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Journal of the Optical Society of America B

Optically Induced Homogeneous Line Narrowing

A. Szabó, Johann Heber

Published Jan 1, 1984• 0 citations
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Abstract

Recently there has been growing interest in optical dephasing (homogeneous linewidth) mechanisms in solids, both for scientific and technological1 reasons. The role of spin flip-flops (SFF) in producing dephasing has long been recognized in nuclear and electron magnetic resonance, and these studies are now being extended to optical transitions. In particular direct proof of host nuclear SFF optical dephasing of unlike dopant nuclei has been achieved by the observation of magic- angle homogeneous line narrowing.2 This work reports on a new technique for homogeneous line narrowing that demonstrates the existence of electronic SFF optical dephasing by like spins in ruby. The technique relies on selective depopulation of ground- state levels by R2 optical pumping as well as on novel spin thermodynamics in the ground state produced by the strong dipolar coupling between electron spins.

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Optical spin polarization in ruby enhances slow light by high-contrast transient spectral hole-burning

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Recent optical free-induction-decay (FID) measurements of the impurity ion ${\mathrm{Pr}}^{3+}$ in La${\mathrm{F}}_{3}$ 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 $^{19}\mathrm{F}$ nuclei (100 kHz). In this regime, the homogeneous broadening arises from local field fluctuations, as in NMR, and is due to the $^{19}\mathrm{F}$ nuclei which undergo resonant flip-flops and modulate the ${\mathrm{Pr}}^{3+}$ 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${\mathrm{F}}_{3}$ 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 ${\mathrm{Pr}}^{3+}$ phase history as subgroups of $^{19}\mathrm{F}$ 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 $^{19}\mathrm{F}$ spins contribute substantially to the homogeneous width, a result which shows for the first time that spin-flip correlations are not significant. Furthermore, a ${\mathrm{Pr}}^{3+}$ 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 $^{141}\mathrm{Pr}(I=\frac{5}{2})$ magnetic moment increases with ${I}_{z}$, 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.

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We report experimental and theoretical studies of optical hole burning in the inhomogeneous ${R}_{1}$ line of ruby at low temperatures. Both Stark-shifting and pump-probe techniques using narrow-band single-frequency lasers were employed. In addition to the observation of narrow holes, we have found that a large (up to 70%) decrease in absorption occurs outside the hole and that the relative size of this decrease is constant over the entire inhomogeneous line. This effect is ascribed to fast resonant cross-spin relaxation in the ground-state levels which drives all spins within the optically pumped volume to a common spin temperature. A theoretical model is formulated which describes the power-broadened hole shapes as well as the off-resonance decrease in the absorption coefficient. Fair agreement with experiment is obtained for the case of a magnetic field applied along the $c$ axis; however, sizable deviations from the theory are seen for zero field. We conclude that further studies are needed to elucidate the nature of the Al superhyperfine-broadening mechanism. An upper limit of 1200 nm is deduced for the size of macroscopically broadened regions in ruby.

Physical review. B, Condensed matter•Feb 1, 1980•43 citations
Recently there has been growing interest in optical dephasing (homogeneous linewidth) mechanisms in solids, both for scientific and technological1 reasons. The role of spin flip-flops (SFF) in producing dephasing has long been recognized in nuclear and electron magnetic resonance, and these studies are now being extended to optical transitions. In particular direct proof of host nuclear SFF optical dephasing of unlike dopant nuclei has been achieved by the observation of magic- angle homogeneous line narrowing.2 This work reports on a new technique for homogeneous line narrowing that demonstrates the existence of electronic SFF optical dephasing by like spins in ruby. The technique relies on selective depopulation of ground- state levels by R2 optical pumping as well as on novel spin thermodynamics in the ground state produced by the strong dipolar coupling between electron spins.
The R1{R}_{1}R1​ dephasing time in ruby (0.05 wt.% Cr2{\mathrm{Cr}}_{2}Cr2​O3{\mathrm{O}}_{3}O3​) is observed to increase by an order of magnitude when selected transitions of the R2{R}_{2}R2​ line are pumped. Spin flip-flop dephasing in the ground state is suppressed by optically induced depopulation of the $^{4}A_{2}(\ifmmode\pm\else\textpm\fi{}\frac{1}{2})$ levels.
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+
The spin-lattice relaxation time in the 4 A 2 ground state of C r 3 + in ruby can be on the order of magnitude of seconds at liquid helium temperatures in low magnetic fields B | | c . This allows for highly efficient optical pumping of the spin levels in this system. Such pumping can then in turn be employed to drastically increase the optical density of the inhomogeneously broadened R 1 ( ± 3 / 2 ) or R 1 ( ± 1 / 2 ) lines and also to narrow the spectral hole width because Cr–Cr electron-spin flips (cross relaxation) are suppressed in the ground state, leading to longer dephasing times T 2 ∗ . Both effects can be employed to further reduce the group velocity of light pulses propagating through a transient spectral hole.
Spin decoupling and line narrowing are observed for the first time in an optical transition, $^{3}H_{4}\ensuremath{\leftrightarrow}^{1}D_{2}$ of Pr3+{\mathrm{Pr}}^{3+}Pr3+ in LaF3{\mathrm{F}}_{3}F3​ at 2\ifmmode^\circ\else\textdegree\fi{}K, with use of optical free-induction decay. The 19F^{19}\mathrm{F}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^{19}\mathrm{F}19F-19F^{19}\mathrm{F}19F dipolar interaction is thereby quenched and the optical linewidth drops from \ensuremath{\sim}10 to \ensuremath{\sim}2 kHz, as predicted in a theory of spin diffusion.
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.
We report experimental and theoretical studies of optical hole burning in the inhomogeneous R1{R}_{1}R1​ line of ruby at low temperatures. Both Stark-shifting and pump-probe techniques using narrow-band single-frequency lasers were employed. In addition to the observation of narrow holes, we have found that a large (up to 70%) decrease in absorption occurs outside the hole and that the relative size of this decrease is constant over the entire inhomogeneous line. This effect is ascribed to fast resonant cross-spin relaxation in the ground-state levels which drives all spins within the optically pumped volume to a common spin temperature. A theoretical model is formulated which describes the power-broadened hole shapes as well as the off-resonance decrease in the absorption coefficient. Fair agreement with experiment is obtained for the case of a magnetic field applied along the ccc axis; however, sizable deviations from the theory are seen for zero field. We conclude that further studies are needed to elucidate the nature of the Al superhyperfine-broadening mechanism. An upper limit of 1200 nm is deduced for the size of macroscopically broadened regions in ruby.