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+
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.
Using optical detection, we have observed rf nutation, free-induction decay, and echoes, on the 16.70-MHz nuclear hyperfine transition of dilute
Pr3+ in La
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 $^{1}D_{2}\ensuremath{\leftrightarrow}^{3}H_{4}$ and $^{3}P_{0}\ensuremath{\leftrightarrow}^{3}H_{4}$ transitions are as long as \ensuremath{\sim}20 \ensuremath{\mu} sec.
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+ ions in La
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 and
3H4.
The optical Bloch equations which incorporate the phenomenological population
(T1) and dipole dephasing
(T2) times have been tested recently by optical free-induction-decay (FID) measurements on an impurity-ion crystal
Pr3+:
La3 at 1.6 K. At low optical fields, the observed
Pr3+ optical linewidth is dominated by magnetic fluctuations arising from pairs of fluorine nuclear flip-flops where the condition ${T}_{1}\ensuremath{\gg}{T}_{2}$ prevails. At elevated fields, this nuclear broadening mechanism is quenched and the Bloch equations are violated with ${T}_{2}\ensuremath{\rightarrow}{T}_{1}$. In this paper, a microscopic theory appropriate for a low-temperature impurity solid is presented which reveals the above features both for optical and radio frequencies, and a simple physical interpretation of this line narrowing phenomenon is given. Modified Bloch equations of a novel form are derived to second order and yield analytic FID solutions over the entire range of optical-field strength. A discussion of the earlier NMR theories is given, pointing out similarities and differences.
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.