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Modified dipole–dipole interactions on optically excited pair transitions

Juan Francisco Lam, Stephen Colby Rand

Published Apr 26, 1987• 0 citations
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Abstract

The absorption of single photons by coupled pairs of ions in rare-earth solids was first observed by Varsanyi and Dieke.1 They noticed that weak absorption of light occurred in PrCl3 at frequencies close to the sum of transition frequencies of individual Pr ions, giving rise to rare-earth fluorescence. This effect was explained by the perturbation theory of Dexter.2 He showed that weak multipole or exchange interactions between rare-earth ions permitted the simultaneous promotion of two ions to excited states by the action of one absorbed photon in an electric dipole allowed transition. Similarly, two ions initially in excited states could emit one sum frequency photon in a cooperative manner.

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The absorption of single photons by coupled pairs of ions in rare-earth solids was first observed by Varsanyi and Dieke.1 They noticed that weak absorption of light occurred in PrCl3 at frequencies close to the sum of transition frequencies of individual Pr ions, giving rise to rare-earth fluorescence. This effect was explained by the perturbation theory of Dexter.2 He showed that weak multipole or exchange interactions between rare-earth ions permitted the simultaneous promotion of two ions to excited states by the action of one absorbed photon in an electric dipole allowed transition. Similarly, two ions initially in excited states could emit one sum frequency photon in a cooperative manner.
The absorption of a single photon by the simultaneous excitation of two rare-earth ions was first reported by Varsanyi and Dieke in 1961.1 D. L. Dexter explained this unusual observation by including the electron-electron interactions (that also give rise to energy transfer) between the rare earth ions with perturbation theory.2 In the 70's Dexter became interested in electronic-vibrational coupling. A theory of two-center optical transitions was developed for a rare-earth ion weakly coupled to a high energy, internal vibrational mode of a near-lying ion.3 Using theoretical techniques that had been developed for rare-earth ion pairs, intensities and selection rules could be determined.
tion of a single photon by a pair of rare-earth ions in a crystal, acting in cooperation. Neither ion by itself could possibly absorb the photon, since no single-ion state exists at the photon energies involved. Absorption of light occurs discretely at sums of energy-level separations in the two ions and is detected experimentally by the excitation spectrum of one of the emission lines. This is an extremely important new effect which will doubtless have important practical applications in the future as well as obvious scientific implications. It should be emphasized that this is not, in any significant degree, excitation of a molecular state. The basic reason this phenomenon is so unusual is related to the fact that the interaction of radiation with matter consists of a sum of one-electron operators, A Vi, where A is the vector potential. From this point of view, only one electron at a time could possibly be excited, hence only one ion. In this paper a procedure for computing the probability of this effect is outlined, and some of the implications of the associated phenomena are discussed. These views can be found expressed in greater detail in ref. 2.
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 present an exact, analytic solution for the probability of radiative, cooperative transitions of stationary, weakly coupled atoms in strong light fields. Very simple expressions are obtained for pair-emission and -absorption probabilities by use of the ``dressed-atom'' formalism applied to atoms in solids or nearly at rest in optical traps. Analogies between radiative collisions in gases and the pair transitions encountered in solids, which may be viewed as ``frozen'' radiative collisions, are explored. Conditions are predicted for the occurrence of electric dipole decoupling in the presence of a suitable rotating electric field, similar to the well-known phenomenon of ``magic-angle'' decoupling of magnetic spins due to a rotating magnetic field. Observations of this new effect should permit precision determinations of interaction Hamiltonians in optical pair systems.