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Optica Acta International Journal of Optics

Relaxation of Photon Echoes by Phase-interrupting Collisions during the Second Optical Pulse

Alan V. Durrant, Joy Manners

Published Oct 1, 1984• 3 citations
Publisher

Abstract

It is shown that phase-interrupting collisions occurring during the period of the second excitation pulse in a photon echo experiment do not in general destroy the coherent dipole moments of the perturbed atoms, however hard the collision may be. An effective collision rate for this period is determined; it can be larger or smaller than the actual collision rate, depending on the pulse area. The application to measurements of collisional cross-sections is discussed.

DOI
10.1080/713821406

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Mar 3, 1997•0 citations
It is shown that phase-interrupting collisions occurring during the period of the second excitation pulse in a photon echo experiment do not in general destroy the coherent dipole moments of the perturbed atoms, however hard the collision may be. An effective collision rate for this period is determined; it can be larger or smaller than the actual collision rate, depending on the pulse area. The application to measurements of collisional cross-sections is discussed.
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.
Effects of electric dipole reorienting collisions on photon echoes are investigated. In an extension of the author's earlier work, a general expression is derived, including terms from binary collisions, for the photonecho dipole moment amplitude. The explicit results are worked out for simple cases such as ${j}_{1}=\frac{1}{2}\ensuremath{\leftrightarrow}{j}_{2}=\frac{1}{2}$, ${j}_{1}=1\ensuremath{\leftrightarrow}{j}_{2}=0$, ${j}_{1}=1\ensuremath{\leftrightarrow}{j}_{2}=1$, and ${j}_{1}=\frac{3}{2}\ensuremath{\leftrightarrow}{j}_{2}=\frac{1}{2}$ transitions. While it is shown that echoes resulting from the above simple transitions will not be depolarized by atomic collisions, photon echoes induced by any other transitions are necessarily depolarized by collisions. In addition, it is possible to show that the general expression for the echo dipole moment can be written as a sum of multipole moments. Only the odd moments contribute to the echoes. The importance of this picture is that collision-induced relaxation of each moment is described by a single time constant---as in the model commonly used for Hanle-effect experiments. As a result, for an echo arising from a ${j}_{1}\ensuremath{\leftrightarrow}{j}_{2}$ transition (${j}_{1}\ensuremath{\ge}{j}_{2}$), there must be 12j1(j1+1)\frac{1}{2}{j}_{1}({j}_{1}+1)21​j1​(j1​+1) time constants to describe the collision damping of the echo intensity, j1{j}_{1}j1​ being an integer. The corresponding formula for the half-integer case is 12(j2+12)(j2+32)\frac{1}{2}({j}_{2}+\frac{1}{2})({j}_{2}+\frac{3}{2})21​(j2​+21​)(j2​+23​).
We present solutions for two-photon optical transients from a three-level system which include the effects of (a) direct spontaneous emission to and from the nonresonant intermediate state and (b) phase-interrupting collisions. These effects are, in general, expected to be important for electronic transitions in the visible or ultraviolet region relevant for many two-photon transient experiments on free atoms. The steady-state absorption profile shows power narrowing and desaturation due to spontaneous relaxation. The two-photon delayed optical nutation signal is obtained explicitly. A perturbative calculation of optical nutation shows intensity-dependent damping. We find that for a particular case, namely, when the upper level spontaneous decay rate is twice that of the intermediate level, transient signals have especially simple forms and can be usefully employed for experimental determination of decay constants. The paper is a direct but nontrivial generalization of Schenzle and Brewer's corresponding investigation on one-photon transients.
The method of stimulated photon echo with specially chosen linear polarizations of the pumping pulses of coherent resonant radiation is applied for the investigation of collisional decay of orientation and alignment in the molecular gas SF6 and its mixtures with buffers He and Xe. These relaxation rates are measured as a function of longitudinal velocities. Within the experiment accuracy, no remarkable velocity dependence of the depolarizing collisions rates was detected. This result confirms conventional approach of the depolarizing collisions theoretical treatment. In pure SF6 the rates of elastic depolarizing collisions for orientation and alignment proved smaller than the known rate of velocity changing collisions. It means that only part of the elastic collisions participates in destroying of the level multipole moments.