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The Journal of Chemical Physics

Temporal coherence effects in multiphoton excitation of collisionless molecules

Israel Schek, Joshua Jortner

Published Dec 1, 1984• 7 citations
Publisher

Abstract

In this paper we examine the conditions for the erosion of coherence effects in the multiphoton excitation of a collision-free sparse molecular level structure driven by a laser field, which is characterized by a stabilized amplitude and a fluctuating phase. The stochastic equations of motion for the molecule excited by a phase-diffusing laser field were solved within the framework of second-order cumulant expansion. The kinetic master equation was found to be valid for the description of the dynamics of the multiphoton excitation process provided that the correlation time of the laser phase is considerably shorter than the relevant molecular time scales and that the rate of the slow diffusion of the laser phase considerably exceeds the Rabi frequencies. We conclude that the experimental observation of the celebrated fluence dependence of the efficiency of high-order multiphoton excitation in isolated molecules may sometimes originate from the fluctuations in the laser field rather than from intramolecular vibrational energy redistribution.

DOI
10.1063/1.447512

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Sep 1, 1991•0 citations
In this paper we examine the conditions for the erosion of coherence effects in the multiphoton excitation of a collision-free sparse molecular level structure driven by a laser field, which is characterized by a stabilized amplitude and a fluctuating phase. The stochastic equations of motion for the molecule excited by a phase-diffusing laser field were solved within the framework of second-order cumulant expansion. The kinetic master equation was found to be valid for the description of the dynamics of the multiphoton excitation process provided that the correlation time of the laser phase is considerably shorter than the relevant molecular time scales and that the rate of the slow diffusion of the laser phase considerably exceeds the Rabi frequencies. We conclude that the experimental observation of the celebrated fluence dependence of the efficiency of high-order multiphoton excitation in isolated molecules may sometimes originate from the fluctuations in the laser field rather than from intramolecular vibrational energy redistribution.
Multiphoton excitation and dissociation of large molecules under collisionless conditions is discussed in terms of an intercontinuum random coupling model. The mathematical approach described in a previous paper is used to obtain the general solution for a system of consecutively coupled discrete states, quasicontinuous manifolds, and continuous (dissociative) manifolds of molecular levels (eigenstates of the total molecular Hamiltonian), where the radiative coupling matrix elements are assumed to be given as a linear combination of smoothly varying and randomly varying (over level indices in the molecular manifolds) components. In the range of discrete molecular levels the time evolution is coherent and described in terms of the optical Bloch equation. In the quasicontinuous and continuous ranges the time evolution may be described in terms of Markoffian kinetic equations for the number of photons absorbed by the molecule, provided that the intramolecular vibrational relaxation widths associated with the optically active molecular modes is much larger than the Rabi frequency associated with the excitation of these modes. The kinetic evolution itself consists of direct multiphoton excitation processes (simultaneous transitions from the upper discrete levels to all higher energy molecular manifolds) resulting from the smooth component in the radiative coupling, and a consecutive excitation process described by the Pauli master equation with rates given by the golden rule expression. The interaction which enters into the golden rule expression is the variance in the radiative coupling. The direct excitation component contributes a negligible part of the overall excitation even if the random and smooth radiative coupling components are comparable. The resulting incoherent time evolution of the multiphoton excitation process is consistent with available experimental results. Coherent effects in the time evolution are expected for higher radiation field intensities, where the Rabi frequency becomes comparable to the intramolecular vibrational relaxation rate.
The effect of stochastic laser phase fluctuations on nonlinear optical phenomena are investigated within the phase-diffusion model. Averaged equations of motion are derived in the limit of infinitely short correlation times and the results are applied to multiphoton absorption and to four-wave mixing. The effect of the stochastic phase fluctuations is shown to be equivalent to a T2{T}_{2}T2​ dephasing process, and a procedure is described for the inclusion of this equivalence in many nonlinear-optical problems. When a given mode contributes n photons to a multiphoton absorption process, its contribution to the width of the multiphoton transition is n2{n}^{2}n2 times its own stochastic width. When correlated lasers are used as the excitation sources in four-wave-mixing experiments, (new) stochastic-fluctuation-induced extra resonances in four-wave mixing (SFIER4) will be observed, in complete analogy to the extra resonances induced by collisions [pressure-induced extra resonances in form-wave mixing (PIER4)].
In this paper we present a quantum mechanical theory of multiphoton photodissociation of large, collision-free, molecules, which rests on the notion that the radiative coupling terms between adjacent sets of congested bound molecular states in the quasicontinuum exhibit a wide variation both in terms of magnitude and of sign. Invoking the rotating-wave approximation, neglecting spontaneous infrared decay, and assuming that near-resonant radiative coupling prevails, the equations of motion were solved within the framework of the random radiative coupling model for the radiative interactions in the quasicontinuum. In the low energy range (range I) the equations of motion for the amplitudes are determined by the effective Hamiltonian formalism, while in the quasicontinuum (range II) the populations are governed by kinetic equations for sequential reversible decay. All the features of coherent excitation are preserved for range I, while in range II intramolecular erosion of phase coherence effects prevails. This model provides a set of reasonable predictions.
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.
The effect of amplitude and phase fluctuations on N-photon excitation from N independent lasers is investigated. Each laser is assumed to have a multi-lorentzian line shape. The Fokker-Planck equation is solved to yield atomic density matrix equations which incorporate the fluctuations. Most of the results discussed are for the lowest-order approximation. No enhancement in the Rabi frequency or transition probability appears, but the Stark shift is found to be enhanced by a factor which is independent of the degree of non-linearity of the process. A general expression for the transition probability in the rate equation regime is presented and its characteristic features discussed. The difference between N-photon excitation from N independent lasers and from a single laser is examined.
Using a semiclassical, effective-state approach to laser pulse propagation in a dilute gas of polyatomic molecules, a numerical model of multiphoton excitation which includes quasi- continuum transitions is used to calculate the effects of coherent propagation on multi-photon absorption. The initial laser field is assumed to be a quasimonochromatic Gaussian envelope which is nearly resonant with a portion of the lower vibrational states of the molecule. The molecular model consists of a single ground state and several bands of discrete states which are successively connected via electric dipole transitions. This model correctly mimics some of the major characteristics of multiphoton absorption, such as power threshold, fluence dependent absorption, and complete population inversion at high fluences. The model also allows for the calculation of the polarization induced in the medium by the electric field, and the subsequent influence that the polarization has on the field. As the pulse propagates, the Rabi oscillations induced in the lower level states become encoded onto the pulse, creating a series of peaks and troughs similar to the behavior of pulse propagation in two-level systems. Another coherent propagation effect which can change the excitation process is coherent sideband generation. The temporal distortions and the generation of new frequencies results in changes in the population distribution among the states, as well as changes in the total population transferred to the quasi-continuum. The pulse reshaping occurs while the total fluence of the pulse is decreasing due to energy loss to the quasi-continuum. The effective increase in total population transfer due to propagation effects is offset by the decrease in fluence. The resulting transfer of energy from the pulse to the molecule depends strongly on the initial characteristic of the pulse. These processes play an important role in any system where the efficient transfer of laser energy to the medium is required, such as laser-induced chemistry and laser isotope separation.