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Physical Review A

Collisional decay and revival of the grating stimulated echo

P. R. Berman

Published Apr 1, 1994• 8 citations
Publisher

Abstract

A theory is presented that describes collision-induced modifications of the grating stimulated echo (GSE) signal. In the GSE [B. Dubetsky, P. R. Berman, and T. Sleator, Phys. Rev. A 46, 2213 (1992)], a spatially modulated atomic population is created which undergoes Doppler dephasing and rephasing as a result of the interaction of the atoms with a number of input pulses. At low pressures, there is a rapid decay of the GSE signal owing to a collisional breaking of the dephasing-rephasing process. At high perturber pressures, however, there can be a revival of the GSE signal owing to a collisional inhibition of the Doppler dephasing. These collisional processes are described in detail, with a special emphasis given to the distinction between ``open'' and ``closed'' atom-field systems. The manner in which the GSE can be used to determine collision kernels and diffusion coefficients is also discussed.

DOI
10.1103/physreva.49.2922

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A theory of four-wave mixing including effects of velocity-changing collisions is presented. Three fields with frequencies \ensuremath{\omega}, \ensuremath{\omega}, and \ensuremath{\omega}+\ensuremath{\delta} are incident on a vapor of ``two-level'' atoms having upper state b and lower state a. Two of the fields are counterpropagating and the third (of frequency \ensuremath{\omega}+\ensuremath{\delta}) makes a small angle with one of the others. The frequency \ensuremath{\omega} is a nearly resonant (inside the Doppler width) with the a-b transition frequency. The phase-conjugate signal emitted at frequency \ensuremath{\omega}-\ensuremath{\delta} is calculated as a function of \ensuremath{\delta}. Using a simple collision model in which collisions are phase interrupting in their effect on atomic coherence and velocity-changing in their effect on level populations, we discuss the conditions under which resonances characterized by the upper or lower radiative and collision rates can be observed. Assuming that the total (a+b) state population is conserved in the absence of collisions, it is shown that velocity-changing collisions can ``open'' the system and lead to a resonance characterized by the lower-state width (convoluted with the residual Doppler width). With increasing pressure, the width of this induced resonance structure decreases monotonically. For sufficiently high pressure, the collisional redistribution of velocity classes is complete---the system ``recloses'' and the narrow resonance disappears. The interplay of the collision-induced opening, line narrowing, and reclosing of the system is discussed, as is the relationship of these narrow resonances to the so-called pressure-induced extra resonances of Bloembergen and co-workers [Indian J. Pure Appl. Phys. 16, 151 (1978); Phys. Rev. Lett. 46, 111 (1981)].

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Summary form only given. A ground-state coherence grating involving the magnetic sublevels of the F=3 ground state in /sup 85/Rb is created in Doppler-broadened vapor using an excitation pulse that consists of two traveling waves with orthogonally polarized wave vectors. The decay of the grating that is due to thermal motion is probed by a traveling-wave readout pulse. This results in a scattered signal magnetic grating free-induction decay (MGFID) that is detected using a heterodyne technique. In our experiment, collisional revival can be expected when the mean free path is less than the grating spacing.

Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC)•Jan 1, 1997•0 citations

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Summary form only given. A ground-state coherence grating involving the magnetic sublevels of the F=3 ground state in /sup 85/Rb is created in Doppler-broadened vapor using an excitation pulse that consists of two traveling waves with orthogonally polarized wave vectors. The decay of the grating that is due to thermal motion is probed by a traveling-wave readout pulse. This results in a scattered signal magnetic grating free-induction decay (MGFID) that is detected using a heterodyne technique. In our experiment, collisional revival can be expected when the mean free path is less than the grating spacing.

Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC)•Jan 1, 1997•0 citations

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We have used two sets of orthogonally polarized traveling-wave pulses separated in time to establish and, subsequently, rephase a spatially periodic coherence grating between the magnetic sublevels of the $F=3$ ground state in a cloud of laser-cooled ${}^{85}\mathrm{Rb}$ atoms. The rephasing results in a magnetic grating echo (MGE). We have used the shape of the signals to determine both transverse and longitudinal velocity distributions and to study the effects of magnetic fields. The amplitude of the MGE with counterpropagating pulses is modulated at the atomic recoil frequency, a consequence of matter wave interference.

