Physical Review A

Non-Markovian behavior in stimulated photon echoes: Waiting-time dependence

S. Saikan, J. W-I. Lin, H. Nemoto

Published Dec 1, 1992• 10 citations

Abstract

By using stochastic theory, we analyze the non-Markovian temporal behavior in four types of photon echoes, including the two-pulse echo, stimulated echo, accumulated echo, and heterodyne-detected accumulated echo. In particular, the origin of the exp(-${\mathit{ct}}^{3}$) dependence of the two-pulse echo in the limit of slow modulation is discussed in detail. It is also pointed out that, at the slow-modulation limit, the temporal behavior of the stimulated echo changes from exp(-${\mathit{ct}}^{3}$) dependence to exp(-${\mathit{ct}}^{2}$) dependence as the waiting time (the time interval between the second and the third excitation pulses) is varied.

DOI: 10.1103/physreva.46.7123

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Difference between Coherent-Pulse and Incoherent-Pulse Photon Echoes in Non-Markovian Behavior

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By using stochastic theory, we clarified the difference between coherent and incoherent two-pulse photon echoes from the viewpoint of non-Markovian behavior. At the slow modulation limit, the incoherent two-pulse echo was found to exhibit an exp (- c t 2 ) dependence which is in contrast with the exp (- c t 3 ) dependence in the coherent two-pulse echo.

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修治浅香, Hiroki Nakatsuka, Masahiro Fujiwara +1 more

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Detailed Investigation of temporal behavior in accumulated photon echo

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Physical Review A

Non-Markovian behavior in stimulated photon echoes: Waiting-time dependence

S. Saikan, J. W-I. Lin, H. Nemoto

Published Dec 1, 1992• 10 citations

Publisher

Abstract

{\mathit{ct}}^{3}

) dependence of the two-pulse echo in the limit of slow modulation is discussed in detail. It is also pointed out that, at the slow-modulation limit, the temporal behavior of the stimulated echo changes from exp(-

{\mathit{ct}}^{3}

) dependence to exp(-

{\mathit{ct}}^{2}

) dependence as the waiting time (the time interval between the second and the third excitation pulses) is varied.

DOI: 10.1103/physreva.46.7123

Related papers

Difference between Coherent-Pulse and Incoherent-Pulse Photon Echoes in Non-Markovian Behavior

M. Mikami, S. Saikan

Journal of the Physical Society of JapanOct 15, 19941 citation

Mode suppression in the non-Markovian limit by time-gated stimulated photon echo

Wim P. de Boeij, Maxim S. Pshenichnikov, Douwe A. Wiersma

It is demonstrated that enhanced mode suppression in stimulated photon echo experiments can be obtained by diagonal time gating of the echo. This technique is especially important when the optical dynamics of the system is non-Markovian. A two-mode Brownian oscillator model is used to analyze the effect of time gating on the stimulated photon echo. The method is demonstrated on a dye solution of DTTCI in ethylene glycol at room temperature. Experimentally, time gating of the echo is accomplished by means of femtosecond phase-locked heterodyne detected stimulated photon echo. The vibrational dynamics in this system are explored by conventional stimulated photon echo experiments. Especially stimulated photon echo-maximum shift measurements are found to be particularly useful.It is demonstrated that enhanced mode suppression in stimulated photon echo experiments can be obtained by diagonal time gating of the echo. This technique is especially important when the optical dynamics of the system is non-Markovian. A two-mode Brownian oscillator model is used to analyze the effect of time gating on the stimulated photon echo. The method is demonstrated on a dye solution of DTTCI in ethylene glycol at room temperature. Experimentally, time gating of the echo is accomplished by means of femtosecond phase-locked heterodyne detected stimulated photon echo. The vibrational dynamics in this system are explored by conventional stimulated photon echo experiments. Especially stimulated photon echo-maximum shift measurements are found to be particularly useful.

The Journal of Chemical PhysicsAug 22, 199642 citations

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修治浅香, Hiroki Nakatsuka, Masahiro Fujiwara +1 more

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S. Saikan

Apr 26, 19870 citations

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Masaharu Mitsunaga, Ryuzi Yano, Naoshi Uesugi

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Physical review. B, Condensed matterJun 1, 199227 citations

Optical-density effect in heterodyne-detected accumulated photon echo

S. Saikan, H. Miyamoto, Y. Tosaki +1 more

The effect of optical density on the heterodyne-detected accumulated photon echo is investigated both experimentally and theoretically. The cause of the distortion of the echo temporal behavior observed in the $^{4}G_{\frac{5}{2}}$ manifold of Nd:YAG (where YAG is yttrium aluminum garnet) is attributed to the optical-density effect, which is closely related to the change of the field correlation function as the excitation pulse propagates through the sample.The effect of optical density on the heterodyne-detected accumulated photon echo is investigated both experimentally and theoretically. The cause of the distortion of the echo temporal behavior observed in the $^{4}G_{\frac{5}{2}}$ manifold of Nd:YAG (where YAG is yttrium aluminum garnet) is attributed to the optical-density effect, which is closely related to the change of the field correlation function as the excitation pulse propagates through the sample.

Physical review. B, Condensed matterSep 15, 198737 citations

{\mathit{ct}}^{3}

{\mathit{ct}}^{3}

) dependence to exp(-

{\mathit{ct}}^{2}

) dependence as the waiting time (the time interval between the second and the third excitation pulses) is varied.

An analytic theory and experimental studies of the accumulated photon echo is presented. We define a temporal correlation function

\tilde{G}

of the excitation field E ( t ) as

\tilde{G}(\tau,t)=(1/T_{1})\int_{0}^{\infty}\mathrm{d}t'E(t-t')E(t-t'-\tau)\cdot\exp(-t'/T_{1})

, where T 1 is the population relaxation time of the sample, and call the width of

\tilde{G}

with respect to τ a temporal correlation time

\tilde{\tau}_{\text{c}}(t)

. It is proved that the echo intensity is written by the temporal correlation functions when (1) T 1 and the duration of the excitation light τ p are much longer than

\tilde{\tau}_{\text{c}}(t)

in order to make the function

\tilde{G}((\tau,t)

well-defined, (2) T 1 and τ p are much longer than the homogeneous dephasing time T 2 , and (3) one can find a time interval Δ t such that

\tilde{G}(\tau,t)

does not change much between t and t + Δ t , where

\varDelta t{\gg}\tilde{\tau}_{\text{c}}

. Then we can show that the time resolution of the accumulated photon echo is determined by the averaged

\tilde{\tau}_{\text{c}}(t)

over an interval of the integration of the echo signal. This discussion is valid for any excitation source if the above conditions are satisfied, and applies to almost all cases of the practical accumulated photon echo experiment. A discussion is also made on the spurious spike on the echo decay curve near zero delay time that appeared in an experiment with a high time resolution in Nd 3+ -doped silicate glass. It is shown that the most probable cause for this spike is uncorrelated inhomogeneous broadenings of the resonant lines of neodymium ions.

^{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.

^{4}G_{\frac{5}{2}}

manifold of Nd:YAG (where YAG is yttrium aluminum garnet) is attributed to the optical-density effect, which is closely related to the change of the field correlation function as the excitation pulse propagates through the sample.