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arXiv:0812.1209 · Physical Review A

Transient dynamics and momentum redistribution in cold atoms via recoil-induced resonances

Joel A. Greenberg, Daniel J. Gauthier

Published Mar 24, 2009• 8 citations
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Abstract

We use an optically dense anisotropic magneto-optical trap to study recoil-induced resonances (RIRs) in the transient high-gain regime. We find that two distinct mechanisms govern the atomic dynamics: the finite, frequency-dependent atomic response time and momentum-space population redistribution. At low input probe intensities, the residual Doppler width of the atoms, combined with the finite atomic response time, result in a linear transient hysteretic effect that modifies the locations, widths, and magnitudes of the resulting gain spectra depending on the sign of the scan chirp. When larger intensities (i.e., greater than a few $\ensuremath{\mu}\text{W}/{\text{cm}}^{2}$) are incident on the atomic sample for several $\ensuremath{\mu}\text{s}$, hole burning in the atomic sample momentum distribution leads to a coherent population redistribution that persists for approximately $100\text{ }\ensuremath{\mu}\text{s}$. We propose using RIRs to engineer the atomic momentum distribution to enhance the nonlinear atom-photon coupling. We present a numerical model and compare the calculated and experimental results to verify our interpretation.

DOI
10.1103/physreva.79.033414

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arXiv:physics/9809002•Physical Review A•Jan 1, 1999•42 citations
We use an optically dense anisotropic magneto-optical trap to study recoil-induced resonances (RIRs) in the transient high-gain regime. We find that two distinct mechanisms govern the atomic dynamics: the finite, frequency-dependent atomic response time and momentum-space population redistribution. At low input probe intensities, the residual Doppler width of the atoms, combined with the finite atomic response time, result in a linear transient hysteretic effect that modifies the locations, widths, and magnitudes of the resulting gain spectra depending on the sign of the scan chirp. When larger intensities (i.e., greater than a few \ensuremathμW/cm2\ensuremath{\mu}\text{W}/{\text{cm}}^{2}\ensuremathμW/cm2) are incident on the atomic sample for several \ensuremathμs\ensuremath{\mu}\text{s}\ensuremathμs, hole burning in the atomic sample momentum distribution leads to a coherent population redistribution that persists for approximately 100 \ensuremathμs100\text{ }\ensuremath{\mu}\text{s}100 \ensuremathμs. We propose using RIRs to engineer the atomic momentum distribution to enhance the nonlinear atom-photon coupling. We present a numerical model and compare the calculated and experimental results to verify our interpretation.
Summary form only given. Recent advances in laser cooling and trapping have led to a growing interest in laser spectroscopy in cold atomic samples. Examples include the work of Guo et al. and Courtois et al. about the recoil-induced resonance, and Bonifacio et al. and Moore et al. about the collective-atomic-recoil lasers (CARL). At the heart of these applications is the atomic recoil by photon absorption and emission. In the work, we explore a recoil-related phenomenon: hole burning resulting from the momentum redistribution of atoms by spontaneous emission, and its possible application in the precision spectroscopy. In the traditional saturation spectroscopy, the hole in the Doppler profile is created by laser excitation of atoms from the ground to the excited level. By contrast, the hole, is produced by removing the atoms in the velocity group, where the hole is burned, into the neighboring velocity groups of the same ground level. This process is accomplished through optical pumping and momentum redistribution by spontaneous emission. As a result, the requirement on the intensities of the driving laser fields is low, limited only by the interaction time. This is in contrast to the traditional saturation spectroscopy where the driving laser intensity has to be comparable to the saturation intensity determined by the decay rate of the excited level.
