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Physical Review A

Doubly resonant coherent anti-Stokes Raman spectroscopy of Ce3+ in LuPO4

David Piehler, Norman M. Edelstein

Published Jun 1, 1990• 15 citations
Publisher

Abstract

We have measured coherent anti-Stokes Raman spectra between crystal-field levels of the $^{2}$${\mathit{F}}_{5/2}$ and $^{2}$${\mathit{F}}_{7/2}$ manifolds of the ${\mathrm{Ce}}^{3+}$ ion diluted in ${\mathrm{LuPO}}_{4}$ at \ensuremath{\sim}10 K. The anti-Stokes signal is nearly resonant with the lowest crystal-field level of the 5${\mathit{d}}^{1}$ configuration of ${\mathrm{Ce}}^{3+}$ at 30 460 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$. For a ${\mathrm{LuPO}}_{4}$ crystal doped with 0.06 mol % ${\mathrm{Ce}}^{3+}$, we found enhancements of the third-order susceptibility \ensuremath{\Vert}${\mathrm{\ensuremath{\chi}}}^{(3)\mathrm{R}}$/${\mathrm{\ensuremath{\chi}}}^{(3)\mathrm{NR}}$\ensuremath{\Vert} as high as 11.6. This enhancement is over 20 times larger than that seen previously in singly resonant experiments with pure rare-earth crystals.

