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Journal of the Optical Society of America B

Variation of the Pr^3+ nuclear quadrupole resonance spectrum across the inhomogeneous optical line in Pr^3+:LaF_3

Lawrence L. Wald, Matjaž Lukač, Erwin Louis Hahn

Published May 1, 1992• 7 citations
Publisher

Abstract

We report nuclear quadrupole resonance (NQR) frequency and linewidth variations of the Pr3+ ground-state hyperfine levels for various positions within the 3H4(Γ1)–1D2(Γ1) inhomogeneous optical line and satellite transitions of Pr3+:LaF3. A linear increase in the broadening of the Pr3+ hyperfine transitions, without a shift of central frequency, is measured by the Stark modulated optical pumping hole-burning technique as the laser is tuned toward the wings of the inhomogeneous optical transition. The linear variation is attributed to electric quadrupole broadening caused by changes in the local density of point defects across the Stark-broadened optical transition. The optically detected NQR spectra of the satellite transitions associated with Pr ion pairs are shifted in frequency and for most satellites are narrower than the NQR spectra found in the wings of the main inhomogeneous optical line.

DOI
10.1364/josab.9.000784

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Physical review. B, Solid state•Dec 1, 1977•114 citations
We report nuclear quadrupole resonance (NQR) frequency and linewidth variations of the Pr3+ ground-state hyperfine levels for various positions within the 3H4(Γ1)–1D2(Γ1) inhomogeneous optical line and satellite transitions of Pr3+:LaF3. A linear increase in the broadening of the Pr3+ hyperfine transitions, without a shift of central frequency, is measured by the Stark modulated optical pumping hole-burning technique as the laser is tuned toward the wings of the inhomogeneous optical transition. The linear variation is attributed to electric quadrupole broadening caused by changes in the local density of point defects across the Stark-broadened optical transition. The optically detected NQR spectra of the satellite transitions associated with Pr ion pairs are shifted in frequency and for most satellites are narrower than the NQR spectra found in the wings of the main inhomogeneous optical line.
The nature of inhomogeneous broadening in rare earth systems plays an important role in the dynamical optical properties of ions in crystals. For this reason much of the work on the nature of the inhomogeneous broadening in rare earth doped systems has concentrated on the investigation of ion-ion interactions such as spectral transfer and up conversion processes.1,3 Variations in homogeneous optical dephasing times across the inhomogeneous optical line have also been reported.4 These studies concentrate on the variations of collective effects of ion- ion interactions at different positions in the inhomogeneous optical line in relatively heavily doped rare earth systems. We report variations in optically detected NQR (ODNQR) linewidths and shifts of Pr3+ hyperfme transitions in the optical ground state as a function of position in the inhomogeneous optical line and for satellite transitions of the 1D2-3H4 transition in lightly doped (0.5 at. %) Pr3+:LaF3.
Photon echo measurements made at 2 °K on the 3H4 - 1D2 transition in Pr3+:LaF3 show that magnetic dipolar couplings between the Pr and F nuclei account for the 56 kHz homogeneous linewidth of this transition.1 The homogeneous broadening arises from the enhanced 141Pr nuclear moment (I=5/2) interacting with the local field fluctuations of the 19F nuclear moments undergoing mutual spin flip transitions. Such resonant fluctuations should, in the absence of a fluorine spin diffusion barrier, produce a homogeneous linewidth of about 200 kHz which is, in fact, roughly what is observed for the inhomogeneous broadening of the Pr3+ hyperfine levels and is considerably broader than that obtained by the photon echo measurements. Shelby et al2 proposed a simple model analogous to the spin diffusion barriers responsible for narrowing the homogeneous lines in certain electron paramagnetic resonance transitions3. In such systems, the field produced by the electron magnetic dipole moment (2-3 orders of magnitude larger than the enhanced nuclear moment associated with the ground state of Pr3+ in LaF3) de-tunes the nearest neighbors from each other, prohibiting mutual spin flips among them. Thus, the fields produced by the neighboring spins are static and their interaction with the paramagnetic ion contributes to the inhomogeneous linewidth and not to homogeneous broadening. The de-tuned neighbors are referred to as the "frozen core." Application of this picture to the case of Pr3+:LaF3 is supported by the calculation of Devoe et al.4 Their Monte Carlo calculation of the Pr3+ optical dephasing times shows that the observed homogeneous linewidth could be explained by deleting the nearest neighbor F spins from the lattice of rapidly fluctuating fluorine moments, in effect, treating them as part of a frozen core.
