We show that a fundamental assumption used in analyzing photon echo decays from interacting molecules—the assumption that the ‘‘pure’’ dephasing rate can be obtained by subtracting one half of the fluorescence decay rate (2T1)−1 from the photon echo decay rate—is generally inconsistent with a fully quantum mechanical treatment. The density matrix evolution for a system of noninteracting dimers is calculated using the retarded electromagnetic coupling between two oscillating dipoles. We are able to properly include the effects of spontaneous emission and Dicke superradiance on the echo decay.
We show that a fundamental assumption used in analyzing photon echo decays from interacting molecules—the assumption that the ‘‘pure’’ dephasing rate can be obtained by subtracting one half of the fluorescence decay rate (2T1)−1 from the photon echo decay rate—is generally inconsistent with a fully quantum mechanical treatment. The density matrix evolution for a system of noninteracting dimers is calculated using the retarded electromagnetic coupling between two oscillating dipoles. We are able to properly include the effects of spontaneous emission and Dicke superradiance on the echo decay.
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.
We present the theory of the photon echo and stimulated photon echo from a four level system that results from a pair of weakly coupled two level systems. This model describes an impurity dimer in a molecular crystal. We include the effect of relaxation processes, focusing on energy transfer between delocalized states. We find that both the photon and stimulated echoes contain information about static level splittings and dynamic energy transfer processes. Moreover, these observables show a dramatic dependence on the excitation power. We discuss implications of our results for recent experiments on concentration dependent dephasing of impurities in molecular crystals. Our analysis casts considerable doubt on the intermolecular interaction interpretation of these experiments.
In this paper we investigate the influence of optical density or superradiance on the photon echo decay using the coupled Maxwell–Bloch equations. Our theory applies to optically thick but dilute media, where the transition dipole–dipole interaction between nearby chromophores is negligible, but the far-field interaction is not. Corrections to the (normalized) echo decay in the optically thin limit, INe(tπ)=exp [−4tπ/T2] (tπ and T2 are the interpulse separation times and the coherence relaxation times, respectively), are found by expanding the polarization, excited state population and pulse electric fields in powers of ζ=αz, where α is the inverse Beer’s absorption length, and z is the coordinate along the pulse propagation axis. Numerical solutions for optically thick samples are also presented, and when ζ≫1 the normalized echo intensity is found to obey the simple analytic form: INe(tπ)=2 exp [−tπ/T1]−1, when tπ/T1<ln 2 and INe(tπ)=0 for longer times. (T1 is the population relaxation time.) In this limit the echo decay is independent of the coherence relaxation time T2, illustrating the profound effect intermolecular coupling may have on any nonlinear optical measurement. We show that at low temperatures, when T2=2T1, the echo decay rate increases as the optical density increases. However, for higher temperatures, when T2 is sufficiently shorter than 2T1, the opposite behavior results, that is, the echo decay rate decreases as the optical density increases.
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.
For a crystal with both diagonal disorder (inhomogeneous broadening) and substitutional disorder we have calculated the contribution to the photon echo decay due to purely electronic intersite interactions. We have considered the two important limiting cases of macroscopic and microscopic inhomogeneous broadening. In the case of macroscopic broadening we find that the optical dephasing rate constant 1/T2∼f J, where f is the fractional concentration of impurities and J is the nearest-neighbor intersite interaction in frequency units. This result is valid for f≪1. In the opposite limit of microscopic inhomogeneous broadening, we find that 1/T2∼f J2/δ̄, where δ̄ is the width in frequency units of the inhomogeneous distribution. This result is valid for arbitrary f, including f=1, and for J≪δ̄. In the case that f≪1 and J≪δ̄, 1/T2 is much smaller for microscopic broadening than for macroscopic broadening. We discuss our results in relation to several experiments on mixed molecular crystals and to an experiment on the stoichiometric material EuP5O14.
Spontaneous decay is a phenomenon that has been described for the first time by Dirac, Wigner
and Weisskopf, at the early ages of the development of quantum electrodynamics. The theory is
applicable to a multi-body system only when atoms don’t interact during their decay. Dicke introduces
in his seminal paper the case where this assumption doesn’t hold.
The results he obtains not only tell that the system emits pulses, but the pulse duration now depends
on 1/N, where N is the number of participating atoms to the process. The pulses temporal profile
is described by a squared hyperbolic secant function. The resulting emission intensity scales as N^2.
The atomic system radiates more intensively than the ordinary fluorescent emission, this is the reason
why the process is called superradiance, or by a generalization to extended systems, superfluorescence.
The superradiant emission has preferential escape directions, depending on the atomic sample shape.
Superradiance is a collective process and it takes place when the group of excited atoms is left unper-
turbed during the formation of of the macroscopic dipole. A fundamental difference compared to the
spontaneous and stimulated emission processes is that all atoms act together as a single entity and it
isn’t possible to identify single atoms involved.
This remarkable behaviour is manifest when the atomic coherence of the system, while influenced by
environmental interactions that cause dephasing in atoms, persists for a sufficient interval of time.
Typical dephasing mechanisms, such as collisions in gases or lattice phonon interactions in crystals,
make its experimental observation difficult. A possible solution to this problem is the use of optical
crystals doped with rare-earths that are characterized by long and narrow levels lifetimes.