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The Journal of Chemical Physics

Excitation with Monochromatic Light of a Vibronically Broadened Molecular Band

Juan Alberto Beswick, R. Lefèbvre, A. M. Plumejeau

Published Apr 15, 1972• 7 citations
Publisher

Abstract

This paper studies the effect of a monochromatic electromagnetic field of arbitrary strength and duration on an isolated molecule presenting the energy level scheme which is the basis for current theories of radiationless processes in the so-called statistical limit: the system is assumed to possess bands of excited levels which are due to the dilution of well separated electric dipole allowed states into a dense set of forbidden states. The frequency of the light is set approximately equal to the transition frequency of one of these bands. Two models are set up, a quantized one with a n-photons one-mode field, and a semiclassical one with an oscillating electric field. They yield identical results. Two limiting cases, termed weak field and strong field can be obtained. In the weak field case, two different steps can be distinguished: first, the excitation of the dipole allowed state; second, the selective excitation of the molecular states at resonance with the field. The strong field case corresponds to a nonlinear response characterized by a damped nutation between ground and allowed states. After a long irradiation time the molecule is left in states which are distributed according to the level scheme corresponding to the ``molecule dressed with photons''. The spontaneous emission rate after the light is switched off is found not to depend on the particular form which is obtained for the initial state. This result, which is shown to hold for more general forms of the electric field in the semiclassical treatment, is a consequence of the analytical properties of the amplitudes.

DOI
10.1063/1.1677809

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This paper studies the effect of a monochromatic electromagnetic field of arbitrary strength and duration on an isolated molecule presenting the energy level scheme which is the basis for current theories of radiationless processes in the so-called statistical limit: the system is assumed to possess bands of excited levels which are due to the dilution of well separated electric dipole allowed states into a dense set of forbidden states. The frequency of the light is set approximately equal to the transition frequency of one of these bands. Two models are set up, a quantized one with a n-photons one-mode field, and a semiclassical one with an oscillating electric field. They yield identical results. Two limiting cases, termed weak field and strong field can be obtained. In the weak field case, two different steps can be distinguished: first, the excitation of the dipole allowed state; second, the selective excitation of the molecular states at resonance with the field. The strong field case corresponds to a nonlinear response characterized by a damped nutation between ground and allowed states. After a long irradiation time the molecule is left in states which are distributed according to the level scheme corresponding to the ``molecule dressed with photons''. The spontaneous emission rate after the light is switched off is found not to depend on the particular form which is obtained for the initial state. This result, which is shown to hold for more general forms of the electric field in the semiclassical treatment, is a consequence of the analytical properties of the amplitudes.
Light scattering by isolated small and intermediate-size molecules is studied theoretically. A quantum-mechanical model is developed that treats the molecule and the radiation field on equal terms and allows a nonperturbative solution for arbitrary wave forms and field strengths. The molecular states are described in terms of a basis set of zeroth-order states chosen so as to minimize the number of excited molecular states in the laser frequency range that combines radiatively with the initial (ground) state, i.e., that act as doorways for the field. Detailed calculations are restricted to the case of a single doorway. Closed-form expressions are obtained for the frequency-resolved scattering rates and time-resolved scattering spectra, including fluorescence and Rayleigh–Raman components, for a variety of conditions, including δ(t) excitation, excitation by a Lorentzian light pulse, by a coherent train of pulses and stationary excitation. The case of nonlinear scattering by very intense pulses is also investigated. Model calculations are reported for systems of 1–3 molecular levels. It is found that in general phase relations are maintained so that the coherence survives as long as the signal.
The problem of resonant interaction between an electromagnetic radiation field and a vibronic system, such as a molecule or a localized electronphonon system, is considered. The vibronic coupling is assumed to result from displaced and distorted potential energy surfaces for the vibrational motion in the electronic quantum states involved in the resonant interaction with the radiation field. Furthermore, the vibrational energy relaxation is taken into account without assumptions about Markovian-type relaxation. In order to study correlation properties of higher than second order in the electric field strength of the light emitted a method of calculation of the expectation value of an arbitrary product combination of effective time evolution operators of the vibronic system is developed. The calculations are performed by utilizing Feynman's disentangling and operator ordering techniques and yield closed solutions in the low-temperature limit. The theory is used for studying the intensity and the normally ordered intensity correlation function of the resonance fluorescence light from a two-atom molecule excited by a relatively weak laser field, which undergoes phase fluctuations. It is shown that the vibronic coupling can give rise to an anticorrelation effect which is substantially stronger than in the case of resonance fluorescence from an atom. For the case of small vibrational damping a general formula which directly connects the asymptotic long-time behaviour of the normalized intensity correlation function with the vibrational relaxation in the molecule is deduced. It should be convenient for the determination of very small vibrational decay rates.
A mathematical modeling of the time evolution of the populations of the states of a five-level molecule during transformation of resonant monochromatic irradiation and spontaneous emission from the highest-energy state excited by a short pulse of light is performed. The formalism of the optical Bloch equations and quantum theory of radiation are applied a composite system consisting of a molecule and a quantized radiation field. The results of simulation of the evolution of the population of the states of the molecule in the case of spontaneous emission are similar for both of these two approaches, but differ significantly in the case of conversion by the molecule of monochromatic radiation. These differences are the greater, the higher the intensity of resonance Rayleigh scattering or (and) relaxed fluorescence, as a result of which the molecule returns to the initial ground state. An explanation of the nature of these differences is given.
We present a novel approach to molecular spectroscopy with light pulses of arbitrary strength and duration. The key quantity is the frequency-resolved net energy transfer dE/dω which reveals at which frequencies energy is transferred from the field to the molecule (absorption) or from the molecule to the field (stimulated emission). It is shown that dE/dω can be expressed as the Fourier transform of the cross-correlation function of the molecular polarization P(t) and the time derivative of the applied field, dℰ/dt. In this sense, it is formally equivalent to the absorption cross section under weak-field conditions which, as commonly known, can be represented as the Fourier transform of the autocorrelation function S(t). The time-dependent polarization P(t) is determined by exact integration of the time-dependent Schrödinger equation including the light-matter interaction to all orders. It is shown that under weak-field conditions the expression for dE/dω reduces to the well-known cross section formula in the time-dependent picture of spectroscopy, multiplied by the spectral intensity of the light pulse. Therefore, we consider the expression for the frequency-resolved energy transfer, which is valid for arbitrary electric fields, as the natural extension of the absorption cross section in the weak-field limit. Furthermore, dE/dω is shown to be formally equivalent to the change of the spectral intensity, ΔI(ω), of an optical pulse after transmission through a sample, the latter being derived by solving Maxwell’s equations under well-known approximations. The theory is applied to a simple one-dimensional model with two electronic states and the frequency-resolved energy transfer is investigated as a function of the field strength. For sufficiently strong fields, dE/dω exhibits transitions between essentially all vibrational levels in the ground and all states in the excited electronic manifold. The new expression distinguishes between absorption and emission and that is clearly seen in the spectra.
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.
Unquantized field calculations are extended to include the effect of an atom's field acting back upon the atom. It is shown that, in the absence of an applied field, semiclassical theory predicts that an atom will decay spontaneously from an excited state with a characteristic time equal to the reciprocal of the Einstein AAA coefficient for the transition. The theory also predicts that the frequency of the light radiated during a transition will have a small time dependence. The corresponding frequency shifts are compared with the Lamb shift in hydrogen. The derived equations are used to study the response of a many-level atom to an applied, monochromatic field. In the case of a three-level system, it is predicted that optical nutations are not just limited to the resonant transition, but are also present in the fluorescence involving the other level.