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arXiv:quant-ph/9803022 · Physical Review A

Effects of atomic diffraction on the collective atomic recoil laser

M. G. Moore, Pierre Meystre

Published Oct 1, 1998• 54 citations
arXivHTMLPDF

Abstract

We formulate a wave-atom-optics theory of the collective atomic recoil laser (CARL) where the atomic center-of-mass motion is treated quantum mechanically. By comparing the predictions of this theory with those of the ray-atom-optics theory, which treats the center-of-mass atomic motion classically, we show that for the case of a far off-resonant pump laser the ray-optics model fails to predict the linear response of the CARL when the temperature is of the order of the recoil temperature or less. This is due to the fact that in this temperature regime one can no longer ignore the effects of matter-wave diffraction on the atomic center-of-mass motion.

DOI
10.1103/physreva.58.3248

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We present a wave atom optics theory of the Collective Atomic-Recoil Laser, where the atomic center-of-mass motion is treated quantum mechanically. It extends the previous ray atom optics theory, which treated the center-of-mass atomic motion classically, to the realm of ultracold atoms. For the case of a far off resonant pump laser we derive an analytical solution which gives the linear response of the CARL system for both the quantum and classical regimes. A linear stability analysis reveals significant qualitative differences between these two regimes, which arise from the effects of diffraction on the atomic center-of-mass motion.

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We formulate a wave-atom-optics theory of the collective atomic recoil laser (CARL) where the atomic center-of-mass motion is treated quantum mechanically. By comparing the predictions of this theory with those of the ray-atom-optics theory, which treats the center-of-mass atomic motion classically, we show that for the case of a far off-resonant pump laser the ray-optics model fails to predict the linear response of the CARL when the temperature is of the order of the recoil temperature or less. This is due to the fact that in this temperature regime one can no longer ignore the effects of matter-wave diffraction on the atomic center-of-mass motion.
We present a wave atom optics theory of the Collective Atomic-Recoil Laser, where the atomic center-of-mass motion is treated quantum mechanically. It extends the previous ray atom optics theory, which treated the center-of-mass atomic motion classically, to the realm of ultracold atoms. For the case of a far off resonant pump laser we derive an analytical solution which gives the linear response of the CARL system for both the quantum and classical regimes. A linear stability analysis reveals significant qualitative differences between these two regimes, which arise from the effects of diffraction on the atomic center-of-mass motion.
We perform a study of a collective atomic recoil laser (CARL) that goes beyond the initial growth period. The study is based on a theory that treats both internal and external degrees of atomic freedom quantum mechanically but regards the laser light as a classical field obeying Maxwell's equations. We introduce the concepts of momentum families and diffraction groups and organize the matter wave equations in terms of diffraction groups. The steady-state lasing conditions are discussed in connection with the probe gain in the recoil-induced resonances. The nontrivial steady states and the linear stability analysis of the steady states are both carried out by the method of two-dimensional continued fractions. Both stable and unstable nontrivial steady states are calculated and discussed in the context of regarding the CARL as multiwave mixing involving many modes of matter waves and two optical fields.
Summary form only given. The collective atomic recoil laser (CARL) was proposed as an atomic analog of the free electron laser. Recently, there has been an increased interest in the CARL primarily because it can be regarded as a parametric amplifier for the momentum side modes. Our CARL model consists of a cavity CARL signal of wave number k/sub 1/, and an opposing non-depletion pump field of k/sub 2/, and a steady flow of an ultra-cold two-level atomic beam along a direction normal to the propagation of the fields. Both fields are assumed to be far-off resonance. A momentum change of /spl planck/K, where K = k/sub 1/ + k/sub 2/, takes place in each virtual two-photon process. This allows us to divide the total momentum space into different momentum families, and each momentum family into different diffraction groups.
We experimentally investigate cold thermal atoms in a single sidedly pumped optical ring resonator for temperatures between 0.4 and $9\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{K}$. The threshold for collective atomic recoil lasing (CARL) is recorded for various pump-cavity detunings. The resulting stability diagram is interpreted by simulating the classical CARL equations. We find that the stability diagram for thermal atoms shows the same asymmetry as observed for Bose-Einstein condensates in previous experiments. Whereas for condensates the asymmetry is well explained by a Dicke-type quantum model we here discuss a simplified classical model. It complements the quantum model and provides an intuitive explanation based on the change in the long-range atomic interaction with pump-cavity detuning.
We present a theoretical study of the interaction between light and a cold gasof three-level, ladder configuration atoms close to two-photon resonance. In particular, weinvestigate the existence of collective atomic recoil lasing (CARL) instabilities in differentregimes of internal atomic excitation and compare to previous studies of the CARL instabilityinvolving two-level atoms. In the case of two-level atoms, the CARL instability is quenchedat high pump rates with significant atomic excitation by saturation of the (one-photon)coherence, which produces the optical forces responsible for the instability and rapid heatingdue to high spontaneous emission rates. We show that in the two-photon CARL schemestudied here involving three-level atoms, CARL instabilities can survive at high pump rateswhen the atoms have significant excitation, due to the contributions to the optical forces frommultiple coherences and the reduction of spontaneous emission due to transitions betweenthe populated states being dipole forbidden. This two-photon CARL scheme may form thebasis of methods to increase the effective nonlinear optical response of cold atomic gases.