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Physical Review A

Grating stimulated echo

B. Dubetsky, P. R. Berman, Tycho Sleator

Published Sep 1, 1992• 11 citations
Publisher

Abstract

A theory of a grating simulated echo (GTE) is developed. The GSE involves the sequential excitation of atoms by two counterpropagating traveling waves, a standing wave, and a third traveling wave. It is shown that the echo signal is very sensitive to small changes in atomic velocity, much more sensitive than the normal stimulated echo. Use of the GSE as a collisional probe or accelerometer is discussed.

DOI
10.1103/physreva.46.r2213

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Physical Review A•Feb 13, 2009•12 citations
A theory of a grating simulated echo (GTE) is developed. The GSE involves the sequential excitation of atoms by two counterpropagating traveling waves, a standing wave, and a third traveling wave. It is shown that the echo signal is very sensitive to small changes in atomic velocity, much more sensitive than the normal stimulated echo. Use of the GSE as a collisional probe or accelerometer is discussed.
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.
Precision measurements of gravitational acceleration g have far reaching applications in navigation and sensing as well as for tests of general relativity. Grating-echo atom interferometers (AIs) utilize simple setups and distinctive excitation schemes that involve a single excitation laser, and do not require velocity selection. They have demonstrated measurements of gravity precise to 75 parts per billion (ppb) by dropping laser-cooled atomic samples through ~ 1 cm. Here we describe progress toward realizing a cold atom gravimeter using an echo AI designed for drop heights of ~30 cm. The experimental technique involves illuminating the falling sample of laser-cooled rubidium atoms with two standing wave (sw) pulses separated by time t = T. The sw pulses are composed of two traveling-wave components, each having a wave vector of magnitude k = 2π/λ. Momentum state interference produces one-dimensional density gratings with a period λ/2 immediately after each excitation pulse. These gratings dephase due to the velocity distribution of the sample along the sw axis. The AI uses an echo technique to cancel the effect of velocity dephasing and observe a rephased density grating in the vicinity of the echo time τ = 2Τ. The grating contrast and phase are measured by coherently backscattering a traveling wave readout pulse from the sample. The grating phase, measured with respect to a vibrationally stabilized inertial reference frame, scales as 2kgΤ2. A drawback of echo AIs is the signal-to-noise ratio, which is limited by the contrast of the grating and systematic effects due the refractive index of the sample. Here, we review improvements to the experimental design and investigate methods of improving the signal-to-noise ratio by optimizing the atom-field coupling. We describe progress toward realizing our goals of increasing the grating contrast and the backscattered signal. The improved contrast is expected to allow the experiment to be carried out at a lower density to reduce corrections due to the refractive index. We discuss a variety of excitation schemes for achieving a target precision of a few ppb.
We have initiated a new class of coherent transient experiments with Doppler-broadened atoms confined in a vapor cell. A spatially modulated coherence is created between magnetic sublevels of the F=3 ground state of /sup 85/Rb by a standing pulse. This pulse consists of two opposite circularly polarized traveling waves with wave vectors K/sub 1/ and K/sub 2/ at a small angle /spl theta/. The coherence grating is probed by the application of a readout pulse along K/sub 2/. The resulting coherent emission along K/sub 1/ is detected by a heterodyne technique.
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.
The three pulse stimulated echo, long known in magnetic resonance (1), has more recently been demonstrated on optical transitions(2). An interesting way of looking at the stimulated-echo-formation relies on the fact that the first two excitation pulses create an "ordered" population as a function of detuning .This ordered population can also be looked upon as a " grating " in frequency space from which a probe pulse can "reflect" an echo. Since a grating in only one of the levels suffices, a corollary is that the echo may be stimulated at some entirely different frequency ω2 than the one ω1, at which the grating was prepared. We report the observation of such a connected two-color stimulated echo(C2CSE) in a solid and use it to confirm the relaxation out of the 747 cm−1 vibrational state of the S1 manifold of pentacene in naphthalene. It has also been realized (3) that after redistribution of the initially excited population grating, that the echo may be stimulated from any state into which the grating has relaxed. We report here the first observation of such a relaxed two-color stimulated echo(R2CSE) and note that this echo can be seen as the optical analogue of the cross-relaxation peak in a two-dimensional nmr spectrum. The rise and fall of this relaxed echo can be used as a probe for the vibrational deactivation pathway(s) subsequent to excitation of various vibrational levels in the S1 manifold. Prior to discussing briefly some of the results we note that from an analysis of this echo effect it is clear that a necessary prerequiste to observation of such two-color photon echoes is that the inhomogeneous broadening on the selected transitions is strongly correlated. Furthermore we note that in these echo effects interference with stimulated emission and super -fluorescence must be avoided by using small-angle excitation pulses. Some of the results are shown in Fig.1. In (A) the decay of the C2CSE is presented with the solid line being a fit to a population decay parameter of the 747 cm-1 level of 33 psec. In (B) the rise of the R2CSE is shown where the probe wavelength is at the pure electronic transition. The dashed line is the expected echo-intensity rise if the initially excited vibration would directly decay into the vibrationless state. The mismatch between the dashed curve and the experimental one shows that intermediate levels in the relaxation pathway must exist. The solid line in (B) is a fit to a model where one intermediate bottleneck level is assumed with a lifetime of 16±2 psec. Other examples will be presented at the meeting.
We have developed a technique for measuring the atomic recoil frequency using a single-state echo-type atom interferometer that manipulates laser-cooled atoms in the ground state. The interferometer relies on momentum-state interference due to two standing-wave pulses that produce density gratings. The interference is modified by applying a third standing-wave pulse during the interferometer pulse sequence. As a result, the grating contrast exhibits periodic revivals at the atomic recoil frequency ${\ensuremath{\omega}}_{r}$ as a function of the time at which the third pulse is applied, allowing ${\ensuremath{\omega}}_{r}$ to be measured easily and precisely. The contrast is accurately described by a coherence function, which is the Fourier transform of the momentum distribution, produced by the third pulse and by the theory of echo formation. If the third pulse is a traveling wave, loss of grating contrast is observed, an effect also described by a coherence function. The decay of the grating contrast as a function of continuous-wave light intensity is used to infer the cross section for photon absorption.