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Molecular Physics

The influence of intermolecular coupling on spontaneous emission

David Parker Craig, T. Thirunamachandran

Published Jun 1, 1996• 4 citations
Publisher

Abstract

The spontaneous fluorescence emission rate (the Einstein rate) from an isolated molecule A is changed by non-identical neighbours of species B, as in vapour phase mixtures, liquid solutions or solids. In this paper the underlying pairwise A–B interactions are analysed in their effect on the rate of emission by A. The effects are reported for all separation distances using non-relativistic quantum electrodynamics with full account of retardation. The Einstein rate for molecule A in isolation is taken as standard. For short A–B distances the two larger changes are due to a reduction in the transition moment after wavefunction renormalization and to the change in emission frequency, i.e., the spectral shift, usually a red shift. Other important changes include some emission by the ‘passive’ molecule B, and a change in the emission rate of A through its coupling to B, even before the change in transition moment is brought in. A novel feature is that the emission by B induced by one-photon exchange between A a...

DOI
10.1080/00268979609482443

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The spontaneous fluorescence emission rate (the Einstein rate) from an isolated molecule A is changed by non-identical neighbours of species B, as in vapour phase mixtures, liquid solutions or solids. In this paper the underlying pairwise A–B interactions are analysed in their effect on the rate of emission by A. The effects are reported for all separation distances using non-relativistic quantum electrodynamics with full account of retardation. The Einstein rate for molecule A in isolation is taken as standard. For short A–B distances the two larger changes are due to a reduction in the transition moment after wavefunction renormalization and to the change in emission frequency, i.e., the spectral shift, usually a red shift. Other important changes include some emission by the ‘passive’ molecule B, and a change in the emission rate of A through its coupling to B, even before the change in transition moment is brought in. A novel feature is that the emission by B induced by one-photon exchange between A a...
Abstract “Spontaneous emission of radiation” calculates the rate of spontaneous electric-dipole emission of a photon by an excited atom or molecule. The calculation proceeds by using basic quantum mechanics (i.e. not using the short cuts of Chapter 19); it uses quantum electrodynamics but is not, on that account, particularly difficult. A 2p–1s transition in hydrogen is used as exemplar; the radiation is elliptically polarized. The spectral line profile (lineshape function) is approximately Lorentzian, but has a high-frequency cut-off, needed to prevent the power radiated from diverging. A radiation-induced frequency shift is negligible. The width of the line profile agrees with the Einstein A-coefficient. A high-frequency cut-off is shown to apply similarly in the derivation of Golden Rule Number Two.
Summary form only given. Over the last three decades of the 20 th century many experiments have demonstrated that the rate of spontaneous emission for an emitter is determined by its electromagnetic surrounding. This phenomenon has been usually studied for atoms or molecules placed in the vicinity of mirrors or in optical resonators. Furthermore, it is also well-known that the fluorescence lifetime of an emitter changes after being embedded in dielectric media where aside from a change in the refractive index, it experiences the local fields in the dielectric. For a spherical medium larger than the order of a wavelength it is known that the coupling to Mie modes of this dielectric resonator has a large influence on the emission rate of an emitter inside. However, when the medium becomes comparable or smaller than a wavelength one can no longer speak of resonator modes. Here we report on an experiment where we have studied the variation of the spontaneous emission rate as the dielectric medium surrounding an emitter is made smaller and smaller down to a few nanometers.
In this paper, we study cooperative two-photon transitions in a system of two (nonoverlapping) atoms for two processes: two-photon spontaneous emission and two-photon resonance fluorescence. Expressions are obtained for the energy shifts and decay rates due to the interaction of the atoms with and via the field. The altered decay rates signal the existence of superradiance and subradiance in the two-atom system. The energy shifts of the single-excitation states are found to be proportional to ${\mathit{R}}^{\mathrm{\ensuremath{-}}6}$ for small atomic separations R, and to ${\mathit{R}}^{\mathrm{\ensuremath{-}}2}$ for large separations.
Recent theoretical and experimental work has shown that the simplest form of the Einstein equation relating induced absorption and spontaneous emission probabilities (characterized by Σ and τ−1) is not generally valid for impurities or color centers in solids, liquids, or molecules. Separate computations of these probabilities in systems exhibiting sizeable Stokes's shifts resolve some of the problems; they also disclose the difficulties involved in obtaining any connection between Σ and τ. Here we consider how the transition probabilities between a pair of electronic-vibrational states are related. Observable quantities, i.e., integrated absorption cross section and the radiative decay time, involve sums and averages over the vibrational states, and no definite theoretical information relates these quantities. However, there is a simple connection between induced and spontaneous emission probabilities. New experiments which could yield information about the rate of lattice relaxation are suggested from this point of view.
Radiation can change the energy state of matter via three optical processes: spontaneous emission, absorption and stimulated emission. In spontaneous emission, an excited atomic or molecular state decays to a lower energy state with the emission of a photon of energy equal to the difference in the quantum state energies. Photon absorption is the reverse process, with a photon causing excitation from a lower to an excited quantum state. Stimulated emission was first proposed by Einstein in a paper published in 1917. He attempted to balance spontaneous emission and photon absorption, but could not get the correct balance without the postulated process of stimulated emission (see Section 4.2). With stimulated emission, an excited quantum state is stimulated to decay to a lower quantum state by an impinging photon. The existing photon survives with another identical photon being created (so that energy is conserved). The rates at which radiative transitions occur can be calculated using quantum mechanics. The time-dependent Schrodinger equation is used with the system wavefunction comprising time-varying linear combinations of the two wavefunctions for the lower and upper quantum states. In semi-classical treatments, an atom is treated quantum mechanically with the radiation field treated classically. There is a perturbation in energy associated with, say, the electric field of the radiation interacting with the electric dipole of the atom, though other interactions can be significant if the electric dipole interaction energy is small. In absorption, for example, a differential equation representing the change in ‘weighting’ of the wavefunction from the lower to upper state is obtained. A ‘time constant’ for the speed of change represents the rate of the radiative process. We examine the quantum mechanical nature of radiation absorption in Section 10.1 before discussing (Section 10.3) another important parameter arising with radiative transitions between discrete bound quantum states: the lineshape function. Quantum Theory of the Atom–Radiation Interaction An expression for the Einstein B-coefficient for photo-absorption is derived using quantum mechanics in this section. Einstein determined the detailed balance relationship between the rates of spontaneous emission, photo-absorption and stimulated emission when light interacts with an atom by considering an atomic system of two energy levels which are in equilibrium with a black-body radiation field. We use a semi-classical treatment where the atom is treated quantum mechanically and the radiation field is treated as a classical oscillating electric field.
The fluorescence of individual pairs of perylenemonoimide chromophores coupled via a short rigid linker is investigated. Photon antibunching is reported, indicating collective effects in the fluorescence, which are further substantiated by the observation of collective triplet off times and triplet lifetime shortening. The experimental findings are analyzed in terms of singlet-singlet and singlet-triplet annihilation based on Förster type energy transfer. The results reported here demonstrate that the statistical properties of the emission light of isolated single quantum systems can serve as a hallmark of intermolecular interactions.