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.
The lifetime of two-vibron bound states in the overtone region of a one-dimensional anharmonic molecular lattice is investigated. The anharmonicity, introduced within an attractive Hubbard Hamiltonian for bosons, is responsible for the formation of bound states which belong to a finite linewidth band located below the continuum of two-vibron free states. The decay of these bound states into either bound or free states is described by considering the coupling between the vibrons and a thermal bath formed by a set of low-frequency acoustic phonons. The relaxation rate is expressed in terms of the spectral distribution of the vibron/phonon coupling and of the two-vibron Green operator which is calculated exactly by using the number states method. The behavior of the two-vibron bound states relaxation rate is analyzed with a special emphasis on the influence of the anharmonicity. It is shown that the rate exhibits two distinct regimes depending on the thermal bath dimension. When the bath dimension is equal to unity, the rate increases with the anharmonicity and the decay of the two-vibron bound states into the other bound states appears as the main contribution of the rate. By contrast, when the bath dimension is equal to 2 and 3, the rate decreases as the anharmonicity increases, indicating that the two-vibron bound states decay into the two-vibron free states continuum.
A nonperturbative treatment of the dynamical behavior of a vibronic system in a resonant, coherent, driving light field is developed. The potential energy surfaces for the vibrational motion in the electronic ground and excited state are assumed to be displaced and distorted relative to one another. A system of three integrodifferential equations is derived from the infinite set of density-matrix equations. Both approximate analytical and numerical solutions are presented for the intensity and the intensity-correlation function of the scattered light. The results are valid for arbitrary ratios of the Rabi frequency to the relaxation rates. A system with fast vibrational relaxation behaves as a two-level system. For systems with slow vibrational relaxation, the applicability of perturbation theory requires pump fields that are weaker than those of a two-level system. The Rabi oscillations occurring in a strong pump field are damped less than those of a two-level system, and the intensity substantially decreases. The long-time behavior (determined by the vibrational relaxation time) is characterized by the increase of the intensity toward its stationary value.
The spontaneous radiative decay to the ground state of an atomic system initially in the higher of two excited states, coupled in a radiationless fashion by an external field, is investigated by the method of multiple-time-scale perturbation theory. The coupled differential equations of motion for the probability amplitudes are solved to second order, while the usual secular behavior of conventional time-dependent perturbation theory is eliminated in terms of two natural time scales: a fast time scale corresponding to the reciprocal of the level transition frequency and a slower time scale associated with the inverse of the radiation linewidth. Expressions are obtained to this order for the energy shifts and decay characteristics of the excited states and the energy distribution of the final-state photons, quantities previously determined by Fourier analysis and contour integration and by the phenomenological approach of Weisskopf and Wigner. A detailed comparison of these various methods of solution includes conditions under which the present results agree to second order with the previous calculations.
This paper presents the results of a functional-integral approach to the dynamics of a two-state system coupled to a dissipative environment. It is primarily an extended account of results obtained over the last four years by the authors; while they try to provide some background for orientation, it is emphatically not intended as a comprehensive review of the literature on the subject. Its contents include (1) an exact and general prescription for the reduction, under appropriate circumstances, of the problem of a system tunneling between two wells in the presence of a dissipative environment to the "spin-boson" problem; (2) the derivation of an exact formula for the dynamics of the latter problem; (3) the demonstration that there exists a simple approximation to this exact formula which is controlled, in the sense that we can put explicit bounds on the errors incurred in it, and that for almost all regions of the parameter space these errors are either very small in the limit of interest to us (the "slow-tunneling" limit) or can themselves be evaluated with satisfactory accuracy; (4) use of these results to obtain quantitative expressions for the dynamics of the system as a function of the spectral density $J(\ensuremath{\omega})$ of its coupling to the environment. If $J(\ensuremath{\omega})$ behaves as ${\ensuremath{\omega}}^{s}$ for frequencies of the order of the tunneling frequency or smaller, the authors find for the "unbiased" case the following results: For
s<1 the system is localized at zero temperature, and at finite
T relaxes incoherently at a rate proportional to $\mathrm{exp}\ensuremath{-}{(\frac{{T}_{0}}{T})}^{1\ensuremath{-}s}$. For
s>2 it undergoes underdamped coherent oscillations for all relevant temperatures, while for
1<s<2 there is a crossover from coherent oscillation to overdamped relaxation as
T increases. Exact expressions for the oscillation and/or relaxation rates are presented in all these cases. For the "ohmic" case,
s=1, the qualitative nature of the behavior depends critically on the dimensionless coupling strength $\ensuremath{\alpha}$ as well as the temperature
T: over most of the ($\ensuremath{\alpha}$,
T) plane (including the whole region $\ensuremath{\alpha}>1$) the behavior is an incoherent relaxation at a rate proportional to ${T}^{2\ensuremath{\alpha}\ensuremath{-}1}$, but for low
T and $0<\ensuremath{\alpha}<\frac{1}{2}$ the authors predict a combination of damped coherent oscillation and incoherent background which appears to disagree with the results of all previous approximations. The case of finite bias is also discussed.
The stationary second-order spectrum of the resonance-fluorescence light from a vibronic system is studied in a nonperturbative manner. In the model used the potential energy surfaces for the vibrational motion in the electronic ground state and in the excited state are assumed to be displaced and distorted relative to each other. The calculations are performed for the case when the frequency of the driving laser field is tuned to the vibrationless electronic transition. In particular, in the high-driving-field limit the vibrationless transition exhibits a triplet structure, the sidebands being narrower and higher in comparison with the well-known two-level case. The Raman lines are shifted and split into doublets, the linewidths being determined by the electronic as well as the vibrational relaxation rates.