DOI
10.1103/physreva.41.6406

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We have measured coherent anti-Stokes Raman spectra between crystal-field levels of the ^{2}$${\mathit{F}}_{5/2} and ^{2}$${\mathit{F}}_{7/2} manifolds of the Ce3+{\mathrm{Ce}}^{3+}Ce3+ ion diluted in LuPO4{\mathrm{LuPO}}_{4}LuPO4​ at \ensuremath{\sim}10 K. The anti-Stokes signal is nearly resonant with the lowest crystal-field level of the 5d1{\mathit{d}}^{1}d1 configuration of Ce3+{\mathrm{Ce}}^{3+}Ce3+ at 30 460 cm\ensuremath−1{\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}cm\ensuremath−1. For a LuPO4{\mathrm{LuPO}}_{4}LuPO4​ crystal doped with 0.06 mol % Ce3+{\mathrm{Ce}}^{3+}Ce3+, we found enhancements of the third-order susceptibility \ensuremath{\Vert}\ensuremathχ(3)R{\mathrm{\ensuremath{\chi}}}^{(3)\mathrm{R}}\ensuremathχ(3)R/\ensuremathχ(3)NR{\mathrm{\ensuremath{\chi}}}^{(3)\mathrm{NR}}\ensuremathχ(3)NR\ensuremath{\Vert} as high as 11.6. This enhancement is over 20 times larger than that seen previously in singly resonant experiments with pure rare-earth crystals.
The coherent anti-Stokes Raman spectroscopy (CARS) of electronic states of the Ce3+ ion in a CeF3 crystal at 3.8 K is reported. CARS resonances involving the ground state of the 2F5/2 manifold and the Stark components of the 2F7/2 manifold at 2161 and 2239 cm−1 have been detected. Measurements were made with both visible (λ1 ≈ 476 nm, λ2 = 532 nm) and near-ultraviolet (λ1 = 355 nm, λ2 ≈ 385 nm) lasers. The enhancement of the third-order susceptibility owing to the electronic transitions, |χ(3)R/χ(3)NR|max, is as great as 4.8. This represents an order-of-magnitude increase over that in singly resonant electronic CARS experiments in other rare-earth crystals. The CARS data also yielded accurate measurements of the Ce3+ electronic Raman cross sections. In the visible region, σzz(2161 cm−1) = (5.0 ± 1.1) × 10−30 cm2 and σzz(2239 cm−1) = (1.9 ± 0.7) × 10−30 cm2. One could calculate both the absolute magnitude and the dispersion of |χ(3)R|max by modeling the virtual intermediate states as a single degenerate 5d state at 45 000 cm−1.
Saturation effects in coherent anti-Stokes Raman scattering (CARS) spectroscopy are discussed. The discussion is limited to Raman-resonant CARS (${\ensuremath{\omega}}_{l}\ensuremath{-}{\ensuremath{\omega}}_{s}\ensuremath{\simeq}{\ensuremath{\omega}}_{21}$, where ${\ensuremath{\omega}}_{l,s}$ are the frequencies of the pump fields with powers Pl,s{P}_{l,s}Pl,s​, and ${\ensuremath{\omega}}_{21}$ is the frequency of the Raman transition $|1〉\ensuremath{\rightarrow}|2〉$) with the possible addition of a one-photon resonance (${\ensuremath{\omega}}_{l}\ensuremath{\simeq}{\ensuremath{\omega}}_{31}$ is the frequency of the electronic transition $|1〉\ensuremath{\rightarrow}|3〉$). For these cases we show that the CARS polarization pCARS{\mathcal{p}}_{\mathrm{CARS}}pCARS​ is proportional to the off-diagonal density-matrix element ${\ensuremath{\rho}}_{21}$. In order to determine ${\ensuremath{\rho}}_{21}$, we use Laplace transforms to solve the Bloch equations for the effective two-level system ∣1〉|1〉∣1〉 and ∣2〉|2〉∣2〉 when ${\ensuremath{\omega}}_{l}$ is far from resonance, or for the three-level system ∣1〉,∣2〉|1〉,|2〉∣1〉,∣2〉, and ∣3〉|3〉∣3〉, when ${\ensuremath{\omega}}_{l}\ensuremath{\simeq}{\ensuremath{\omega}}_{31}$. The steady-state expression for pCARS{\mathcal{p}}_{\mathrm{CARS}}pCARS​ in the former case gives ${\mathcal{p}}_{\mathrm{CARS}}\ensuremath{\propto}{P}_{l}{P}_{s}^{\frac{1}{2}}$ at low powers and ${\mathcal{p}}_{\mathrm{CARS}}\ensuremath{\propto}{P}_{l}^{0}{P}_{s}^{\frac{\ensuremath{-}1}{2}}$ at high powers. In the three-level system, we show that when the pressure is low and at least one field is weak, the slow time dependence of ${\ensuremath{\rho}}_{21}$ must be considered. When one field is strong and the other weak, the CARS spectrum is Stark split. When Pl{P}_{l}Pl​ is high, for example, ${\mathcal{p}}_{\mathrm{CARS}}\ensuremath{\propto}{P}_{l}^{0}{P}_{s}^{\frac{1}{2}}$ for ${\ensuremath{\omega}}_{s}\ensuremath{\simeq}{\ensuremath{\omega}}_{32}$ and ${\mathcal{p}}_{\mathrm{CARS}}\ensuremath{\propto}{({P}_{l}{P}_{s})}^{\frac{1}{2}}$ when ${\ensuremath{\omega}}_{s}\ensuremath{\simeq}{\ensuremath{\omega}}_{32}\ifmmode\pm\else\textpm\fi{}{V}_{13}$ where V13{V}_{13}V13​ is the one-photon Rabi frequency for the $|1〉\ensuremath{\rightarrow}|3〉$ transition. The Wilcox-Lamb approximation is used to reduce the three-level Bloch equations to rate equations containing one- and two-photon terms. When the fields are so weak that both one- and two-photon terms are small compared to the decay terms, the usual expression for pCARS{\mathcal{p}}_{\mathrm{CARS}}pCARS​ is reproduced. If only the direct two-photon processes are important, the effective-two-system results are reproduced. When both fields are intense and nearly resonant, the steady state is rapidly achieved. The results for the case where one field is much stronger than the other are essentially the same as those for one strong and one weak field. When the fields are of comparable strength, ${\mathcal{p}}_{\mathrm{CARS}}\ensuremath{\propto}{P}_{l}^{\frac{1}{2}}{P}_{s}^{0}$ for ${\ensuremath{\omega}}_{l}\ensuremath{\simeq}{\ensuremath{\omega}}_{31}$ and ${\ensuremath{\omega}}_{s}\ensuremath{\simeq}{\ensuremath{\omega}}_{32}$, and the CARS spectrum is split into five components.
I report the observation of Raman resonances due to the 3H4^{3}\mathrm{H}_{4}3H4​${\ensuremath{\rightarrow}}^{3}$F2{\mathrm{F}}_{2}F2​ transition in Pr3+{\mathrm{Pr}}^{3+}Pr3+ ions by coherent anti-Stokes Raman scattering. The very weak resonances could only be measured in PrF3{\mathrm{PrF}}_{3}PrF3​ under cryogenic conditions (2 K). The ratio C=\ensuremath{\Vert}${\ensuremath{\chi}}^{(3)R}$/${\ensuremath{\chi}}^{(3)\mathrm{NR}}$${\mathrm{\ensuremath{\Vert}}}_{\mathrm{max}}$ did not exceed 0.5 for the most intense resonances. This value is in good agreement with realistic estimations for the resonant contribution ${\ensuremath{\chi}}^{(3)R}$ of the Pr3+{\mathrm{Pr}}^{3+}Pr3+ ions and ${\ensuremath{\chi}}^{(3)\mathrm{NR}}$ due to the host crystal.
Rare-earth-doped crystals can be attractive materials for quantum information processing, because of the long coherence times that can be expected, in particular, from non-Kramers ions. In this paper, Ho3+-doped yttrium and lutetium vanadate single crystals have been investigated using linear and coherent optical spectroscopy. For Ho3+:YVO4, the crystal-field levels of the I-5(8), F-5, F-5(4) and S-5(2) multiplets have been determined and compared with crystal-field level calculations. This allowed us to unambiguously assign most of the observed transitions, although some results suggest that the site symmetry of the Ho3+ ion could deviate from D-2d. Similar conclusions were reached for Ho3+:LuVO4. Hole burning measurements indicate that the coherence time of the I-5(8)-F-5(5) optical transitions is rather short in both compounds (around 40 ns). Assuming that the coherence is limited by spin interactions, this is accounted for by the high nuclear moment of the nearby vanadium ions, since the large crystal-field level splittings of the I-5(8) and F-5(5) multiplets do not favour a large enhanced nuclear Zeeman effect.
We are interested, in this work, in determining the Stark sub-level of Er3+ ions doping a KY3F10 single crystal with a molar concentration of 1%. We have used a new method of measurement of energies of the ground level and emitting levels from excitation and anti-Stokes emission spectra recorded at liquid nitrogen temperature. This technique is based on a spectral analysis of the anti-Stokes emissions recorded after selective excitation with a red dye tunable laser. Thus, we could determine the Stark sub-levels of the ground and the principal emitting levels in the infrared, visible and near-UV ranges with a very good precision.