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Physical Review Letters

Optically Detected Coherent Transients in Nuclear Hyperfine Levels

Robert M. Shelby, Constantino S. Yannoni, R. M. Macfarlane

Published Dec 18, 1978• 91 citations
Publisher

Abstract

Using optical detection, we have observed rf nutation, free-induction decay, and echoes, on the 16.70-MHz nuclear hyperfine transition of dilute ${\mathrm{Pr}}^{3+}$ in La${\mathrm{F}}_{3}$ at 2 K. From a comparison of free-induction decay and echo decay we find that the previously observed linewidth of 200 kHz is inhomogeneous and that the homogeneous width is 19 kHz. On the basis of these measurements it is suggested that optical dephasing times for the $^{1}D_{2}\ensuremath{\leftrightarrow}^{3}H_{4}$ and $^{3}P_{0}\ensuremath{\leftrightarrow}^{3}H_{4}$ transitions are as long as \ensuremath{\sim}20 \ensuremath{\mu} sec.

DOI
10.1103/physrevlett.41.1739

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Physical review. B, Condensed matter•Apr 1, 1981•79 citations
Using optical detection, we have observed rf nutation, free-induction decay, and echoes, on the 16.70-MHz nuclear hyperfine transition of dilute Pr3+{\mathrm{Pr}}^{3+}Pr3+ in LaF3{\mathrm{F}}_{3}F3​ at 2 K. From a comparison of free-induction decay and echo decay we find that the previously observed linewidth of 200 kHz is inhomogeneous and that the homogeneous width is 19 kHz. On the basis of these measurements it is suggested that optical dephasing times for the 1D2\ensuremath↔3H4^{1}D_{2}\ensuremath{\leftrightarrow}^{3}H_{4}1D2​\ensuremath↔3H4​ and 3P0\ensuremath↔3H4^{3}P_{0}\ensuremath{\leftrightarrow}^{3}H_{4}3P0​\ensuremath↔3H4​ transitions are as long as \ensuremath{\sim}20 \ensuremath{\mu} sec.
Optical free-induction dephasing times as long as 16 \ensuremath{\mu}sec, corresponding to an optical homogenous linewidth of 10 kHz, have been observed for the $^{3}H_{4}\ensuremath{\leftrightarrow}^{1}D_{2}$ transition of Pr3+{\mathrm{Pr}}^{3+}Pr3+ ions in LaF3{\mathrm{F}}_{3}F3​ at 2\ifmmode^\circ\else\textdegree\fi{}K. Measurements are facilitated by a frequency-locked cw dye laser and a new form of laser frequency switching. Zeeman studies reveal a Pr-F dipole-dipole dephasing mechanism where the Pr nuclear moment is enhanced in both 1D2^{1}D_{2}1D2​ and 3H4^{3}H_{4}3H4​.
The hyperfine structure and relaxation character of the terminal levels of the $^{3}P_{0}\ensuremath{-}^{3}H_{4}$ (4777 \AA{}) transition in LaF3{\mathrm{F}}_{3}F3​: Pr3+{\mathrm{Pr}}^{3+}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{10}^{5}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^{3}P_{0}3P0​ and 3H4^{3}H_{4}3H4​ states. In the 3P0(3H4)^{3}P_{0}(^{3}H_{4})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^{3}H_{4}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.
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.
Contributions to the homogeneous linewidth of the 3^{3}3H4{\mathit{H}}_{4}H4​(1)${\ensuremath{\rightarrow}}^{1}$D2{\mathit{D}}_{2}D2​(1) transition for the two crystallographic sites of Pr3+{\mathrm{Pr}}^{3+}Pr3+ in Y2{\mathrm{Y}}_{2}Y2​SiO5{\mathrm{SiO}}_{5}SiO5​ 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^{89}\mathrm{Y}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 3^{3}3H4{\mathit{H}}_{4}H4​ ground state for each site; the hyperfine levels of the lowest component of the 1^{1}1D2{\mathit{D}}_{2}D2​ 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.
The dephasing time of coherently prepared Pr3+{\mathrm{Pr}}^{3+}Pr3+ impurity ions in a La F3{\mathrm{F}}_{3}F3​ crystal is measured by optical free-induction decay. Above 4\ifmmode^\circ\else\textdegree\fi{}K, phonon processes severely shorten the decay time. Below 4\ifmmode^\circ\else\textdegree\fi{}K, we observe a temperature-independent decay time of 0.38 \ensuremath{\mu}sec. This is surprisingly short considering that there are no contributions from first-order hyperfine, phonon, or Pr3+{\mathrm{Pr}}^{3+}Pr3+-Pr3+{\mathrm{Pr}}^{3+}Pr3+ interactions.
Recent optical free-induction-decay (FID) measurements of the impurity ion Pr3+{\mathrm{Pr}}^{3+}Pr3+ in LaF3{\mathrm{F}}_{3}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^{19}\mathrm{F}19F nuclei (100 kHz). In this regime, the homogeneous broadening arises from local field fluctuations, as in NMR, and is due to the 19F^{19}\mathrm{F}19F nuclei which undergo resonant flip-flops and modulate the Pr3+{\mathrm{Pr}}^{3+}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 LaF3{\mathrm{F}}_{3}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+{\mathrm{Pr}}^{3+}Pr3+ phase history as subgroups of 19F^{19}\mathrm{F}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^{19}\mathrm{F}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+{\mathrm{Pr}}^{3+}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=52)^{141}\mathrm{Pr}(I=\frac{5}{2})141Pr(I=25​) magnetic moment increases with Iz{I}_{z}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.