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Physical Review A

Spherical-tensor treatment of coherent transients

Thomas M. Baer

Published Dec 1, 1978• 18 citations
Publisher

Abstract

I present a spherical-tensor treatment of coherent transient effects induced in atoms by an optical pulse resonant with a dipole transition. The resonant pulse is shown to excite electronic multipole moments in the atom which can be higher than the dipole. The dependence of these moments on the length and intensity of the applied pulse is derived. It is shown that information about the damping of these moments due to thermal collisions is contained in photon-echo signals.

DOI
10.1103/physreva.18.2570

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Coherent responses of resonance atom layer to short optical pulse excitation are numerically considered. The inhomogeneous broadening of one-photon transition, the near dipole-dipole interaction, and the substrate dispersion are involved in analysis. Under certain intensity of incident pulses, a strong coherent interaction in the form of sharp spikes of superradiation is observed in transmitted radiation. The Lorentz field correction and the substrate dispersion weaken the effect, providing additional spectral shifts. Specific features of photon echo in the form of multiple echoes to a double or triple pulse excitation in the presence ofnear dipole-dipole interaction is discussed.

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The effect that may be exerted by an interatomic near dipole-dipole interaction upon optical transient processes in dense resonance media is analyzed. The behavior of the macroscopic polarization after a one-pulse excitation of a dense ensemble of two-level atoms is considered. It is shown that the free polarization signal is of oscillatory nature, with the oscillation frequency varying in time and being dependent on the dipole-dipole interaction constant, the intensity and duration of the exciting pulse, and the detuning of its carrier frequency from the resonance. The free polarization signal decay, which depends on the magnitude and sign of the sum of the detuning of the exciting pulse carrier frequency from the resonance and the Lorentz frequency, may obey either a power or an exponential law. The signal decay rate is determined not only by the inhomogeneous broadening, but also by the ratio of the above parameters. The peculiarities of echo-responses under one- or two-pulse excitation conditions are studied.

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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 $\frac{1}{2}{j}_{1}({j}_{1}+1)$ time constants to describe the collision damping of the echo intensity, ${j}_{1}$ being an integer. The corresponding formula for the half-integer case is $\frac{1}{2}({j}_{2}+\frac{1}{2})({j}_{2}+\frac{3}{2})$.

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Transit-time effects in coherent transient spectroscopy

J. L. Cohen, P. R. Berman

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.

Physical Review A•Dec 1, 1996•7 citations
I present a spherical-tensor treatment of coherent transient effects induced in atoms by an optical pulse resonant with a dipole transition. The resonant pulse is shown to excite electronic multipole moments in the atom which can be higher than the dipole. The dependence of these moments on the length and intensity of the applied pulse is derived. It is shown that information about the damping of these moments due to thermal collisions is contained in photon-echo signals.
When an intense and short laser pulse or a fast-switching-on/off laser field interacts with a resonant absorbing medium, several optical coherent transient effects can be observed, including the self-induced transparency effect, photon echo effect, optical nutation effect, and the optical free induction decay effect. The study of these effects enables us to gain a deeper understanding of the coherent transient interaction of an intense pulsed or rapidly switched optical field with the resonant medium, and to measure the magnitude of the dipole-moment matrix elements, relaxation parameters, and spectral broadening mechanisms of the investigated materials. On the other hand, these optical coherent transient effects can also be applied for developing special techniques of optical pulse delay, pulse reshaping, and optical pulse manipulation.
Coherent responses of resonance atom layer to short optical pulse excitation are numerically considered. The inhomogeneous broadening of one-photon transition, the near dipole-dipole interaction, and the substrate dispersion are involved in analysis. Under certain intensity of incident pulses, a strong coherent interaction in the form of sharp spikes of superradiation is observed in transmitted radiation. The Lorentz field correction and the substrate dispersion weaken the effect, providing additional spectral shifts. Specific features of photon echo in the form of multiple echoes to a double or triple pulse excitation in the presence ofnear dipole-dipole interaction is discussed.
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.
The effect that may be exerted by an interatomic near dipole-dipole interaction upon optical transient processes in dense resonance media is analyzed. The behavior of the macroscopic polarization after a one-pulse excitation of a dense ensemble of two-level atoms is considered. It is shown that the free polarization signal is of oscillatory nature, with the oscillation frequency varying in time and being dependent on the dipole-dipole interaction constant, the intensity and duration of the exciting pulse, and the detuning of its carrier frequency from the resonance. The free polarization signal decay, which depends on the magnitude and sign of the sum of the detuning of the exciting pulse carrier frequency from the resonance and the Lorentz frequency, may obey either a power or an exponential law. The signal decay rate is determined not only by the inhomogeneous broadening, but also by the ratio of the above parameters. The peculiarities of echo-responses under one- or two-pulse excitation conditions are studied.
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 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.