Optical and hyperfine parameters of the 3H4–1D2 transition are investigated in Pr3 +:La2(WO4)3 for doping concentrations ranging from 0.02 to 3 at.%, at liquid helium temperatures. This includes optical inhomogeneous and homogeneous linewidths, peak absorption, excited-state population decays, spectral hole lifetime and inhomogeneous and homogeneous hyperfine linewidths. Optical inhomogeneous broadening with increasing Pr3 + concentration is limited due to close atomic radii between Pr3 + and La3 +. The peak absorption coefficient increases with increasing Pr3 + doping, reaching up to 28 cm−1. At the highest Pr3 + concentration, optical coherence lifetime is 4.6 μs and hole lifetime 2 s, which should allow one to transfer coherences and tailor the optical inhomogeneous linewidth, as required for rare earth-based optical quantum memories. Raman echo experiments show that hyperfine inhomogeneous linewidth and coherence lifetime (50 kHz and 250 μs respectively) are independent of Pr3 + concentration. These results suggest that highly doped crystals are useful for efficient and long-storage time quantum memories.
Due to their narrow homogeneous linewidths, rare-earth ions in inorganic crystals at low temperatures have recently been given considerable attention as test materials for experiments in coherent quantum optics. Because these narrow linewidth transitions have been buried in a wide inhomogeneous line, the scope of experiments that could be carried out in these materials has been limited. However, here we present spectroscopic techniques, based on spectral hole burning and optical pumping, which allow hyperfine transitions that are initially buried within an inhomogeneously broadened absorption line to be studied with no background absorption from other transitions. A sequence of hole-burning pulses is used to isolate selected transitions between hyperfine levels, which makes it possible to directly study properties of the transitions, e.g., transition strengths, and gives access to information that is difficult to obtain in standard hole-burning spectroscopy, such as the ordering of hyperfine levels. The techniques introduced are applicable to absorbers in a solid with long-lived sublevels in the ground state and where the homogeneous linewidth and sublevel separations are smaller than the inhomogeneous broadening of the optical transition. In particular, this includes rare-earth ions doped into inorganic crystals and in the present work the techniques are demonstrated in spectroscopy of Pr3+{\mathrm{Pr}}^{3+}Pr3+ in Y2SiO5{\mathrm{Y}}_{2}{\mathrm{SiO}}_{5}Y2​SiO5​. Information on the hyperfine structure and relative transition strengths of the $^{3}H_{4}\text{\ensuremath{-}}^{1}D_{2}$ hyperfine transitions in Pr3+:Y2SiO5{\mathrm{Pr}}^{3+}:{\mathrm{Y}}_{2}{\mathrm{SiO}}_{5}Pr3+:Y2​SiO5​ has been obtained from frequency-resolved absorption measurements, in combination with coherent and incoherent driving of the transitions.
Remarkably narrow optical homogeneous linewidths of the order of 1 kHz have now been observed in low temperature zero‐phonon transitions of dilute impurity ion crystals, such as Pr3+ in LaF3. Novel nonlinear optical resonance techniques have been devised for this purpose using ultrastable phase locked cw dye lasers where the measurements are performed either in the frequency domain (hole burning) or in the time domain (coherent optical transients). These studies effectively bring the Mossbauer effect into the optical region. Hence, the observed linewidths are no longer limited by inhomogeneous strain broadening (∼5 GHz) or even by static local fields due to neighboring spins (∼100 kHz). However, weak magnetic field fluctuations from local spins are readily detected. As an example, spin decoupling and line narrowing, which are well known in NMR, are observed in an optical transition of Pr3+:LaF3 at 2 K where the 19F– 19F dipolar interaction is quenched and the optical linewidth drops from 10 to 2 kHz, clearly demonstrating the spin broadening mechanism. Results will be discussed in terms of a Monte Carlo line broadening theory.
The sizable ground-state nuclear polarization which accompanies the optical pumping of the $^{3}H_{4}\ensuremath{-}^{1}D_{2}$ (16 872-${\mathrm{cm}}^{\ensuremath{-}1}$) $\ensuremath{\sigma}$ transition of Pr3+{\mathrm{Pr}}^{3+}Pr3+ in LaF3{\mathrm{F}}_{3}F3​ was utilized to observe enhanced and saturated absorptions within the inhomogeneously broadened spectral line. The observed hyperfine splittings of the lowest 1D2^{1}D_{2}1D2​ state are 3.7 and 4.7 MHz at 2.0\ifmmode^\circ\else\textdegree\fi{}K. These splittings were fitted by a spin Hamiltonian $\mathcal{H}=D[{I}_{z}^{2}\ensuremath{-}\frac{I(I+1)}{3}]+(\frac{E}{2})({I}_{+}^{2}+{I}_{\ensuremath{-}}^{2})$, where $D=\ensuremath{-}1.10\ifmmode\pm\else\textpm\fi{}0.05$ and $E=\ensuremath{-}0.48\ifmmode\pm\else\textpm\fi{}0.05$ MHz. The observed linewidths (including the exciting laser linewidth) were 0.8 MHz. The deconvoluted optical transition linewidths (full widths at half-maximum) are 0.20\ifmmode\pm\else\textpm\fi{}0.05 MHz.