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The Journal of Physical Chemistry A

Intrapulse Dynamical Effects in Multiphoton Processes: Theoretical Analysis

Jianshu Cao, Jianwei Che, Kent R. Wilson

Published Feb 20, 1998• 28 citations
Publisher

Abstract

Stationary and nonstationary multilevel models are formulated to analyze ultrafast multiphoton processes with emphasis on electronic and nuclear coherence of a near-resonant intermediate state. By identifying and characterizing three intrapulse dynamical mechanisms (sequential-resonance, chirp-following, and time-delay), a clear physical picture is developed for understanding the subtle chirp dependence in intrapulse pump−probe processes. The theoretical analysis in the paper provides not only a possible interpretation for a recent three-photon experiment but also a general theoretical framework for studying ultrafast multiphoton processes in atoms and molecules.

DOI
10.1021/jp973097t

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•Aug 1, 2010•1 citation
Stationary and nonstationary multilevel models are formulated to analyze ultrafast multiphoton processes with emphasis on electronic and nuclear coherence of a near-resonant intermediate state. By identifying and characterizing three intrapulse dynamical mechanisms (sequential-resonance, chirp-following, and time-delay), a clear physical picture is developed for understanding the subtle chirp dependence in intrapulse pump−probe processes. The theoretical analysis in the paper provides not only a possible interpretation for a recent three-photon experiment but also a general theoretical framework for studying ultrafast multiphoton processes in atoms and molecules.
Time - dependent behaviors of molecular coherence in resonant multiphotoni onization spectra of molecules are theoretically investigated . An expression for the transition probability of time-resolved two-photon ionization processes via coherently excited resonant intermediate states is derived in the perturbative density matrix formalism. Model calculations of the probability of ionization are performed to predict appearance of quantum beats in pump-probe two-photon ionization experiments. The quantum beat signals in the time-resolved ionization spectra are compared with those in time-resolved total photon emission spectra.
We develop a consistent formalism for the treatment of temporal atomic or molecular coherence in multiphoton absorption. The formalism is fully quantum mechanical under the assumption that the exciting laser fields are well described by coherent states. We make use of the language and methodology of resonance physics to the extent possible, but deliberately avoid the rotating-wave approximation, and do not restrict the allowed atomic states to be finite in number or the electric field strengths to be small in magnitude. For compactness in the presentation only electric dipole transitions are considered. As all of the transitions, both stimulated and spontaneous, are due to the activation of quantum mechanical dipoles, it is most efficient to construct the formalism so that it emphasizes the role of dipole operators, and we do this. The one strong restriction imposed here, but avoided in a following paper, is to consider only multiphoton transitions that have one resonance between initial and final states and no intermediate resonance. We describe, in effect, the time dependences associated with the early multiphoton absorption calculations of Bebb and Gold.
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.
A recently proposed collisional time-correlation function method for resonance laser–target interactions in molecular targets is modified and extended to include time-delayed multiphoton processes in the dynamics. The explicitly time-dependent laser and target dynamics in this method is separated into laser electric field and molecular target dipole/susceptibility correlation functions. The first and second order laser field correlation functions, also known as Glauber field correlation functions, are evaluated in a continuum mode description of photon number representation for both resonance and time-delayed multiphoton processes. We show that such a description allows for the incorporation of laser pulse shape and phase coherence in the formalism, while the laser–target interaction dynamics is still described similarly to the resonance single- and multiphoton processes. As an example, the transition rates for a two-photon Gaussian pump–probe dynamics are derived in which we show that the phase coherence between the Gaussian pump and probe pulses can be incorporated and controlled through a single delay-time-dependent parameter.
A review is given of experimental and theoretical achievements in studies of multiphoton spontaneous scattering processes in atomic and molecular media. An analysis is made of integral multiphoton scattering, particularly of scattering in statistically inhomogeneous media with short-range quasiorder. A study of the intensity of the noncoherent multiphoton scattering component provides direct information on the nonlinear polarizability of atoms and molecules whilst the coherent component is associated with various atomic and molecular correlation mechanisms. An analysis of the spectra of elastic and inelastic multiphoton scattering processes yields information on the translational and rotational motion of the molecules. In particular, it is possible to measure the higher-order rotational relaxation times and to verify the adequacy of the various stochastic models of molecular motion. Observations of the spectral lines of three- or more-photon scattering, which obeys new selection rules, yield detail on the fine structure of the molecules and their linear and nonlinear vibrations. Examples are given of the most interesting spectra of three- or more-photon scattering in gases, liquids, and crystals obtained in singleand multichannel systems. The stochastic theory of multiphoton scattering in liquids is discussed, using the spherical tensor concept. The derived general expression reduces to known results for certain cases.
In this thesis, we present work on coherent control of multilevelquantum systems in the strong field limit using shaped ultrafastlaser pulses. In recent years there have been numerous multiphotonabsorption experiments in two,three, and four-level atomic/molecularsystems and many are performed in the limit of weak fields whereperturbation theory is valid. Here, we describe a series ofexperiments aimed at exploring and understanding multiphotontransitions when the exciting field is strong and perturbationtheory breaks down. Our approach to strong field control utilizesboth parameterized scans of various pulse shapes and closed-looplearning control to identify a pulse shape that is optimal forpopulating a target quantum state. With this we will highlight thedifference between sequential population transfer and adiabaticrapid passage in multilevel systems with multiphoton couplingbetween levels. Additionally, we examine strong field control of afour-level atomic interferometer and show how interference in atarget state changes from resonant pathways in the frequency domainto time-domain interference via a singe path.Further, we use shaped femtosecond pulses to demonstrate aphenomenon in which a three-level atom becomes a modulator of anultrafast pulse. The results are based on a pump-probe scheme thatis very similar to Electromagnetically Induced Transparency (EIT).Important dynamics associated with a time-dependent coupling fieldare examined. Lastly, we extend previous work on two-photon drivensuperfluorescence from a shaped ultrafast drive laser and show howstimulated emission near threshold can turn modest coherent controlyields into essentially perfect discrimination between systems wherea control factor of about 104 is achieved between atomic andmolecular species.