Physical Review A•Nov 1, 1998•20 citations
A theory is presented that describes collision-induced modifications of the grating stimulated echo (GSE) signal. In the GSE [B. Dubetsky, P. R. Berman, and T. Sleator, Phys. Rev. A 46, 2213 (1992)], a spatially modulated atomic population is created which undergoes Doppler dephasing and rephasing as a result of the interaction of the atoms with a number of input pulses. At low pressures, there is a rapid decay of the GSE signal owing to a collisional breaking of the dephasing-rephasing process. At high perturber pressures, however, there can be a revival of the GSE signal owing to a collisional inhibition of the Doppler dephasing. These collisional processes are described in detail, with a special emphasis given to the distinction between open'' and closed'' atom-field systems. The manner in which the GSE can be used to determine collision kernels and diffusion coefficients is also 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.
A theory of four-wave mixing including effects of velocity-changing collisions is presented. Three fields with frequencies \ensuremath{\omega}, \ensuremath{\omega}, and \ensuremath{\omega}+\ensuremath{\delta} are incident on a vapor of ``two-level'' atoms having upper state b and lower state a. Two of the fields are counterpropagating and the third (of frequency \ensuremath{\omega}+\ensuremath{\delta}) makes a small angle with one of the others. The frequency \ensuremath{\omega} is a nearly resonant (inside the Doppler width) with the a-b transition frequency. The phase-conjugate signal emitted at frequency \ensuremath{\omega}-\ensuremath{\delta} is calculated as a function of \ensuremath{\delta}. Using a simple collision model in which collisions are phase interrupting in their effect on atomic coherence and velocity-changing in their effect on level populations, we discuss the conditions under which resonances characterized by the upper or lower radiative and collision rates can be observed. Assuming that the total (a+b) state population is conserved in the absence of collisions, it is shown that velocity-changing collisions can ``open'' the system and lead to a resonance characterized by the lower-state width (convoluted with the residual Doppler width). With increasing pressure, the width of this induced resonance structure decreases monotonically. For sufficiently high pressure, the collisional redistribution of velocity classes is complete---the system ``recloses'' and the narrow resonance disappears. The interplay of the collision-induced opening, line narrowing, and reclosing of the system is discussed, as is the relationship of these narrow resonances to the so-called pressure-induced extra resonances of Bloembergen and co-workers [Indian J. Pure Appl. Phys. 16, 151 (1978); Phys. Rev. Lett. 46, 111 (1981)].
Summary form only given. A ground-state coherence grating involving the magnetic sublevels of the F=3 ground state in /sup 85/Rb is created in Doppler-broadened vapor using an excitation pulse that consists of two traveling waves with orthogonally polarized wave vectors. The decay of the grating that is due to thermal motion is probed by a traveling-wave readout pulse. This results in a scattered signal magnetic grating free-induction decay (MGFID) that is detected using a heterodyne technique. In our experiment, collisional revival can be expected when the mean free path is less than the grating spacing.
Summary form only given. A ground-state coherence grating involving the magnetic sublevels of the F=3 ground state in /sup 85/Rb is created in Doppler-broadened vapor using an excitation pulse that consists of two traveling waves with orthogonally polarized wave vectors. The decay of the grating that is due to thermal motion is probed by a traveling-wave readout pulse. This results in a scattered signal magnetic grating free-induction decay (MGFID) that is detected using a heterodyne technique. In our experiment, collisional revival can be expected when the mean free path is less than the grating spacing.
We have used two sets of orthogonally polarized traveling-wave pulses separated in time to establish and, subsequently, rephase a spatially periodic coherence grating between the magnetic sublevels of the F=3F=3F=3 ground state in a cloud of laser-cooled 85Rb{}^{85}\mathrm{Rb}85Rb atoms. The rephasing results in a magnetic grating echo (MGE). We have used the shape of the signals to determine both transverse and longitudinal velocity distributions and to study the effects of magnetic fields. The amplitude of the MGE with counterpropagating pulses is modulated at the atomic recoil frequency, a consequence of matter wave interference.