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Physical review. B, Condensed matter

Stimulated-photon-echo spectroscopy. II. Echo modulation in Pr3+ : YAlO3

Masaharu Mitsunaga, Ryuzi Yano, Naoshi Uesugi

Published Jun 1, 1992• 27 citations
Publisher

Abstract

Stimulated-photon-echo measurements as a function of both the first-to-second (\ensuremath{\tau}) and the second-to-third (T) pulse separations were conducted to study the echo-modulation behavior for the $^{3}$${\mathit{H}}_{4}$${\mathrm{\ensuremath{-}}}^{1}$${\mathit{D}}_{2}$ transition of a cryogenic ${\mathrm{Pr}}^{3+}$:${\mathrm{YAlO}}_{3}$ sample. When T is shorter than the excited-state lifetime ${\mathit{T}}_{1}$, deep echo modulations along both the \ensuremath{\tau} and T axes are observed, the frequencies of which correspond to the excited-state sublevel splittings. When T exceeds ${\mathit{T}}_{1}$, the modulation is still observed, although only along the \ensuremath{\tau} axis. A density-matrix theory is developed in a perturbative manner to explain these coherent dynamical properties. The numerically simulated three-dimensional plots of the echo intensity versus \ensuremath{\tau} and T are presented, predicting quite satisfactorily the seemingly complicated experimental modulation patterns.

DOI
10.1103/physrevb.45.12760

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Spectroscopy and multiwave mixing in Pr3+ : LaF3

