Based on the master equation approach, an expression for the time dependent fluorescence intensity has been derived taking into account both collision effects resulting from the elastic and inelastic scattering from the heat bath and the statistical properties of the incident light. The degree of coherence for the molecular eigenstates is defined. The pure dephasing constant between the excited states attenuates the degree of coherence for the molecular eigenstates during and after the light pulse duration; on the other hand, the pure dephasing between the ground and excited states attenuates it during the pulse duration. A separable nonstationary correlation function for the incident radiation field is introduced to investigate the effects of the field coherence on the time dependent fluorescence. Model calculations of the quantum beats in the fluorescence from molecules with two levels in the excited state in the weak radiation field have been performed to demonstrate the effects of the dephasing constants and the field coherence as well as those of the population decay constants.
Based on the master equation approach, an expression for the time dependent fluorescence intensity has been derived taking into account both collision effects resulting from the elastic and inelastic scattering from the heat bath and the statistical properties of the incident light. The degree of coherence for the molecular eigenstates is defined. The pure dephasing constant between the excited states attenuates the degree of coherence for the molecular eigenstates during and after the light pulse duration; on the other hand, the pure dephasing between the ground and excited states attenuates it during the pulse duration. A separable nonstationary correlation function for the incident radiation field is introduced to investigate the effects of the field coherence on the time dependent fluorescence. Model calculations of the quantum beats in the fluorescence from molecules with two levels in the excited state in the weak radiation field have been performed to demonstrate the effects of the dephasing constants and the field coherence as well as those of the population decay constants.
We develop a theory of quantum beats in molecular fluorescence taking into account collision effects (such as pure dephasing due to elastic collision) without invoking the Markoff approximation. Model calculations of the time dependent fluorescence from molecules with two excited levels are performed in order to see how the non-Markoffian character in the collision process exerts influence upon the quantum beat pattern. It is suggested that if the pure dephasing between the excited states is a Markoffian ‘‘the degree of modulation of the beats’’ decreases exponentially with time; if it is in the static limit the degree of modulation of the beats decreases as a Gaussian function (the non-Markoffian behavior in the quantum beats). A given case can be classified as either Markoffian or non-Markoffian, depending on the relative magnitudes of the collision duration time τc, the beat frequency ω, and the coupling strength v which is characteristic of the pure dephasing process. The Markoff approximation holds only if the condition ω<v<1/τc is satisfied; the non-Markoffian behavior appears in the quantum beat pattern when ω>v, even if v2τ2c<1 .
Bath-induced coherence transfer effects on a time- and frequency-resolved resonant light scattering spectrum is theoretically investigated using the Markoff master equation. According to Eberly and Wódkiewicz, a general expression for an experimentally observable spectrum in terms of a molecular response function is derived within the density matrix formalism. To generalize our previous results of the bath-induced coherence transfer which were derived based on a displaced harmonic oscillator model [Y. Ohtsuki and Y. Fujimura, J. Chem. Phys. 91, 3903 (1989)], an eigenstate basis is used to represent a relevant system for investigating characteristics of the transfer. By the present model, we clarify the dependence of the bath-induced coherence transfer on the energy-level structure of the intermediate states associated with the transfer, i.e., energy mismatch effects. It is shown that if the energy mismatch of these states is smaller than dephasing rates, the bath-induced coherence transfer occurs resonantly. In the other cases, the energy mismatch brings about a modulation in the time evolution of the superposition state created by the bath-induced coherence transfer, which strongly diminishes the efficiency of the transfer. The resonance condition is derived analytically and is confirmed by numerical calculations of quantum beats induced by the bath-induced coherence transfer. The possibility of very rapid dephasing of a quantum beat signal which cannot be explained in terms of dephasing rates is also shown, when the transition moments have such values that give π-phase-shifted quantum beats in bath-induced fluorescence.
When a diatomic molecule is photodissociated on a singlet molecular potential energy surface to give two singlet atoms, one of which is electronically excited, the atoms are left in pure angular momentum states referred to the molecular quantization axis. Transformation of such pure states to a laboratory frame of reference gives atomic wave functions that are described as coherent superpositions of states. Application of an external magnetic field to an ensemble of excited atoms causes quantum beats, or, alternately, a Hanle effect to appear in the fluorescence emitted by the atoms. Calculations show that the interference effects are observed only for certain geometrical arrangements of the electric vector of the photodissociating radiation, the external field, and the polarization direction accepted by the fluorescence detector. The expressions for the fluorescence intensity show that the phase and modulation depth of the quantum beat can be used to determine the asymmetry parameter for recoil of the photofragments.
The response of a collision-broadened gas sample to driving coherent radiation is studied theoretically, taking into account effects of coherent excitations of two or more atoms (or molecules). In analogy to the Bloch-type master equation for one-atom coherences, describing the motion of a single atom "dressed" by the relevant (incident and detected) field modes, a master equation is derived for two-atom coherences, including an effective interaction of the Bethe-Salpeter---type, accounting for the mutual interaction of the coherently driven pair. The master equation includes also all symmetrization effects owing to resonance exchange between identical atoms, and is limited to nonreactive gas atoms (or molecules) undergoing binary collisions, including otherwise all (internal and translational) relaxation effects. The self-energy kernels are expressed in a nonperturbative fashion, in terms of binary-collision scattering amplitudes, and include renormalization effects due to coincidence of radiative couplings with the collisions (optical and radiative collisions). The concept of two-atom coherences is generalized to higher coherence ranks by constructing a hierarchy of master equations, including vertex operators that upgrade or downgrade the coherence rank, as a prelude to a diagrammatic method for calculating continuous-wave spectra. This hierarchy is compared with prevalent Agarwal-type master equations, based on the Dicke pseudospin method, and used in the study of two-level atoms.
Analytical expressions for describing the dynamics of the populations of the states of a five-level model molecule during fluorescence reflecting the quantum beats of the populations of its two excited degenerate states coupled by dynamic interaction are derived. The cases of excitation of the molecule by a short light pulse in a state with an energy higher than the energy of the degenerate states and into one of the degenerate states are considered. The populations of states are determined by solving the Schrödinger equation for the amplitudes of probability of populating the states of the composite system comprised of the molecule and a quantized radiation field. It was found that the resulting expressions satisfy the optical Bloch equations for the considered dynamics of the populations of the molecule’s states. Significant distinctions of the present results on the simulation of quantum beats from the corresponding simulation results reported in some works, performed based on different approaches, are revealed. The reasons for these differences are discussed.
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.