In this paper we report on the first purely ``pump-probe'' nonlinear laser spectroscopy results in a slow atomic beam. We have observed Raman, Rayleigh, and recoil-induced resonances (RIR) in a continuous beam of slow and cold cesium atoms extracted from a two-dimensional (2D) magneto-optical-trap (MOT) with the moving molasses technique. The RIR enabled us to measure the velocity distribution, therefore the average speed (0.6--4 m/s) and temperature (50--500 \ensuremath{\mu}K) of the atomic beam. Compared to time of flight, this technique has the advantage of being local, more sensitive in the low-velocity regime (v<1m/s),(v<1 \mathrm{m}/\mathrm{s}),(v<1m/s), and it gives access to transverse velocities and temperatures. Moreover, it may be extended to measure atomic velocities in the 2D MOT source of the atomic beam.
Recoil-induced resonances (RIR) can be detected in experiments involving light-atom interaction where atomic external degrees of freedom play an important role. In pump-probe experiments the recoil of atoms due to absorption and emission of radiation is responsible for the amplification and attenuation of the probe beam under certain circumstances, resulting in a disperse and narrow (of the order of 10 kHz) feature in the spectrum of the probe beam. Backward four-wave mixing (BFWM) signals, via recoil-induced resonances, using cold atoms as nonlinear medium were also extensively studied during the past years. In this work it will be presented a systematic study of forward four-wave mixing (FFWM) via RIR. It will be also presented a simple theoretical model that allowed us to predict the lineshapes of the observed signals and to better understand the phenomenon studied. The model is also compared with results that are already known in order to verify its validity and predict the possibility of measure the velocity distribution of the atomic cloud in a future experiment.
In this paper we report an experiment on the observation of the recoil-induced resonances (RIR) and electromagnetically induced absorption (EIA) of cold 87Rb^{87}\text{R}\text{b}87Rb atoms in diffuse light. The pump light of the RIR and the EIA comes from the diffuse light in an integrating sphere, which also serves the cooling light. We measured the RIR and the EIA signal varying with the detuning of the diffuse laser light, and also measured the number and the temperature of the cold atoms at the different detunings. The mechanism of RIR and EIA in the configuration with diffuse-light pumping and laser probing are discussed, and the difference between the nonlinear spectra of cold atoms in a diffuse-light cooling system and in a magneto-optical trap is studied.
We present experimental observation of recoil-induced resonance (RIR) in an operating cesium magneto-optical trap (MOT) by both pump–probe absorption and four-wave mixing spectra simultaneously. We investigate the dependence of amplitudes of these two spectra on pump beam intensity and frequency. The measurement results agree well with the recoil-induced theory with modifications of Raman transition effect and atomic number. The systematical study on RIR spectra is meaningful for the diagnostic measurement of cold atoms in an operating MOT.
The theories of recoil-induced resonances (RIR) [J. Guo, P. R. Berman, B. Dubetsky, and G. Grynberg, Phys. Rev. A 46, 1426 (1992)] and the collective atomic recoil laser (CARL) [R. Bonifacio and L. De Salvo, Nucl. Instrum. Methods Phys. Res. A 341, 360 (1994)] are compared. Both theories can be used to derive expressions for the gain experienced by a probe field interacting with an ensemble of two-level atoms that are simultaneously driven by a pump field. It is shown that the underlying formalisms of the RIR and CARL are equivalent. Differences between the RIR and CARL arise because the theories are typically applied for different ranges of the parameters appearing in the theory. The RIR limit is one in which the time derivative of the probe field amplitude, dE2/dt,{\mathrm{dE}}_{2}/dt,dE2​/dt, depends locally on E2(t){E}_{2}(t)E2​(t) and the gain depends linearly on the atomic density, while the CARL limit is one in which ${\mathrm{dE}}_{2}/dt={\ensuremath{\int}}_{0}^{t}{f(t,t}^{\ensuremath{'}}{)E}_{2}{(t}^{\ensuremath{'}}{)dt}^{\ensuremath{'}},$ where f is a kernel, and the gain has a nonlinear dependence on the atomic density. Validity conditions for the RIR or CARL limits are established in terms of the various parameters characterizing the atom-field interaction. The probe gain for a probe-pump detuning equal to zero is analyzed in some detail, in order to understand how gain arises in a system which, at first glance, appears to have a symmetry that would preclude the possibility for gain. Moreover, it is shown that these calculations, carried out in perturbation theory, have a range of applicability beyond the recoil problem. Experimental possibilities for observing CARL are discussed.