Abstract The dependence of dynamics of coherent resonant energy transfer of electronic excitation between impurity ions in condensed media on the initial conditions of the donor excitation is investigated. Their crucial role in the coherence of the energy transfer process is shown. Validity criteria of different limiting cases of the energy resonant transfer are specified taking into account initial conditions of excitation. The “excitation trapping” effect at the coherent energy transfer is also shown to be present.
Calculations made of the rates for several processes involving interactions between rare earth ions in crystals, such as resonance energy transfer, cooperative excitation transfer and cooperative optical transitions. These processes are assumed to originate from the electric multipole interactions between the ions concerned. A tensor operator method is employed in order to take account of the individual characters of the energy levels involved in the transition. Evaluation of the typical transition probability is also made on the lowest-order parity-allowed processes in nearest neighbour ions. The rates for the resonance transfer and cooperative transfer processes thus estimated are much smaller than those obtained by Miyakawa and Dexter.
We have visited the nonradiative electron transfer process between optically active ions in luminescent materials. In contrast to the earlier formulations using multipolar expansion of instantaneous coulomb interaction between electrons, we have utilized a quantum electrodynamics (QED) approach to study the process of energy transfer from an excited ion to another. Such energy transfers occur in both sensitized luminescence and cross relaxations in the excited state. We have here investigated the nonradiative energy transfer processes specifically mediated by electric dipole moment-magnetic dipole moment and magnetic electric dipole moment-magnetic dipole moment interactions using a Feynman diagrammatic method. We have shown how experimentally relevant transfer rates could be obtained using a QED formulation involving discrete energy levels and spectral line shape function for emission and absorption profiles of interactive ions. Additional features of the dependence of the energy transfer rates on the interionic distance arising from retarded interaction potential have been pointed out.
It is shown that, in general, the interaction between relaxing quantum systems and radiation is described by non-Markov transport equations for the density matrix ρ p and the relaxation matrix depends on the properties of the radiation. The usual Markov-type equations for ρ p are obtained from these equations if γτ c ≪1 and (∊ 2 +4 V 2 ) 1/2 τ c ≪1 (γ is the width of the investigated transition in a quantum system, rc is the correlation time of the perturbations causing relaxation, e is the frequency detuning, and V is the energy of the interaction between the system and the radiation field). When the second inequality is disobeyed, the relaxation process deviates strongly from the Markov type. In the case of small values of V , this results in a non-Lorentzian profile of the absorption lines characterized by a steep descent in the wings. In the range of high values of V , when 2 V τ c 1, the whole relaxation process becomes greatly modified: the dependence of the relaxation coefficients on V becomes strong and a coupling appears between the relaxations of the diagonal and the nondiagonal elements of the density matrix. This is manifested, in particular, in the saturation effect: the term describing saturation in the expression for the polarizability changes considerably and the expression for the line width loses the component due to the adiabatic (elastic) perturbation.
Attention is called to the existence of new decay modes for deep impurities in solids associated with coherence in the resonant-energy transfer between them. The theoretical decay rate
R of the two-impurity complex is of the form $R(t)={C}_{1}\mathrm{exp}(\ensuremath{-}{\ensuremath{\gamma}}_{1}t)+{C}_{2}\mathrm{exp}(\ensuremath{-}{\ensuremath{\gamma}}_{2}t)+\mathrm{exp}[\ensuremath{-}\frac{1}{2}({\ensuremath{\gamma}}_{1}+{\ensuremath{\gamma}}_{2})t]\ifmmode\times\else\texttimes\fi{}\mathrm{Re}D\mathrm{exp}(\ensuremath{-}i\ensuremath{\Delta}t)$, with
Cn, ${\ensuremath{\gamma}}_{n}$ real positive, $\ensuremath{\Delta}$ real, and
D complex. The oscillations in time
t exhibited by the third term in the expression for
R provide an experimental test for the coherence effect. The partial rate ${R}_{\ensuremath{\nu}}(t)$ for radiative decay is of the same form as the total rate
R(t). In the analysis, use is made of an analogy between the decay of the excited impurity complex and that of
K0 mesons in particle physics, where similar coherent oscillations have been observed experimentally.
Abstract The non‐resonant energy transfer at zero temperature between two interacting two‐level quantum systems in the presence of relaxation is studied by aid of the density matrix formalism in the framework of the Markoff approximation. This gives the time evolution of the four probabilities to find the system in each of the four levels owing to the fact that at the initial time, the energy is in the excited state of the donor. The results obtained lead to the Davydov and Serikov solutions for resonant transfer of energy, and to the special one for the indirect coupling between a single level and a continuous medium.