We consider the spectral diffusion of a chromophore coupled through dipolar interactions to a regular lattice of flipping two-level systems. In particular, we calculate the spectral diffusion kernel, P(ω,t‖ω0), which is the conditional probability density that the chromophore will have transition frequency ω at time t, given that it had frequency ω0 at time 0. At very short times we find that the spectral diffusion kernel is Lorentzian, for any value of the two-level system excitation probability, p. For longer times the form of the spectral diffusion kernel depends on the value of p. We derive several approximate expressions for the spectral diffusion kernel, all of which go to the correct equilibrium distribution of frequencies for long times. For p≂1/2, when the frequency distribution is nearly Gaussian, we find that the spectral diffusion kernel is not at all Gaussian for short times. We compare all of our approximate expressions with numerically exact results. Motivated by certain optical spectral diffusion experiments on individual molecules in solids, we also calculate P(Δ;t), the distribution of spectral jumps, which is the probability density that the chromophore’s frequency will change by an amount Δ in time t. In a subsequent paper we will analyze these spectral diffusion experiments with our results.
The inhomogeneous broadening caused by dipole–dipole interactions between molecules having strongly allowed optical transitions is considered for the case in which the chromophores are randomly distributed at low concentration in a transparent matrix. Model calculations show that absorption in the wings of the spectrum is caused almost exclusively by strongly interacting pairs of chromophores. This result has important implications for the interpretation of recent experiments in which the spectra of single dye molecules have been observed in organic matrices. The generalized lineshape in these wings is shown to be proportional to the inverse square of the detuning from line center. The line shape is also somewhat asymmetric, with the red wing being more intense than the blue.
The present paper treats the electromagnetically induced transparency (EIT), i.e., the absorption spectrum of a weak probe field, near-resonant to a material transition, in the presence of a strong amplitude-phase fluctuating field which couples the upper level of the transition to another excited level. The coupling field is assumed to be chaotic (i.e., a complex Gaussian process with a Lorentzian spectrum) and so strong that the material relaxation and the detuning can be neglected. In addition, we consider the Fourier transform of the spectrum
Uaa(t), which determines absorption of a probe field with a time-dependent intensity. The quantity
Uaa(t) equals a diagonal element of the average reduced evolution operator of the two-level system (TLS), coupled by the strong field. As a starting point, we use the stationary, partially averaged stochastic Schr\"odinger equation, which has the form of a set of two second-order differential equations. The theory is developed by combining analytical and numerical approaches. For the most important regime, when the rms Rabi frequency
V0 is much greater than the coupling-field bandwidth $\ensuremath{\nu},$ we obtain scaling relations for the EIT line shape and the TLS evolution. In particular, the absorption at the minimum (i.e., at the resonance frequency) scales as ${\ensuremath{\nu}}^{1/3}{V}_{0}^{\ensuremath{-}4/3},$ whereas the evolution function
Uaa(t) performs damped oscillations with the decay rate on the order of ${(V}_{0}^{2}\ensuremath{\nu}{)}^{1/3}.$ These results differ significantly from those following from the uncorrelated-jump model. The results of this paper are shown to be applicable to more general models of amplitude-phase fluctuations than the Gaussian-Markovian chaotic field.
A modified theoretical model of photon echoes (PE) in low-temperature doped glasses based on the tunneling two-level system (TLS) and stochastic sudden jump models has been developed. The distinguishing feature of the model is its adaptation for Monte Carlo technique. The developed approach is more general than usual PE theories and allows us to take into account the different microscopic parameters of spectral dynamics in doped amorphous solids: in particular, the minimal radius of interaction between TLS and chromophore molecules, the dispersion of this coupling constant, and the changes of matrix properties nearby chromophore (shell-effect). The developed theory was applied for calculations of two-pulse PE decays for an organic amorphous system with typical parameters. It was found that the slope of temperature dependence of the homogeneous line width is decreased with an increase in the above-mentioned minimal radius. This effect could be one of the main reasons for the discrepancy between some PE experimental results versus calculation using standard PE theory.
We propose a density-matrix theory for the four-level system consisting of a single optical two-level system (OTLS) coupled to a single two-level system tunneling along a vibrational coordinate (VTLS). Phonons induce jumping rates of the VTLS, but coherent tunneling has to be considered explicitly as well, because the Born-Oppenheimer potential of the tunnel variable may change upon optical excitation. The OTLS is subject to spontaneous emission and driven by a laser wave with arbitrary strength. Numerical simulations for various coupling cases reproduce limiting behaviors previously discussed separately in the literature, such as motional narrowing, cross transitions, optical saturation and pumping, and nonlinear effects. Our model also perfectly fits recent measurements of the spectra of a single molecule coupled to a single tunneling system in a disordered crystal.