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Physical Review A

Photon echoes in standing-wave fields: Time separation of spatial harmonics

J.-L. Le Gouët, P. R. Berman

Published Sep 1, 1979• 25 citations
Publisher

Abstract

A calculation is presented to describe the response of an atomic system subjected to two strong standing-wave field pulses separated in time. One finds a sequence of output pulses following input pulses which is reminiscent of classical photon echoes. A physical picture of the processes involved in echo formation is presented, and connection is made with the classical picture of photon echoes. The application of these techniques to collision studies is emphasized. It is shown that studies of echoes produced by standing-wave fields can prove advantageous for exploring the effects of small-angle scattering on both level populations and atomic coherences.

DOI
10.1103/physreva.20.1105

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Photon echoes in standing wave fields: Time separation of spatial harmonics

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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
A calculation is presented to describe the response of an atomic system subjected to two strong standing-wave field pulses separated in time. One finds a sequence of output pulses following input pulses which is reminiscent of classical photon echoes. A physical picture of the processes involved in echo formation is presented, and connection is made with the classical picture of photon echoes. The application of these techniques to collision studies is emphasized. It is shown that studies of echoes produced by standing-wave fields can prove advantageous for exploring the effects of small-angle scattering on both level populations and atomic coherences.
A calculation is presented to describe the response of an atomic system subjected to two strong standing wave field pulses separated in time. One finds a sequence of output pulses following the input ones, reminiscent of classical photon echoes. A physical picture of the processes involved in echo formation is presented and connection is made with the classical picture of photon echoes. The application of these techniques to collision studies is emphasized. It is shown that studies of echoes produced by standing wave fields can prove advantageous for exploring the effects of small angle scattering on both level populations and atomic coherences. (Author)
A theoretical study is made of the photon echo which appears in a rarefied gaseous medium as a result of successive action of traveling and standing wave pulses, polarized linearly at an angle ψ. This photon echo represents a superposition of two opposite traveling waves, one of which has the polarization of a standing wave pulse, the other has a linear polarization which depends on ψ and on the parameters of a resonant atomic transition. Similar polarization features are exhibited also by coherent radiation from a resonant medium subjected to steady-state fields of the traveling and standing waves separated by some distance in space. The possibility of obtaining a characteristic narrow resonance is discussed.
Experimental observations are reported of coherent emission from an absorbing rarefied gas following the interaction with two standing-wave pulses separated by a time T. The emission occurred at a time 2T after the first pulse and was associated with the spatial transport of polarization and the formation of spatial polarization harmonics because of a phase jump following two-photon interaction with the field of the second pulse. The formation of spatial polarization harmonics was responsible for the appearance of Ramsey resonances in the optical region. Intensity oscillations were observed at the center of the absorption line on tuning the frequency of the exciting laser and varying the delay time between the pulses.
We consider the interference of atoms caused by the wave nature of their motion. Coherently interfering beams of particles may be obtained by using the diffraction of atoms from separated standing waves resonant with the transition between the ground and excited states of the atoms. Interference arises with and without spatial separation of the diffracted atomic beams. A problem concerning two-quantum perturbation of the wave function of an atom in the ground state by a standing-wave field has been solved. Both amplitude and phase perturbation are taken into account. We show that in spite of the absence of coherence in the incident beam and a rapid decay of the coherence induced by the standing wave for scattered spatially overlapping beams, the interference can be observed for the conditions of an echo. We first consider the phenomenon of an echo under the quantum-mechanical action of light on the translational degrees of freedom. We show that owing to this phenomenon phase memory can be transferred through the ground state over unlimitedly large distances. Owing to the interference of the density harmonics, a periodic structure in the spatial distribution of the atomic density with a period of less than one wavelength of the light is localized at distances of the order of the distance between the fields. The harmonic amplitude is calculated for instantaneous excitation in the case in which the duration of the excitation is comparable with the backward Doppler linewidth in the beam and for scattering under Bragg conditions. In the latter case we show that the effective temperature of the atoms participating in the interference is less than one recoil energy.
A theory of photon echoes using double-resonance optical pulses (PEDROP) is presented. Two double-resonance pulses, separated by a time interval T, are used to cause transitions among three states of an atom. Each double-resonance pulse consists of two simultaneously applied laser pulses that drive coupled transitions in the atom. It is shown that for time t > T, six photon echoes are produced (three on each of the coupled transitions) at five distinct times. Moreover, a nonradiating macroscopic coherence is also produced between states of the same parity. With the use of an interrogation pulse to monitor this coherence, three additional photon echoes can be produced on either of the coupled transitions. A Doppler phase diagram is constructed that enables one easily to predict the times and conditions of echo formation. PEDROP combines features of both two-photon and trilevel echoes but offers advantages over these methods for studying relaxation phenomena.
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.