Spectral Hole-Burning and Related Spectroscopies: Science and Applications
Multi-timescale stochastic theory of time-resolved hole-burning in low-temperature ion-doped crystals. Application to laser-dependent dephasing and spectral diffusion in ruby
S. Ya. Kilin, Alexander P. Nizovtsev, N. S. Onishchenko
Recent experiments on time-resolved hole-burning (TRHB) [1-3] and nonexponential photon-echo decays [4,5] in low-temperature ion-doped crystals have demonstrated the multi-timescale dynamics of host nuclei whose spin flips provide the main source of stochastic fluctuations Ut of an impurity ion transition frequency ωab(ωabt=ωab+Ut) leading to optical dephasing and spectral diffusion. Such complicated spin dynamics results from the existence around the impurity ion of the "frozen core" of nuclear spins with their flip rates to be greatly slowed compared to the unperturbed bulk spins.
Recent experiments on time-resolved hole-burning (TRHB) [1-3] and nonexponential photon-echo decays [4,5] in low-temperature ion-doped crystals have demonstrated the multi-timescale dynamics of host nuclei whose spin flips provide the main source of stochastic fluctuations Ut of an impurity ion transition frequency ωab(ωabt=ωab+Ut) leading to optical dephasing and spectral diffusion. Such complicated spin dynamics results from the existence around the impurity ion of the "frozen core" of nuclear spins with their flip rates to be greatly slowed compared to the unperturbed bulk spins.
Transient hole-burning and free induction decay (FID) in low-temperature ion-doped crystals are studied consistently using the model of two jump processes Ut equals Ut1 + Ut2 characterized by essentially different jump rates v1 >> v2 and distribution widths (sigma) 1 << (sigma) 2 for the impurity ion optical transition frequency fluctuations Ut due to the bulk and the frozen core spin flipping. At short pump/probe pulsewidth T and short delay time (tau) d ((tau) d, T << v2-1) the calculated hole shape is narrow with the hole width determined by Ut1 process characteristics only. The hole width in this case coincides with the calculated FID rate. At long delay (tau) d >= v2-1 the hole becomes a wide lorentzian with the halfwidth 2(sigma) 2. The theory fits well the experimental data by A. Szabo et. al. on narrow hole burning and FID in ruby under low and high magnetic fields supposing the fluctuations Ut1 to be rather slow ((sigma) 21/v21 equals 0.5).
Random frequency modulations exist in many systems, such as magnetic system and glasses at low temperature, dye solution. In magnetic systems, spin flips of doped ions or nuclei in the host lattice can cause the magnetic fluctuations at the impurity site, and hence the stochastic change of the transition frequency of the impurity ions. It is the main source of doped ions' optical dephasing at low temperature. Because the interactions have various time scales and strengths, they can lead to a time dependent broadening spectral line (heterogeneous line), the process is socalled spectral diffusion. Several theoretical methods have been used to explain this phenomenon. They all divided the interactions into only two time scales, the fast one results from spin flipping of the bulk nuclei, and the slow one comes from the contributions of the nearby nuclear spins in a frozen core. However, to describe the complete dynamic process in practical systems, these two time scales are obviously not enough. In addition, spectral diffusion is a typical frequency domain process, but almost no theoretical work started from the pure frequency domain point.In this paper , the spectral diffusion in paramagnetic ions doped system at high field, in which has the modulation frequency dependent jump rates, is studied in both frequency and time domains. In general, the spectral diffusion goes as [1-exp(- WT w )] x . Without frozen core, the values of x are 1/2 and 1 for frequency and time domains, respectively. Considering frozen core effect, the spectral diffusions are slow down by the factor of ( ω eff / ω 0) 2, where ω 0 is the frequency characterized frozen core, and ω eff are ω max and H ∞ for frequency and time domains, respectively. When the frozen core is large enough, the spectral diffusions in two domains tend to have the same form as x ≈0 22.
