Cooperative luminescence (CL) occurs in spectral regions in which single ions do not have energy levels. It was first observed more than 40 years ago, and all results reported so far are from a pair of ions. In this work, upconverted CL of three Yb 31 ions was observed in the ultraviolet (UV) region under near-infrared (NIR) excitation. The UV CL intensity showed a cubic dependence on the NIR pump power, whereas the luminescence lifetime was nearly one-third the luminescence lifetime of single Yb 31 ions. The triplet CL (TCL) has a clear spectral structure, in which most emission peaks are consistent with the self-convoluted spectra from single Yb 31 ions. Blue shifts were observed for certain peaks, indicating complex interactions among the excited Yb 31 ions. The probability of the TCL process versus the average distances among three Yb 31 ions was derived via the first-and second-order corrections to the wave functions of lanthanide ions, indicating that the formation of Yb 31 clusters containing closely spaced ions favors the occurrence of the multi-ion interaction processes. Furthermore, the cooperative sensitization of one Gd 31 ion by four excited Yb 31 ions (Yb 31 -tetramer) was demonstrated experimentally, which exhibited a novel upconversion mechanism-cluster sensitization. Our results are intriguing for further exploring quantum transitions that simultaneously involve multiple ions. Keywords: cooperative luminescence; cooperative sensitization; quantum transition; ytterbium cluster INTRODUCTION Cooperative luminescence (CL) usually describes the processes by which a pair of ions emits one photon by simultaneous depopulation from their excited states. It represents a special type of electronic transitions occurring in spectral regions where the individual ions do not have absorption or emission. Experimental CL results are essential clues to understanding the nature of cooperative quantum transitions, such as the energy shifts of pair levels from their parent single-ion levels, the selection rules obeyed by the cooperative transitions, and quantum entanglement in multibody systems. [1][2][3] The first CL was demonstrated with a pair of excited Yb 31 ions in 1970. 4 Since then, the CL from Yb 31 -dimers has been studied extensively due to their unique 4f 13 configuration with two multiplets ( 2 F 5/2 , 2 F 7/2 ) and the relatively large absorption cross-section at ,980 nm. Various applications, such as scintillators, structural probes in solids and optical bistability, have been demonstrated with the CL from Yb 31 -dimers. [5][6][7][8][9][10][11] However, the relatively low emission cross-section impedes further experimental investigation of multi-ion cooperative processes.Nevertheless, CL is fundamentally fascinating from a purely theoretical perspective. More than 50 years ago, Dexter explained the cooperative processes based on first-order perturbation theory, 12 in which Coulomb coupling between two ions allows for their cooperative transition as a pair of ions. For processes involving three ions si...

The formation energy, transition level and binding energy of defects in Yb3+-doped CaF2 were calculated with DFT/HSE06.

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