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Spectral Hole-Burning and Related Spectroscopies: Science and Applications

Experimental Tests of the Optical Bloch Equations for Solids

Alex Szabo

Published Jan 1, 1992• 0 citations
Publisher

Abstract

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.

DOI
10.1364/shbl.1992.tua1

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An optical coherence phenomenon–power- dependent optical line narrowing—is reported for the first known time. The effect is observed in a low-temperature impurity- ion solid, Pr3+:LaF3, using a coherent transient technique for which saturation conditions prevail. Current theories of saturation, based on the optical Bloch equations or on rate equations, fail to explain our experimental results. We have therefore developed a microscopic coherence theory that introduces dephasing into the density-matrix equations of motion in a manner equally valid at low and high power and that agrees closely with our experimental results. This work thus represents the first reported observation of the failure of the optical Bloch equations in a low-temperature impurity-ion solid.

•Jun 18, 1984•0 citations
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 studies of the failure of the optical Bloch equations (OBE) in describing optical saturation in a solid are extended to test another aspect of the OBE, namely the time dependence of free-induction decay (FID) predicted by the SWB theorem on optical transients [Schenzle, Wong, and Brewer, Phys. Rev. A 22, 635 (1980)]. This theorem states that, following an arbitrarily shaped excitation pulse of length T, the FID will vanish at time T following the end of the excitation pulse. Experiments with ruby violate SWB in that FID decay at least twice as long as the excitation pulse is observed. Numerical and analytical calculations using a Gauss-Markov model for the modified OBE show an extended FID decay, however, the theoretical decay shape does not agree with experiment. Thus as with earlier studies on saturation broadening, we find that the modified OBE provides only a qualitative description of radiation-atom interaction in a solid.
In a recent experiment of DEVOE and BREWER [1], it was concluded that the optical Bloch equations are incapable of describing the saturation phenomena observed. Optical free-induction decay (FID) measurements of the impurity ion crystal Pr3+:LaF3 were conducted,where the Pr3+ ions are cohertntly prepared by a laser field under steady-state conditions,and then freely precess when the driving field is removed. At low optical fields, the observed Pr3+ optical line width is dominated by magnetic fluctuations.arising from pairs of fluorine nuclear flip-flops. At high optical fields, this nuclear broadening mechanism is quenched.and the Bloch equations are seriously violated. On physical grounds, this failure is due to a time-averaging of the magnetic interaction as the optical nutation frequency increases [2]. The phenomenological dipole dephasing time T2 of the Bloch equations is therefore not a true constant,but lengthens with increasing field strength.
Measurements of optical rotary-echo decay of the R1{R}_{1}R1​(-1/2),\ensuremath{\sigma} transition of Cr3+{\mathrm{Cr}}^{3+}Cr3+ in dilute ruby at 2 K are described and compared with predictions of two recent modifications (Gauss-Markov and random-telegraph models) of the optical Bloch equations (OBE's). While the modified OBE approximately describes the free-induction decay behavior both in Pr3+{\mathrm{Pr}}^{3+}Pr3+:LaF3{\mathrm{LaF}}_{3}LaF3​ and ruby, we show that rotary-echo decay in ruby is instead described by the standard OBE. Various aspects of the spin flip-flop model used in the theories are discussed in regard to ruby, as well as other possible dephasing contributions.
Frequency-domain optical hole burning of the R1{\mathit{R}}_{1}R1​ line [4{[}^{4}[4A2{\mathit{A}}_{2}A2​(-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. % Cr2{\mathrm{Cr}}_{2}Cr2​O3{\mathrm{O}}_{3}O3​) 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.
Recent studies by DeVoe and Brewer [Phys. Rev. Lett. 50, 1269 (1983)] have shown that the conventional optical Bloch equations markedly fail to describe the optical saturation behavior of the D1{D}_{1}D1​ line in the solid Pr3+{\mathrm{Pr}}^{3+}Pr3+:LaF3{\mathrm{LaF}}_{3}LaF3​. In this paper we extend these studies to another solid, ruby, using free-induction-decay observations obtained by pulse excitation of the R1{R}_{1}R1​ line at 693.4 nm with an ultranarrow-linewidth dye laser. Comparison of the results with Gauss-Markov and random-telegraph-dephasing theories shows approximate agreement for a fluctuation correlation time ${\ensuremath{\tau}}_{c}$=T2{T}_{2}T2​, the dephasing time. This result is remarkably similar to that obtained for Pr3+{\mathrm{Pr}}^{3+}Pr3+:LaF3{\mathrm{LaF}}_{3}LaF3​. However, for theoretical and experimental reasons, we conclude that the theories do not consistently explain the current as well as other data. A qualitative discussion of another dephasing model is given.
An optical coherence phenomenon–power- dependent optical line narrowing—is reported for the first known time. The effect is observed in a low-temperature impurity- ion solid, Pr3+:LaF3, using a coherent transient technique for which saturation conditions prevail. Current theories of saturation, based on the optical Bloch equations or on rate equations, fail to explain our experimental results. We have therefore developed a microscopic coherence theory that introduces dephasing into the density-matrix equations of motion in a manner equally valid at low and high power and that agrees closely with our experimental results. This work thus represents the first reported observation of the failure of the optical Bloch equations in a low-temperature impurity-ion solid.