Mechanisms of intermolecular dephasings revealed in the time-resolved coherent anti-Stokes Raman scattering (CARS) spectra of a molecular ensemble are theoretically studied by deriving the microscopical expression for the scattered photon intensity averaged over the heat-bath variables. The intermolecular dephasing means the decay of the intermolecular coherence created by the pumping process, i.e., a linear combination of the vibrational Raman transitions of the molecules at different sites. The intensity of the time-resolved CARS is expressed in terms of time-development matrix elements of the intermolecular coherence. An equation of motion for the intermolecular coherence is derived by using the projection operator method. The structure of the intermolecular-dephasing constant is clarified. The intermolecular-dephasing constant consists of the sum of population decay constants and the intermolecular pure dephasing constant that originates from an elastic interaction between the relevant molecules and a common heat-bath mode. The intermolecular pure dephasing constant is expressed in terms of the intramolecular pure dephasing constants and destructive interference of the intramolecular pure dephasings between the relevant two molecules. The intermolecular-dephasing constant is expressed as the sum of the intramolecular-dephasing constants of the relevant molecules when there is no common heat-bath mode. Inhomogeneous effects on the time-resolved CARS spectra are also investigated. A degree of the structural order is introduced to qualitatively express the inhomogeneity of local structures in the molecular ensemble. The microscopic expression derived in this paper has taken into account both incoherent and coherent optical processes in the thermally distributed molecular ensemble.
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.
A theory is developed to describe the effect of simultaneously occurring vibrational relaxation on intermolecular excitation transfer in the presence of radiative and nonradiative sinks. The basis is a master equation whose rates are combinations of the F\"orster-Dexter transfer rates and the Montroll-Shuler relaxation rates. Exact solutions are obtained for the probabilities of occupation of single vibrational levels as well as of site occupation, and for quantum yields and differential photon count rates. It is shown how phenomena exhibiting dependence of quantum yields or similar quantities on the wavelength of initial excitation can be quantitatively approached with the help of this analysis. The concept of time-dependent transfer rates is developed, and it is shown that at long times the transfer rate could tend to a value different from the thermalized F\"orster-Dexter rate. It is also shown how the relaxation process can result in an effective transfer rate (for singlets) whose dependence on the intermolecular distance
R is other than ${R}^{\ensuremath{-}6}$.
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.
We have developed a full quantum microscopic theory to analyze the time evolution of transversal and longitudinal components of an exciton-single photon system coupled to bulk acoustic phonons. These components are subjected to two decay processes. One is radiative relaxation and the other is pure dephasing due to exciton-phonon interaction. The former results in a decay with an exponent linear to time, while the latter causes a faster initial decay than the radiative decay. We analyzed the dependence of the components on the duration of the input one-photon pulse, temperature, and radiative relaxation rates. Such a quantitative analysis is important for the developments of atom-photon interfaces which enable coherent transfer of quantum information between photons and atomic systems. We found that, for a GaAs spherical quantum dot in which the exciton interacts with bulk phonons, the maximal probability of the excited state can be increased up to 75%. This probability can be considered as the efficiency for quantum information transfer from photon to exciton.
One of the most pertinent problems in the debate on non-trivial quantum effects in biology concerns natural photosynthesis. Since sunlight is composed of thermal photons, it was argued to be unable to induce quantum coherence in matter, and that quantum mechanics is therefore irrelevant for the dynamical processes following photoabsorption. Our present analysis of a toy 'molecular aggregate'—composed of two dipole–dipole interacting two-level atoms treated as an open quantum system—however shows that incoherent excitations indeed can trigger persistent, coherent dynamics in both the site and the exciton bases: we demonstrate that collective decay processes induced by the dipole–dipole interactions create coherent intermolecular transport—regardless of the coherence properties of the incoming radiation. Our analysis shows that the steady state coherence is mediated by the population imbalance between the molecules and, therefore, increases with the energy difference between the two-level atoms. Our results establish the importance of collective decay processes in the study of ultrafast photophysics, and especially their potential role to generate stationary coherence in incoherently driven quantum transport.