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Physical Review A•Oct 1, 1989•3 citations
Stimulated-photon-echo measurements as a function of both the first-to-second (\ensuremath{\tau}) and the second-to-third (T) pulse separations were conducted to study the echo-modulation behavior for the ^{3}$${\mathit{H}}_{4}$${\mathrm{\ensuremath{-}}}^{1}$${\mathit{D}}_{2} transition of a cryogenic Pr3+{\mathrm{Pr}}^{3+}Pr3+:YAlO3{\mathrm{YAlO}}_{3}YAlO3​ sample. When T is shorter than the excited-state lifetime T1{\mathit{T}}_{1}T1​, deep echo modulations along both the \ensuremath{\tau} and T axes are observed, the frequencies of which correspond to the excited-state sublevel splittings. When T exceeds T1{\mathit{T}}_{1}T1​, the modulation is still observed, although only along the \ensuremath{\tau} axis. A density-matrix theory is developed in a perturbative manner to explain these coherent dynamical properties. The numerically simulated three-dimensional plots of the echo intensity versus \ensuremath{\tau} and T are presented, predicting quite satisfactorily the seemingly complicated experimental modulation patterns.
Systematic measurements of stimulated-photon-echo intensities as a function of the first-to-second (\ensuremath{\tau}) and second-to-third (T) pulse separations allow the investigation of the dynamical properties of the spectral diffusion for the 7^{7}7F0{\mathit{F}}_{0}F0​${\mathrm{\ensuremath{-}}}^{5}$D0{\mathit{D}}_{0}D0​ transition of a cryogenic Eu3+{\mathrm{Eu}}^{3+}Eu3+:YAlO3{\mathrm{YAlO}}_{3}YAlO3​ sample. The existence of spectral diffusion was verified by the significant broadening (from 1.2 to 7.2 kHz) of the homogeneous linewidth (\ensuremath{\Gamma}) as T increases from microseconds to milliseconds, the effect being attributed to the flip flop of nearby aluminum nuclear spins surrounding the Eu3+{\mathrm{Eu}}^{3+}Eu3+ ion. A similar broadening effect (from 0.61 kHz, to a few kHz) was also observed in the presence of a static magnetic field H0{\mathit{H}}_{0}H0​=137 G, but with a much slower diffusion rate. To explain these observations, we use three theoretical models: the Bai-Fayer model, the diffusion-equation model, and the Monte Carlo model. Each agrees reasonably well with the experimental data and indicates the flip rates of sub-kHz order at H0{\mathit{H}}_{0}H0​=0 and an order of magnitude lower at 137 G.
We report a systematic study of the stimulated-photon-echo relaxation on the 3^{3}3P0{\mathit{P}}_{0}P0​${\mathrm{\ensuremath{-}}}^{3}$H4{\mathit{H}}_{4}H4​ transition of Pr3+{\mathrm{Pr}}^{3+}Pr3+:LaF3{\mathrm{LaF}}_{3}LaF3​ and the 3^{3}3P0{\mathit{P}}_{0}P0​${\mathrm{\ensuremath{-}}}^{3}$H4{\mathit{H}}_{4}H4​ and 1^{1}1D2{\mathit{D}}_{2}D2​${\mathrm{\ensuremath{-}}}^{3}$H4{\mathit{H}}_{4}H4​ transitions of Pr3+{\mathrm{Pr}}^{3+}Pr3+:YAG (yttrium aluminum garnet). The stimulated-echo intensity is measured as a function of the delay between the first and the second pulses and the delay between the second and the third pulses. The stimulated-echo relaxation is modulated by the hyperfine interaction in the ground and the excited electronic states. We find that the modulation patterns can be quite distinct from those for two-pulse photon-echo relaxation and give complementary information about the hyperfine structures. We use the density-matrix theory of stimulated-photon-echo modulation, and the resulting simulation shows satisfactory agreement with the experimental data.
A novel coherent transient spectroscopy, cw photon echo, is described. A medium is exposed to broadband cw laser radiation and then to a pulsed laser, resulting in a continuous emission signal from the medium. The temporal profile of this signal is studied using full density-matrix theory for the cases of a two-level system and a multilevel system. It is shown that such signal decays with a homogeneous dephasing time T2{\mathit{T}}_{2}T2​ and can have a quantum-beat-type modulation, reproducing in a single shot the conventional two-pulse photon echo plot versus first-to-second pulse separation. Experimental demonstrations are given for the 7^{7}7F0{\mathit{F}}_{0}F0​${\mathrm{\ensuremath{-}}}^{5}$D0{\mathit{D}}_{0}D0​ transition of Eu3+{\mathrm{Eu}}^{3+}Eu3+ and the 3^{3}3H4{\mathit{H}}_{4}H4​${\mathrm{\ensuremath{-}}}^{1}$D2{\mathit{D}}_{2}D2​ transition of Pr3+{\mathrm{Pr}}^{3+}Pr3+; both ions are doped in YAlO3{\mathrm{YAlO}}_{3}YAlO3​. The Eu ions exhibit a single exponential decay with a slight modulation due to the ground-state hyperfine splittings. The temperature dependence of the signal is also studied. The Pr ions show a very deep modulation pattern, which provides excellent agreement with the independent two pulse echo measurement. A numerical simulation based on the modulation theory also agrees with the observed decay curves and the nuclear axis configuration in this crystal is discussed.
Two-pulse photon-echo measurements on the 0.1 at. % Pr3+{\mathrm{Pr}}^{3+}Pr3+:YAlO3{\mathrm{YAlO}}_{3}YAlO3​ 3^{3}3H4{\mathit{H}}_{4}H4​${\mathrm{\ensuremath{-}}}^{1}$D2{\mathit{D}}_{2}D2​ transition suggest that the relaxation time depends on the density of excited states created by the excitation pulses. The dependence of the relaxation time on the intensity of each excitation pulse shows that our results are inconsistent with instantaneous spectral diffusion, a model often invoked in this type of experiment, where excited states created by the second pulse chiefly influence the relaxation time. A homogeneous linewidth contribution, noted in previous work as being of unknown origin, is eliminated at low excitation fluences.
Multipulse photon echoes are observed from LaF3{\mathrm{LaF}}_{3}LaF3​:Pr3+{\mathrm{Pr}}^{3+}Pr3+ and are shown to be primarily stimulated echoes. The various contributions to the echoes were measured using a three-pulse photon-echo sequence that resolved the image of the echo generated by the first two pulses, and the echo generated by the second and third pulses and that of the first and third pulses from the stimulated echo. By use of a theoretical model of Shoemaker [in Laser and Coherence Spectroscopy, edited by J. I. Steinfeld (Plenum, New York, 1978)] and relaxation theory of Hu and Hartmann [Phys. Rev. B 9, 1 (1974)], the image echo contributions to the third echo is shown to be less than 10% of the total for the pulse widths and Rabi frequencies used in the measurements. As a result, multipulse photon echoes will find limited use in measuring coherence decay until very short high-intensity pulses are used to excite the echoes.
Photon-echo and stimulated-photon-echo experiments in Pr3+{\mathrm{Pr}}^{3+}Pr3+:LaF3{\mathrm{LaF}}_{3}LaF3​ on the three transitions, 3P0^{3}\mathrm{P}_{0}3P0​-(3{(}^{3}(3H5{\mathrm{H}}_{5}H5​)1{)}_{1})1​, 3P0^{3}\mathrm{P}_{0}3P0​-(3{(}^{3}(3H5{\mathrm{H}}_{5}H5​)2{)}_{2})2​, and 3P0^{3}\mathrm{P}_{0}3P0​-(3{(}^{3}(3H6{\mathrm{H}}_{6}H6​)1{)}_{1})1​ [none of which, therefore, involves the (3{(}^{3}(3H4{\mathrm{H}}_{4}H4​)1{)}_{1})1​ ground state] at liquid-He temperatures have revealed the presence of anomalously large residual homogeneous linewidths. The subscripts (e.g., 1,2) denote the crystal-field-split levels of the Pr3+{\mathrm{Pr}}^{3+}Pr3+ ion states. Amplitude-modulated trilevel echoes were observed involving the 3P0^{3}\mathrm{P}_{0}3P0​-(3{(}^{3}(3H5{\mathrm{H}}_{5}H5​)1{)}_{1})1​ and 3P0^{3}\mathrm{P}_{0}3P0​-(3{(}^{3}(3H5{\mathrm{H}}_{5}H5​)2{)}_{2})2​ transitions while no trilevel echoes were observed involving the 3P0^{3}\mathrm{P}_{0}3P0​-(3{(}^{3}(3H4{\mathrm{H}}_{4}H4​)1{)}_{1})1​ and 3P0^{3}\mathrm{P}_{0}3P0​-(3{(}^{3}(3H6{\mathrm{H}}_{6}H6​)1{)}_{1})1​ transitions. Photon echoes were observed on many of the satellite lines of the principal resonance 3P0^{3}\mathrm{P}_{0}3P0​-(3{(}^{3}(3H4{\mathrm{H}}_{4}H4​)1{)}_{1})1​ transitions.