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Physical review. B, Condensed matter

Optical free-induction decay of the F3+ center in NaF

R. M. Macfarlane, Azriel Z. Genack, Richard G. Brewer

Published Apr 1, 1978• 22 citations
Publisher

Abstract

We have measured the optical dephasing time ${T}_{2}$ of the $^{1}A_{1}\ensuremath{\leftrightarrow}^{1}E$ zero-phonon transition of the ${F}_{3}^{+}$ color center in NaF by optical free-induction decay. In this way we eliminate the effect of the 54-GHz inhomogeneous broadening, and find a homogeneous linewidth of 20 \ifmmode\pm\else\textpm\fi{} 5 MHz ${T}_{2}=16\ifmmode\pm\else\textpm\fi{}4$ nsec). We have also measured a spontaneous emission lifetime of ${T}_{1}=10\ifmmode\pm\else\textpm\fi{}2$ nsec. In the range 1.5-4 K, our results are consistent with the relation ${T}_{2}=2{T}_{1}$, indicating that optical dephasing is limited by population-decay processes. This relation was even more clearly demonstrated by performing the same experiment on the $D$ lines of sodium vapor at 3 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}5}$ Torr, where the effects of collisions are negligible. We find that the dephasing is again limited by radiative decay, and that ${T}_{2}(32\ifmmode\pm\else\textpm\fi{}3 \mathrm{nsec})=2{T}_{1}(16.3\ifmmode\pm\else\textpm\fi{}0.4 \mathrm{nsec})$.

DOI
10.1103/physrevb.17.2821

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We have measured the optical dephasing time T2{T}_{2}T2​ of the 1A1\ensuremath↔1E^{1}A_{1}\ensuremath{\leftrightarrow}^{1}E1A1​\ensuremath↔1E zero-phonon transition of the F3+{F}_{3}^{+}F3+​ color center in NaF by optical free-induction decay. In this way we eliminate the effect of the 54-GHz inhomogeneous broadening, and find a homogeneous linewidth of 20 \ifmmode\pm\else\textpm\fi{} 5 MHz T2=16\ifmmode±\else\textpm\fi4{T}_{2}=16\ifmmode\pm\else\textpm\fi{}4T2​=16\ifmmode±\else\textpm\fi4 nsec). We have also measured a spontaneous emission lifetime of T1=10\ifmmode±\else\textpm\fi2{T}_{1}=10\ifmmode\pm\else\textpm\fi{}2T1​=10\ifmmode±\else\textpm\fi2 nsec. In the range 1.5-4 K, our results are consistent with the relation T2=2T1{T}_{2}=2{T}_{1}T2​=2T1​, indicating that optical dephasing is limited by population-decay processes. This relation was even more clearly demonstrated by performing the same experiment on the DDD lines of sodium vapor at 3 \ifmmode\times\else\texttimes\fi{} 10\ensuremath−5{10}^{\ensuremath{-}5}10\ensuremath−5 Torr, where the effects of collisions are negligible. We find that the dephasing is again limited by radiative decay, and that T2(32\ifmmode±\else\textpm\fi3nsec)=2T1(16.3\ifmmode±\else\textpm\fi0.4nsec){T}_{2}(32\ifmmode\pm\else\textpm\fi{}3 \mathrm{nsec})=2{T}_{1}(16.3\ifmmode\pm\else\textpm\fi{}0.4 \mathrm{nsec})T2​(32\ifmmode±\else\textpm\fi3nsec)=2T1​(16.3\ifmmode±\else\textpm\fi0.4nsec).
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A novel form of laser frequency switching is devised which extends coherent optical transient studies to a 100-psec time scale. The technique incorporates a traveling-wave electro-optic element which imposes with unit efficiency a uniform time-varying phase and thus a frequency shift on a cw laser beam. In contrast to earlier optical traveling-wave modulators which are driven by a microwave oscillator, here the optical phase change is induced rapidly and easily by a dc electric field pulse that propagates in a microwave guide either parallel or antiparallel to the light wave. This advance enables optical free-induction decay (FID) studies on a subnanosecond time scale and reveals such new features as a rapid first-order FID that dephases with the inhomogeneous dephasing time T2∗{T}_{2}^{*}T2∗​. The well-known nonlinear FID can interfere with the first-order component at short times and decays over the much longer period $\frac{{T}_{2}}{[1+{(1+{\ensuremath{\chi}}^{2}{T}_{1}{T}_{2})}^{\frac{1}{2}}]}$, where $\ensuremath{\chi}$ is the Rabi frequency. A complete analytical expression is derived for optical FID of a transition subject to homogeneous and inhomogeneous broadening and supports detailed observations of the sodium D1{D}_{1}D1​ line.
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.
We report the first optical dephasing study of an inorganic impurity system possessing sharp, low frequency mode structure in its ground and excited state spectra. The total dephasing times T2 and population relaxation times T1 for the 1T2g and 1Eg d9s excited states of NaF:Cu+ are determined at a series of temperatures between 1.8 and 296 K. The T2 values are determined by extracting the Lorentzian components from one- and two-photon excitation line shapes. The T1 values caused by nonradiative decay rates are obtained by detecting very low quantum yield emission from the fast-relaxing excited states and applying the formula tnr=Qtr, where t’s are radiative and nonradiative lifetimes and Q is the quantum yield. T1(1T2g)=4.6 ps and T1(1Eg )=2.0 ps at 8 K. Significantly, these are very similar to the T1 values calculated from lowest temperature Lorentzian linewidths by the relationship 1/T2=1/T′2 +1/(2T1). The T1 values stay approximately constant over the temperature range 1.8–45 K, while the linewidths rapidly increase indicating that pure dephasing dominates. Using ground and excited state information on the low frequency modes, we test optical Redfield theory and the nonperturbative harmonic theory for pure dephasing by pseudolocal phonons against data for this system which displays strongly anhamonic progressions. The nonperturbative theory fits the line broadening data to higher temperatures than optical Redfield theory for the least anharmonic excited state potential, 1T2g. Both theories underpredict the broadening with temperature of the extremely anharmonic 1Eg state. A simple anharmonic theory including scattering to overtone levels also fails to predict the observed linewidth temperature behavior, although it is demonstrated these processes should be occurring.
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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​.