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Physical Review A

Propagation, cavity, and Doppler-broadening effects in the collective atomic recoil laser

R. Bonifacio, Gordon R. M. Robb, Brian W J McNeil

Published Jul 1, 1997• 47 citations
Publisher

Abstract

Using a completely semiclassical approach we extend a previous theory of the collective atomic recoil laser to include propagation effects with and without a ring cavity, and to take into account the effects of Doppler broadening. For cold atoms, we determine a mean-field condition under which propagation effects are negligible, and find different dynamical regimes that we classify as ``good'' and ``bad'' cavity limits. We obtain the results of a previous single-mode theory only in the good cavity limit. In the bad cavity limit or in free space collective superradiant behavior dominates. For warm beams, where Doppler-broadening effects are important, a noncollective Raman gain mechanism dominates in general, as recently observed experimentally. The effects of particle trapping in the ponderomotive potential and radiation pressure have been described.

DOI
10.1103/physreva.56.912

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Using a completely semiclassical approach we extend a previous theory of the collective atomic recoil laser to include propagation effects with and without a ring cavity, and to take into account the effects of Doppler broadening. For cold atoms, we determine a mean-field condition under which propagation effects are negligible, and find different dynamical regimes that we classify as good'' and bad'' cavity limits. We obtain the results of a previous single-mode theory only in the good cavity limit. In the bad cavity limit or in free space collective superradiant behavior dominates. For warm beams, where Doppler-broadening effects are important, a noncollective Raman gain mechanism dominates in general, as recently observed experimentally. The effects of particle trapping in the ponderomotive potential and radiation pressure have been described.
We demonstrate that superradiance and collective atomic recoil lasing from cold atoms can be enhanced using a two-frequency pump with frequency difference twice the two-photon recoil frequency ${\ensuremath{\omega}}_{r}$. In the good-cavity regime the atoms behave as a three-recoil-level system, collectively scattering a single-frequency radiation mode. In the bad-cavity regime, the superradiant cascade through the different recoil momentum states is strongly accelerated. The emitted radiation shows a discrete spectrum whose harmonics are separated by $2{\ensuremath{\omega}}_{r}$ and generated by transitions between adjacent momentum levels.
We present a microscopic laser model for many atoms coupled to a single-cavity mode, including the light forces, which result from atom-field momentum exchange. Within a semiclassical description, we solve the equations for the atomic motion and the internal dynamics to obtain analytic expressions for the optical potential and the friction force seen by each atom. When optical gain is maximum at frequencies where the light field extracts kinetic energy from the atomic motion, the dynamics combines optical lasing and motional cooling. From the corresponding momentum-diffusion coefficient we predict sub-Doppler temperatures in the stationary state. This generalizes the theory of cavity-enhanced laser cooling to active cavity systems. We identify the gain-induced reduction of the effective resonator linewidth as the key origin for the faster cooling and the lower temperatures, which implies that a bad cavity with a gain medium can replace a high-QQQ cavity. In addition, this shows the importance of light forces for gas lasers in the low-temperature limit, where atoms can arrange in a periodic pattern maximizing gain and counteracting spatial hole burning. Ultimately, in the low-temperature limit, such a setup should allow us to combine optical lasing and atom lasing in a single device.
We experimentally study the relaxation oscillations and amplitude stability properties of an optical laser operating deep into the bad-cavity regime using a laser-cooled ^{87}Rb Raman laser. By combining measurements of the laser light field with nondemolition measurements of the atomic populations, we infer the response of the gain medium represented by a collective atomic Bloch vector. The results are qualitatively explained with a simple model. Measurements and theory are extended to include the effect of intermediate repumping states on the closed-loop stability of the oscillator and the role of cavity feedback on stabilizing or enhancing relaxation oscillations. This experimental study of the stability of an optical laser operating deep into the bad-cavity regime will guide future development of superradiant lasers with ultranarrow linewidths.
We study the five semiclassical laser equations in the mean-field limit for the simple model of two-level atoms with homogeneous broadening in a single-mode unidirectional ring cavity, taking into account detuning between atomic and cavity frequencies. Our analysis concentrates on the properties of the laser at and beyond the second thresh-old in the bad-cavity case. We first show that the position of the second threshold depends on the excitation mechanism: When the pump parameter is increased either adiabatically or abruptly, two different thresholds occur. The sequence of periodic and chaotic solutions beyond the second threshold is then discussed as a function of the detuning and the pump parameter.
We observe the buildup of a frequency-shifted reverse light field in a unidirectionally pumped high-Q optical ring cavity serving as a dipole trap for cold atoms. This effect is enhanced and a steady state is reached, if via an optical molasses an additional friction force is applied to the atoms. We observe the displacement of the atoms accelerated by momentum transfer in the backscattering process and interpret our observations in terms of the collective atomic recoil laser. Numerical simulations are in good agreement with the experimental results.