. When this shaped laser-pulse transfers the atomic population from the 6s ground state to the 8s excited state, we have found that both positively- and negatively-chirped laser pulses, compared with a Gaussian pulse, enhance this excitation in the strong-field regime of laser-atom interaction. This unusual phenomena is explained because the temporal shape of the laser intensity compensates the effect of dynamic Stark shift for the two-photon resonant condition to be optimally maintained. We provide analytic calculations using the strong-field phase matching, which show good agreement with the experiment.
We present and experimentally demonstrate for the first time the observation and femtosecond coherent control over the temporal evolution of a transient population that is excited via nonresonant two-photon absorption. Based on symmetry properties of the two-photon absorption process, the exciting femtosecond pulses are phase-shaped to photoinduce different evolutions of the transient excited population for a given final excited population. As a study case, we focus here on the attractive case of two-photon dark pulses that, although inducing zero final population (hence, the terminology of "dark pulses"), they induce a transient excited population during the pulse irradiation that can significantly deviate from zero. This nonzero transient population can be viewed as the bright side of such dark pulses. The symmetry-based coherent control is demonstrated first with dark pulses that we shape to induce transient excited population that at all times is kept below different target levels. Then, it is further demonstrated with pairs of dark pulses where one is rationally shaped to induce temporal evolution of the transient excited population that is the inverse of the evolution induced by the other. The work is conducted in the weak-field regime with the sodium atom as the model system. The approach developed here is general, conceptually simple, and very effective.