Laser induced hole burning in optical absorption bands of low temperature solids has been investigated with emphasis on mechanisms for population hole burning, the interactions with the environment which limit the hole widths and the use of hole burning for ultra high resolution spectroscopy. Hole burning was observed in a wide range of solids including organic and organometallic molecules in crystals and rare earth ions in crystals and glasses. The mechanisms for hole burning also varied widely and a new mechanism involving optically induced nuclear spin flips of near neighbor nuclei was discovered. Examples of hole burning in new classes of materials are presented here for the first time, namely inorganic glasses (silicate glasses containing Nd(3+), Pr(3+) or Eu(3+)) and undoped stoichiometric compounds (e.g., EuP5O14). Hole recovery was used to determine nuclear spin lattice relaxation rates in praseodymium doped crystals. For allowed optical transitions (e.g., singlet states of zinc porphyrin, dibromoindigo and color centers in alkali halides) the hole widths at 2K are limited by population decay to approximately 50 MHz. For longer lived optical levels in crystalline materials, e.g., those containing rare earth ions, the hole widths are narrower (less than 10 MHz) and are limited by dynamical interactions with surrounding nuclei. In amorphous materials such as europium doped silicate glass, hole widths are much broader, being limited by low frequency tunneling motions. Hole burning measurements were complemented by time domain coherent transient (photon echo, and optical free decay) measurements of homogeneous linewidths which enabled us to measure optical resonances as narrow as 760 Hz in Eu(3+):Y2O3.
We have measured spectral diffusion in Er3+-doped YLiF4 from the time dependence of spectral hole shapes. The holes were burned in the absorption corresponding to the transition between the lowest Zeeman components of the 4I15/2(1) and 4F9/2(1) levels of Er3+:YLiF4 at 15298.6 cm−1 and were scanned by rapid Zeeman tuning of the erbium energy levels. In an external magnetic field of 26 kG, which supresses erbium–erbium spin flips, the mechanism for spectral diffusion involved local field fluctuations that are due to 19F nuclear spin flips in the perturbing field of the erbium electron spins. Numerical simulation of the fluorine spin dynamics gives semiquantitative agreement with the observed time-dependent hole shapes.
Frequency-domain optical hole burning of the R1 line [4A2(-1/2)\ensuremath{\leftrightarrows}E\ifmmode\bar\else\textasciimacron\fi{}(-1/2) transition] in dilute ruby is studied at 2 K and with a field of 3.6 kG applied along the c axis. A pump-probe (PP) technique is used with precise probe-frequency shifting obtained by an acousto-optic modulator. For sufficiently short PP pulses (50 \ensuremath{\mu}s), two holes (narrow and wide) are observed. The narrow (\ensuremath{\sim}20 kHz half width at half maximum at low power) hole-width dependence on Rabi frequency approximately agrees with that inferred from free-induction-decay measurements. For the present concentration (0.0034 wt. % Cr2O3) and field, the narrow hole width is determined by fluctuating fields produced by Cr-Cr spin flips [A. Szabo, T. Muramoto, and R. Kaarli, Phys. Rev. B 42, 7769 (1990)]. When the PP delay time is varied, the amplitude of the narrow hole decays with a 1/e time constant of \ensuremath{\sim}300 \ensuremath{\mu}s compared to the E\ifmmode\bar\else\textasciimacron\fi{} fluorescence lifetime of 4 ms. The wide hole (\ensuremath{\sim}500 kHz half width at half maximum) is due to Al-Cr superhyperfine interactions and is created by a spectral diffusion mechanism driven by Al-spin flipping in the host lattice.
It has been well established that for many metastable electronic levels of impurity ions in insulators, optical coherence times at liquid helium temperatures are limited by magnetic interactions with host nuclear spins. 1 To understand coherence loss in detail, one needs measurements of optical and spin dephasing, magnetic properties and hyperfine structure of impurity ions, and spin dynamics of host nuclei. To this end techniques such as spectral hole burning, 2 coherent transients (e.g. photon echo), 1,3 and optical-rf double resonance 4 have been used. All of these are limited directly or indirectly by optical T2, and have not directly probed the dynamics of host nuclei.