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.
We report direct evidence for the presence of a spin-diffusion barrier, or frozen core, in Pr3+:LaF3. The evidence is obtained by examining the cross relaxation between the Pr and F nuclei in a magnetic field chosen so that a pair of the optical ground-state Pr3+ hyperfine energy levels matches the F splitting or a multiple of the F splitting. This level-crossing condition permits resonant flip–flop interactions with the nearest-neighbor frozen-core F spins to repopulate Pr3+ hyperfine levels emptied by laser hole burning and is detected as enhanced absorption of the laser beam. The coupling of core F spins to bulk F spins during Pr–F cross relaxation is measured by NMR of the bulk F spin magnetization. The rate of cross relaxation between the Pr spins and the bulk F spins measured in this way is at least 3–4 orders of magnitude slower than that expected in the absence of a spin-diffusion barrier. This reduction of coupling indicates nearly complete detuning of the frozen-core F spins immediately surrounding the Pr3+ ion, cutting off resonant coupling with the bulk F spins.
Recent optical free-induction-decay (FID) measurements of the impurity ion
Pr3+ in La
F3 at 2 \ifmmode^\circ\else\textdegree\fi{}K reveal optical homogeneous linewidths of only a few kilohertz, considerably narrower than the inhomogeneous broadening due to crystalline strains (5 GHz) or the static local magnetic fields of the
19F nuclei (100 kHz). In this regime, the homogeneous broadening arises from local field fluctuations, as in NMR, and is due to the
19F nuclei which undergo resonant flip-flops and modulate the
Pr3+ optical transition frequency. We treat the optical response of a two-level quantum system to an intense coherent field and to fluctuating perturbations using a Monte Carlo computer routine that assumes (1) the La
F3 crystal structure and (2) a sudden fluorine spin-flip model. This procedure avoids many of the approximations of previous analytic theories of spectral diffusion in magnetic resonance and extends the calculation specifically to optical FID. The decay behavior is obtained by sampling statistically the
Pr3+ phase history as subgroups of
19F spins flip randomly in space and time. These fluctuations modify the Bloch equations where the solutions for the preparative and post-preparative periods are obtained by numerical integration. In spite of the large lattice size assumed (2250 fluorines), only a few
19F spins contribute substantially to the homogeneous width, a result which shows for the first time that spin-flip correlations are not significant. Furthermore, a
Pr3+ ion polarizes and detunes the nearest fluorines forming a frozen core that is incapable of resonant spin flipping with the bulk fluorines. We demonstrate that the core grows radially as the
141Pr(I=25) magnetic moment increases with
Iz, but the Pr optical linewidth changes little, producing essentially one rather than three linewidths. Our calculations utilize no free parameters and predict a Lorentzian line shape of 8.4 kHz half-width at half maximum which compares to the optical FID observation of a 10.1-kHz Lorentzian. The Monte Carlo algorithm is verified further by the static local magnetic broadening of a Pr quadrupole transition which is found to be Gaussian, 82 kHz full width at half maximum, in agreement with a second-moment calculation and current observations.
Spin decoupling and line narrowing are observed for the first time in an opticaltransition, 3H4elDZ of Pr3~ in LaF 3 at zOK, using optical FID. The 19F nuclei, when irradiated by an appropriate rf field, undergo forced precession about an effective field at the magic angle in the rotating frame. The fluctuating 19F_19F dipolar interaction is thereby quenched and the optical linewidth drops from -10 to - Z kHz, as predicted in a theory of spin diffusion. In the field of nuclear magnetic resonance (NMR) , there exist several ways of reducing the time-dependent magnetic dipolar interaction between spins. Examples are motional narrowing (l,Z), macroscopic sampIe rotation (3), spontaneous spin flip-flop processes (4), and forced spin precession (5-10). In this article, we report the first observation of this kind in an optical transition of a low temperature solid, LaF 3:Pr 3+, where the dilute nuclear spin (I) is praseodymium and the abundant spin (S) is fluorine. The Pr 3+ ions are coherently prepared by a laser field and thereafter exhibit nonlinear optical free induction decay (FID). The Pr3+ dephasing time, as suggested in earlier work (11), is limited by spin diffusion among the 19F nuclei which undergo resonant flip-flops and impress weak fluctuating fields on the l4lpr nuclei. This action adiabatically modulates the Pr 3+ optical transition frequency through the dipolar I-S interaction and broadens the line. We now show that the half-width half-maximum (HWHM) optical linewidth is reduced from -10 to - Z kHz when the fluorine spin diffusion process is quenched by application of suitable magnetic static snd rf fields, causing the 19F nuclei to precess about an effective magnetic field at the magie angle in the rotating frame. This observation enables us to identify in an unambiguous way that the 19F_19F dipolar interaction is the dominant optical line broadening mechanism and provides the first test of spin diffusion theory' in an optical transition. As we shall see, the behavior at optical and rf frequencies is different. 3+
Contributions to the homogeneous linewidth of the
3H4(1)${\ensuremath{\rightarrow}}^{1}$
D2(1) transition for the two crystallographic sites of
Pr3+ in
Y2SiO5 have been investigated using photon echoes. The effects of excitation-intensity-dependent dephasing or instantaneous diffusion were systematically studied to allow accurate determination of the optical resonance widths. Homogeneous linewidths of 2.8 kHz (site 1) and 1 kHz (site 2) were measured with no applied magnetic field and with sufficiently low laser intensity to minimize the effects of instantaneous diffusion. Using the same excitation intensity, widths of 2.1 kHz (site 1) and 0.85 kHz (site 2) were obtained with an applied magnetic field of 77 G, demonstrating a significant contribution of
89Y nuclear-spin fluctuations to the zero-field homogeneous linewidth. Extrapolation to zero excitation intensity yielded optical resonance widths that were only slightly narrower than the measured values. Optically detected nuclear magnetic resonance measurements determined the hyperfine structure of the
3H4 ground state for each site; the hyperfine levels of the lowest component of the
1D2 manifold for each site were determined using photon echo nuclear double resonance. The relatively large oscillator strength of 3\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}7}$ for a rare-earth ion, in conjunction with long dephasing times makes this material a useful candidate for demonstration of time-domain signal processing and optical data storage.
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 hyperfine structure and relaxation character of the terminal levels of the $^{3}P_{0}\ensuremath{-}^{3}H_{4}$ (4777 \AA{}) transition in La
F3:
Pr3+ (0.03 at.%) were studied using the photon-echo technique. Using two independent nitrogen-laser pumped dye lasers we have observed modulated photon echoes for pulse separations over a \ensuremath{\sim}10-\ensuremath{\mu}sec range. In this interval our modulated photon echoes decay in a simple exponential manner by a factor of
105 and yield a homogeneous linewidth of 70 kHz [full width at half maximum (FWHM)]. Fourier transformation of the echo-modulation data yields directly the nuclear level splittings and their associated linewidths in the
3P0 and
3H4 states. In the
3P0(3H4) state the nuclear splittings are 0.73 and 1.12 MHz (8.48 and 16.68 MHz). The measurements for the nuclear level splittings and associated linewidths in the
3H4 state are in excellent agreement with those obtained from the optical-rf double-resonance experiments of Erickson. We find that the calculated echo modulation is a sensitive function of the relative orientation of the principal axes associated with the ground-and excited-state Hamiltonians. By comparing our experimental and calculated echo-modulation patterns we are able to determine their relative orientations.