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Physical Review A

Collisional relaxation in an extended-pulse photon echo: Weak-field limit

Ruwang Sung, P. R. Berman

Published Jun 1, 1989• 5 citations
Publisher

Abstract

The effect of velocity-changing collisions in an extended-pulse photon echo is studied. In an extended-pulse photon echo, the second excitation pulse has a duration comparable with the relaxation time of an atomic system. We present an analytic solution of the quantum-mechanical transport equation in the perturbation-theory limit and apply it to the extended-pulse photon echo. It is found that the decay rate of the echo signal due to velocity-changing collisions is significantly modified by the variation of the second pulse's duration. The results are compared with those of conventional theories of two- and three-pulse echoes using temporally narrow excitation pulses. A physical interpretation of the results is given using both time- and frequency-domain arguments.

DOI
10.1103/physreva.39.6284

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The effect of velocity-changing collisions in an extended-pulse photon echo is studied. In an extended-pulse photon echo, the second excitation pulse has a duration comparable with the relaxation time of an atomic system. We present an analytic solution of the quantum-mechanical transport equation in the perturbation-theory limit and apply it to the extended-pulse photon echo. It is found that the decay rate of the echo signal due to velocity-changing collisions is significantly modified by the variation of the second pulse's duration. The results are compared with those of conventional theories of two- and three-pulse echoes using temporally narrow excitation pulses. A physical interpretation of the results is given using both time- and frequency-domain arguments.
The interaction between an intense radiation field and atoms that undergo collisions in an atomic vapor is studied. With the assumption that velocity-changing collisions are state independent and weak, we obtain an analytic expression for the time-dependent density-matrix elements by solving a quantum-mechanical transport equation using a dressed-state approach. Our analytical calculation is used to predict the form of the signal in an extended-pulse photon echo. The results show good agreement with an experiment carried out by Yodh et al. [Phys. Rev. Lett. 53, 659 (1984)]. It is found that the decay rate of the echo signal decreases rapidly with increasing duration of the second pulse in the pulse excitation sequence. A comparison between theory and experiment is presented and a physical interpretation of the results is given.
We have developed a general technique for obtaining analytical expressions for coherent transient signals arising from atoms interacting with two or more laser pulses having Gaussian spatial profiles. After deriving the Maxwell-Bloch equations for short laser pulses incident on an ensemble of three-level atoms, we specialize to photon echo spectroscopy. As an example, the stimulated photon echo signal is calculated as a function of the time delay between pulses. Our exact results are compared with both the lowest-order perturbative limit and a calculation in which transit time is treated phenomenologically. We conclude by commenting on the extension of our technique to atoms undergoing velocity-changing collisions. \textcopyright{} 1996 The American Physical Society.
The effect of translational velocity of active atoms and molecules on the properties of photon echo is investigated using the technique of coherent transient processes. A variation in the photon-echo decay with a frequency detuning of the excitation radiation relative to the center of the vibrational-rotational transition 0 ↔ 1 ν3 R(4, 3) is observed in a mixture of 13CH3F with atomic buffers. The results are interpreted using the dependence of the echo decay rate on the magnitude of the translational velocity of active particles. The dependence of the relaxation matrix on the direction of the velocity of active atoms results in a new phenomenon of the collision-induced echo, which is investigated at the transition 0 ↔ 1 174Yb in mixtures with atomic buffers.
We calculate the photon echo decay for a strongly coupled electron–phonon system, without making unrealistic assumptions about excitation pulse durations. We find that asymptotically, the photon echo decay is exponential, and we provide a formal expression for the decay rate 1/T2 which is independent of pulse duration. In contrast to the usual results, our expression for 1/T2 is nonperturbative in the electron–phonon interaction. We calculate the dependences of the echo amplitude on pulse power and duration, finding that the strong electron–phonon coupling modifies the simple two level system result. We also focus on the relationship between the zero phonon line shape in the homogeneous optical absorption spectrum, and the photon echo decay rate. We find that the zero phonon line shape is Lorentzian, with width 1/πT2. We show that the usual optical Bloch equation approach to analyzing time-domain experiments, which normally is only applicable if the electron–phonon coupling is weak, can be extended to the case of strong coupling. These strong coupling Bloch equations are adequate for analyzing the time dependence, but not the pulse power and duration dependences, of time-domain experiments. Our results indicate that within the Condon approximation, electron–phonon coupling cannot explain the very low temperature anomaly of recent photon echo experiments on impurities in molecular crystals.
With regard to the depolarizing collisions the polarization properties of the photon echo formed by two exciting pulses linearly polarized at an angle ψ to each other with arbitrary values of their areas and arbitrary ratios of the durations and the time of reversible Doppler relaxation are obtained. The case of the small area of the first exciting pulse is examined. It is shown that the polarization properties of the photon echo can be described by equations obtained in the limit of small areas for both the first and the second exciting pulses up to the area of the second exciting pulse of the order of unity.