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+
Following a brief review of laser frequency and time domain techniques for overcoming inhomogeneous broadening of optical transitions in solids, recent studies on the failure of the optical Bloch equations (OBE) in describing saturation and coherent transient phenomena in ruby will be discussed. Experiments using free induction decay (FID), as in the original work on the system Pr3+:LaF3 by DeVoe and Brewer1, as well as extensions to rotary echos2 and hole-burning3 will be described. At low fields (~ 0.4 T), the time and frequency domain linewidth variation with Rabi frequency agree provided care is taken to avoid line broadening caused by spectral diffusion4. Recent work at high fields (~ 5 T), where Cr-Cr electron spin flipping is suppressed5, shows that spectral diffusion decreases and the dephasing time increases. Observed frequency domain hole widths as narrow as 18 kHz (FWHM) have been obtained for the 4 A2(−1/2)→E¯(−1/2) optical transition in dilute ruby using a pump-probe technique4. Work with such narrow holes emphasizes the fundamental limits imposed by the uncertainty principle and as an aside, a thought experiment where single photons are transmitted through "frequency slits" will be discussed.
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 a low-strain, isotopically pure crystal of
YLiF4, we have measured extremely narrow inhomogeneous linewidths (as low as 40 MHz) for the optical transitions of
Er3+ impurities. Inhomogeneous broadening due to strains and other defects is so low that a new mechanism limits the inhomogeneous linewidth: local magnetic fields due to fluorine nuclear spins. These ultranarrow lines enabled us to make the first direct measurement of the isotope shifts of f-f transitions in a solid, and we find for the isotopes
164Er,
166Er,
168Er, and
170Er a shift of 76\ifmmode\pm\else\textpm\fi{}2 MHz unit mass on the
4I15/2(1
)4F9/2(1) transition. We show that this is consistent with a mechanism of coupling to zero-point vibrations.
The study of optical relaxation processes in solids at low temperature has progressed tremendously in the last 20 years due to the development of coherent optical techniques. The latter would not have been possible without the advent of narrow-band tunable lasers, on the one hand, and lasers with very short pulses (picoseconds, femtosecoods) on the other hand. Such coherent techniques are necessary because spectral line shapes of solids doped with guest molecules are seldom determined by dynamical interactions but principally by strain or structural disorder. This gives rise to inhomogeneous broadening, rlOh, which in crystalline hosts at low temperature varies between ' 0.1 and 10 cm -I, whereas in glasses it may amount to � 100-500 em-I. One of the techniques to achieve narrowing of spectral lines is site selection spectroscopy (1-3). A sub-ensemble of molecules within thc inhomogeneously broadened absorption band is selectively excited by mcans of a narrow-band laser, and the fluorescence or phosphoresccnce signal is detected with a high-resolution monochromator and/or a Fabry Perot interferometer. Fluorescence line-narrowing ( I) is a special case of this technique (for a review see 3). The intrinsic or homogeneous spectral linewidth, r hom, which yields information on the relaxation processes of the excited state, is given by the effective optical dephasing time, T2:
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.