Physical Review Letters

Temporally Recurrent Spatial Ordering of Atomic Population in Gases: Grating Echoes

THOMAS W. MOSSBERG, Ravinder Kachru, Edward A. Whittaker, Sven R. Hartmann

Published Sep 17, 1979• 39 citations

Abstract

We predict and observe the periodic reformation of spatial gratings in Na vapor commencing $\frac{\ensuremath{\tau}}{2}$ after the application of the second of two resonant ($\ensuremath{\lambda}=5896$ \AA{}) standing-wave excitation pulses which are themselves separated by $\ensuremath{\tau}$. These gratings have spatial periodicity $\frac{\ensuremath{\lambda}}{2}$, and backscatter our laser. One set of alternate echoes relaxes because of velocity-changing collisions; phase-changing collisions play no role. The other set is amplitude modulated with laser detuning $\ensuremath{\Delta}$ as $cos\ensuremath{\Delta}\ensuremath{\tau}$.

DOI: 10.1103/physrevlett.43.851

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Physical Review Letters

Temporally Recurrent Spatial Ordering of Atomic Population in Gases: Grating Echoes

THOMAS W. MOSSBERG, Ravinder Kachru, Edward A. Whittaker, Sven R. Hartmann

Published Sep 17, 1979• 39 citations

Publisher

Abstract

We predict and observe the periodic reformation of spatial gratings in Na vapor commencing

\frac{\ensuremath{\tau}}{2}

after the application of the second of two resonant (

\ensuremath{\lambda}=5896

\AA{}) standing-wave excitation pulses which are themselves separated by

\ensuremath{\tau}

. These gratings have spatial periodicity

\frac{\ensuremath{\lambda}}{2}

, and backscatter our laser. One set of alternate echoes relaxes because of velocity-changing collisions; phase-changing collisions play no role. The other set is amplitude modulated with laser detuning

\ensuremath{\Delta}

cos\ensuremath{\Delta}\ensuremath{\tau}

DOI: 10.1103/physrevlett.43.851

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Optics CommunicationsMay 1, 19814 citations

We predict and observe the periodic reformation of spatial gratings in Na vapor commencing

\frac{\ensuremath{\tau}}{2}

after the application of the second of two resonant (

\ensuremath{\lambda}=5896

\AA{}) standing-wave excitation pulses which are themselves separated by

\ensuremath{\tau}

. These gratings have spatial periodicity

\frac{\ensuremath{\lambda}}{2}

\ensuremath{\Delta}

cos\ensuremath{\Delta}\ensuremath{\tau}

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.

t=0

and

t=T

to diffract and recombine momentum states separated by $2\ensuremath{\hbar}k$ at

t=2T

. Matter wave interference is associated with the formation of a density grating with period $\ensuremath{\lambda}/2$ in the vicinity of this echo time. The grating contrast is measured by recording the intensity of coherently backscattered light. The interferometer is perturbed by an additional pulse applied at $t=2T\ensuremath{-}\ensuremath{\delta}T$ or by continuous-wave background light. If the additional pulse is a standing wave, the momentum states interfering at

t=2T

are displaced and the grating contrast can be completely recovered due to constructive interference. In this case, the contrast shows a periodic modulation at the atomic recoil frequency as a function of $\ensuremath{\delta}T$. In a recent work, it was shown that the atomic recoil frequency can be measured easily and precisely when using coherence functions to model the signal shape. This paper provides an alternative description of the signal shape through an analytical calculation of echo formation in the presence of an additional standing-wave pulse. Using this treatment, it is possible to model the effects of spontaneous emission and spatial profile of the laser beam on the signal shape. Additionally, the theory predicts scaling laws as a function of the pulse area and the number of additional standing-wave pulses. These scaling laws are investigated experimentally and can be exploited to improve precision measurements of the atomic recoil frequency. We also show that coherence functions can be used to make a direct measurement of the populations of momentum states associated with the ground state under conditions where the Doppler-broadened velocity distribution of the sample is much larger than the recoil velocity. These measurements are consistent with Monte Carlo wave-function simulations. If the additional pulse is a traveling wave, we find that the grating contrast measured as a function of $\ensuremath{\delta}T$ can be modeled by a quasiperiodic coherence function as in previous experiments that utilized atomic beams. In this work, we investigate the dependence of the photon scattering rate on the intensity and detuning of the traveling wave. We also study the effects of perturbing the interferometer with continuous-wave light and find that the dependence of the photon scattering rate on the intensity and detuning of the perturbing field is consistent with expectations.

{n}_{1}

and

{n}_{2}

are positive integers and T is the pulse duration in the atomic rest frame, the atom-field interaction results in the creation of atom amplitude and phase gratings having period $\ensuremath{\lambda}/[{2(n}_{1}{+n}_{2})].$ In this manner, one can use optical fields having wavelength \ensuremath{\lambda} to produce atom gratings having periodicity much less than \ensuremath{\lambda}.

F=3

ground state in Doppler broadened

{}^{85}\mathrm{Rb}

vapor. The rephasing results in a magnetic grating echo whose duration is an accurate measure of the velocity distribution. We demonstrate that the time scale of the experiment is determined solely by the transit time of atoms across the laser beam. The shortening of the lifetime due to a perturber (Ar) allows us to infer the Rb-Ar velocity changing collision cross section.