The effects of intense laser pulse trains in coupled multilevel systems (such as pure or mixed molecular crystals) are analyzed by calculating exact density matrix evolutions. It is shown that two-level approximations are inadequate. The contributions of exchange couplings, inhomogeneous broadening, permanent multipole interactions and transition multipole interactions to absorption and photon echo line shapes are calculated. The absorption line shape of 1,4-dibromonaphthalene (DBN) is shown to be predominantly an isotopic substitution effect, as our Monte Carlo results give quantitative agreement with experiment for this model. Average t-matrix approximations to the Green’s function, which have been used to propose a different mechanism for the DBN line shape are shown to be qualitatively inadequate. Dipole–dipole interactions are shown to be an important photon echo decay mechanism in mixed crystals, with the relative importance of permanent and transition multipole interactions dependent on the resonance frequency distribution. Multiple pulse trains, including multiple pulse echoes and optical multiple-quantum sequences, are shown to be capable of distinguishing different types of interactions in the molecular Hamiltonian and reducing optical density effects. Specific pulse sequences are proposed and their effects are calculated.
We numerically investigate optical dephasing from as many as 500 interacting two-level absorbers by making the semiclassical approximation on the radiation–matter interaction which includes retarded dipole–dipole coupling and superradiant coupling. We calculate the superradiant decay rate following single pulse optical excitation, the photon echo decay and the fluorescence. By carrying out an expansion to the second order in time we demonstrate a fundamental difference between the homogeneous free-induction decay and photon echo decay which is due to radiation damping. We show that an echo sequence is capable of reversing superradiant damping in some cases. Specific computations for pentacene doped mixed molecular crystals, where ‘‘domains’’ of resonant impurities are likely to exist, are presented and compared with experimental results.
Optical dephasing due to intermolecular interaction is studied for pentacence molecules introduced in naphthalene and p -terphenyl crystals by measuring the ordinary photon echo and the accumulated three-pulse echo. It is found that the reciprocal of pure dephasing time increases linearly with the guest molecule concentration at low temperature where pure dephasing is known to be temperature-independent. A new model based on virtual transfer of excitation energy, i.e. energy transfer without phonon asistance, between guest molecules is presented to interpret this dephasing process. It is shown that observed linear dependence of the line width representing pure dephasing is well interpreted by this model, and that the calculated relationship between the line width and concentration agrees with the experimental one within a factor of about two.
A method for monitoring the time development of the coherent components in a multilevel system using an observable which can measure only the relative populations in the levels is presented. Using standard density matrix formulation, expressions are obtained for the conventional and this new ’’probe’’ pulse method. For several of the more common coherence experiments, optically detected magnetic resonance of molecular excited triplet states is used to illustrate the principles. The effect of coherent averaging of relaxation terms in the spin Hamiltonian is discussed and specifically applied to excited triplet states in zero field. Finally, experimental results of coherence measurements are presented along with a detailed description of the apparatus and methods used.
A detailed theoretical analysis of optical dephasing measurements performed on complex systems, e.g., glasses, proteins, or complex crystals, is presented. Unlike simple crystals, such systems undergo dynamical processes which have a very broad rate distribution. Dynamics can occur on a variety of time scales ranging from subpicoseconds to seconds, or longer. The formalism is based on a four-point correlation-function description of line-narrowing experiments. The results of optical dephasing measurements (time domain) or linewidth measurements (frequency domain) depend on a time
TW which defines the time scale associated with the particular experimental technique. Detailed information about the rate distribution of the system's dynamics is obtained from the change in the optical dephasing rate as the experimental time scale is changed, not from the dephasing rate measured in any individual experiment. A fundamental result, which is independent of the nature of the rate distribution or the coupling to the optical center, is proven; i.e., the derivative of the optical dephasing rate with respect to
TW, the experimental time scale, is directly proportional to the Laplace transform of the fluctuation rate distribution. As examples, the formal results are applied to two types of systems, optical centers in a glass and in a complex crystal. For the crystalline system
Pr3+:
CaF2,
TW-dependent optical dephasing data from the literature are analyzed quantitatively, where previously only a qualitative description was possible.
We present a nonperturbative theory of the thermal line broadening of optical transitions due to pure dephasing by phonons. The theory extends previous perturbative results of McCumber and Sturge. The theory is applied to experimental results on mixed organic crystals and ruby. We also present a theory of dephasing at T=0 K due to interacting impurities. Our results predict a frequency dependence to 1/T2. We analyze experiments on Y2O3:Eu3+ by Macfarlane and Shelby with this theory, and are able to comment on the nature of inhomogeneous broadening in this system.