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.
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.
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.
We present a formalism to analyze the effects of collisions and intramolecular energy transfer and dephasing processes (
T1 and
T2 relaxation) on level-population dynamics and unimolecular decay of laser-driven gas molecules. Utilizing a Boltzmann or optical Bloch equation for the density matrix to describe laser excitation of a relaxing multilevel absorber, we develop a generalized master equation (GME) to describe the dynamics of level population evolution for multilevel absorbers having arbitrary numbers of quantum levels
N. Because the resulting level-population equations explicitly retain phase memory, the effect of complete or partial phase-coherent driving or incoherent driving by the laser field are all included within the GME solutions. The formalism provides straightforward means to calculate time-dependent solutions for arbitrary
N, where a single expression is valid on transient, post transient, approach to steady state, and steady-state time scales. We illustrate the behavior of these solutions for the special case of three- and eight-level systems, but the method is not restricted with regard to number of levels. In both this and the following paper, we use specific examples and general arguments to show that an ordinary master equation (OME) is invalid even under apparently favorable conditions including saturating field strengths. We demonstrate that, for an
N-level absorber with given coupling elements, there are
2N [or
2(N+1)] independent saturation solutions and that special conditions on the relaxation times are required to produce the ordinary equal-population solution. Explicit forms for the steady-state radiative-transition matrix $W(\ensuremath{\lambda}=0)$ are derived for arbitrary
N, and general arguments are given to show that the correct description of the dynamics given by the GME results from matrix singularities in $W(\ensuremath{\lambda}=0)$ which can never occur in an OME or similar rate equations.
Starting with the complete molecular Liouville equation and making use of the Mori–Zwanzig projection operator formalism we derive generalized rate equations which describe the collisionless dynamics of level populations in the quasicontinuum of molecular multiphoton processes. We define precisely the complete molecular information required for the description of these processes which is expressed in the form of a hierarchy of intramolecular dipole correlation functions. We then discuss the general conditions under which the equations attain the form of simple rate equations and show how the complete molecular information reduces considerably in this case to three relevant quantities per transition: an integrated Rabi frequency, a dephasing time and ratios of statistical weights of the levels.
Description of detailed temporal excitation dyanmics for coherent excitation, such as is produced by idealized laser radiation, contrasts with evaluation of rate coefficients by means of generalized Golden Rule procedures; it requires an appropriate time-dependent Schroedinger equation. When the atom undergoing excitation is also affected by incoherent processes, such as collisions, this equation no longer suffices. The Heisenberg equations, or equivalent density-matrix equations, permit treatment in which coherence and incoherence play comparable roles in the excitation dynamics. Unlike rate equations, such equations must incorporate complexities that originate in the orientation degeneracy expressed by magnetic quantum numbers. In simple cases of coherent excitation, both for single-photon and multiphoton excitation, the sublevels merely require an average of 2J+1 independent Schroedinger equations. Relaxation couples the independent equations. It has been known for some time that appropriate state-multipole operators can simplify the description of many phenomena connected with optical pumping. This memo discusses application of these multipole operators to the description of Raman (or more general multiphoton) coherent excitation. In some simple limiting cases the equations simplify, but in general one has a hierarchy of coupled multipole polarizations and coherences in place of the populations and coherences that occur as variables in nondegenerate systems. 28 refs., 4 figs.
This paper outlines new ways for separating the different channels of optical dephasing of molecules in beams. It is shown that both the population loss and the optical phase relaxation rates can be obtained under collisionless conditions (molecular beams). These dephasing rates, which measure directly the homogeneous width of the prepared resonance, can be obtained with an energy resolution of better than one part in 108. Under these conditions the solution of the density matrix equations of motion is given for effusive and nozzle beams which represent a statistically open ensemble. The results, which we applied to our recent measurements of optical T1 and T2, are discussed in different limits of power broadening, beam geometry, detector characteristics, temperature of the oven (or material container), and the transit time the molecules of different velocities spend in the laser beam. Furthermore, we indicate that the treatment of coherent transients in beams utilizing conventional Bloch equations is not valid since there is a loss of optically excited molecules. Finally, we discuss possible differences between small and large molecules when they undergo radiationless (or reactive) processes following the selective laser excitation (∼10 kHz–10 MHz).