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Journal of the Optical Society of America B

Theory on cooperative quantum transitions of three identical lanthanide ions

Qin Weiping, Sin Cholnam, Liu Zhenyu, Qin Guanshi, Changfeng Wu

Published Jan 16, 2015• 9 citations
Publisher

Abstract

Recently, we observed ultraviolet luminescence in CaF2:Yb3+ under the excitation of a 980 nm laser. In this paper, cooperative transition theory of three identical lanthanide ions is built through perturbed wave functions of a three-body system with electric multipole interactions. The theoretical results show that d-dd-dq and crystal field effected d-dd-dfd are the main mechanisms in the triple transition processes. The transition rate ratio of Yb3+-dimers and Yb3+-trimers in an Yb3+-hexamer is calculated to be ∼1.86×104. This is in reasonable agreement with the experimentally obtained cooperative luminescence intensity ratio of ∼2.0×104 in CaF2:Yb3+ under the excitation of a 980 nm laser.

DOI
10.1364/josab.32.000303

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Recently, we observed ultraviolet luminescence in CaF2:Yb3+ under the excitation of a 980 nm laser. In this paper, cooperative transition theory of three identical lanthanide ions is built through perturbed wave functions of a three-body system with electric multipole interactions. The theoretical results show that d-dd-dq and crystal field effected d-dd-dfd are the main mechanisms in the triple transition processes. The transition rate ratio of Yb3+-dimers and Yb3+-trimers in an Yb3+-hexamer is calculated to be ∼1.86×104. This is in reasonable agreement with the experimentally obtained cooperative luminescence intensity ratio of ∼2.0×104 in CaF2:Yb3+ under the excitation of a 980 nm laser.
A series of Yb3+-doped yttrium aluminum monoclinic Y4Al2O9 (Yb:YAM) single crystals with Yb3+ ion concentrations of 0.1, 1, 5 and 10 at.% was grown by means of micro pulling down method. Blue emission was observed in Yb3+ activated YAM crystals under infrared site-selective laser excitation. Through the excitation and emission spectra, decay time measurements and excitation intensity dependence the process responsible for this anti-Stokes emission was assigned to the cooperative deexcitation of two Yb3+ ions. The results show that at 10% Yb3+ dopant concentration investigated system could be considered as single-site system in which cooperative luminescence is dominated by the energetically lowest Yb3+ site. Theoretical cooperative emission spectrum and the cooperative luminescence rate of Yb3+:YAM were calculated.
We investigate the effect of the dipole-dipole interaction on the quantum jump statistics of three atoms. This is done for three-level systems in a V\mathsf{V}V configuration and in what may be called a D\mathsf{D}D configuration. The transition rates between the four different intensity periods are calculated in closed form. Cooperative effects are shown to increase by a factor of 2 compared to two of either three-level systems. This results in transition rates that are, for distances of about one wavelength of the strong transition, up to 100% higher than for independent systems. In addition the double and triple jump rates are calculated from the transition rates. In this case cooperative effects of up to 170% for distances of about one wavelength and still up to 15% around 10 wavelengths are found. Nevertheless, for the parameters of an experiment with Hg+{\mathrm{Hg}}^{+}Hg+ ions the effects are negligible, in agreement with the experimental data. For three Ba+{\mathrm{Ba}}^{+}Ba+ ions this seems to indicate that the large cooperative effects observed experimentally cannot be explained by the dipole-dipole interaction.
Cooperative luminescence phenomenon of Yb:YAG crystals was studied. Up-converted blue luminescence was obviously observed in Yb:YAG under excitation in the near-infrared region with a wavelength 940 nm. Experimental evidence was provided by the fact that the intensity of 498 nm luminescence shows a quadratic dependence on excitation power, and the intensity of blue luminescence increased with the increase in Yb ion concentration. It is concluded that this luminescence is due to a cooperative process resulting from a strong interaction of Yb ions. The cooperative luminescence is possiblely assigned to the strong interaction of 4f(13) electrons and neighboring Yb3+ ions in a covalent host lattice such as YAG. Theoretical cooperative luminescence spectrum was calculated.
Summary form only given. The migration of excitation energy within dielectric crystals doped with lanthanide ions is a rich area for the study of mechanisms involving both conventional pairwise resonance energy transfer and more complex many-body effects. Within the framework of molecular quantum electrodynamics, we present a delineation of systems undergoing simultaneous transfer from two pre-excited donor ions to a single ground-state acceptor, termed three-centre energy pooling. Calculations lead to the identification of two competing mechanisms of transfer co-existing in each system-one cooperative pathway where the excitation is transferred directly to the acceptor from both donors, alongside an accretive mechanism where the excitation energy of one donor is accrued by a second, with net transfer to the acceptor ensuing.