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arXiv:1906.02000 · Physical Review A

Multimode collective scattering of light in free space by a cold atomic gas

R. Ayllon, José Tito Mendonça, Angel T. Gisbert, N. Piovella, Gordon R. M. Robb

Published Aug 30, 2019• 8 citations
arXivHTMLPDF

Abstract

We have studied collective recoil lasing by a cold atomic gas, scattering photons from an incident laser into many radiation modes in free space. The model consists of a system of classical equations for the atomic motion of $N$ atoms where the radiation field has been adiabatically eliminated. We performed numerical simulations using a molecular dynamics code pepc (Pretty Efficient Parallel Coulomb Solver) to track the trajectories of the atoms. These simulations show the formation of an atomic density grating and collective enhancement of scattered light, both of which are sensitive to the shape and orientation of the atomic cloud. In the case of an initially circular cloud, the dynamical evolution of the cloud shape plays an important role in the development of the density grating and collective scattering. The ability to use efficient molecular dynamics codes will be a useful tool for the study of the multimode interaction between light and cold gases.

DOI
10.1103/physreva.100.023630

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We have studied collective recoil lasing by a cold atomic gas, scattering photons from an incident laser into many radiation modes in free space. The model consists of a system of classical equations for the atomic motion of NNN atoms where the radiation field has been adiabatically eliminated. We performed numerical simulations using a molecular dynamics code pepc (Pretty Efficient Parallel Coulomb Solver) to track the trajectories of the atoms. These simulations show the formation of an atomic density grating and collective enhancement of scattered light, both of which are sensitive to the shape and orientation of the atomic cloud. In the case of an initially circular cloud, the dynamical evolution of the cloud shape plays an important role in the development of the density grating and collective scattering. The ability to use efficient molecular dynamics codes will be a useful tool for the study of the multimode interaction between light and cold gases.
Cold atomic clouds in collective atomic recoil lasing are usually confined by an optical cavity, which forces the light-scattering to befall in the mode fixed by the resonator. Here we consider the system to be in free space, which leads into a vacuum multimode collective scattering. We show that the presence of an optical cavity is not always necessary to achieve coherent collective emission by the atomic ensemble and that a preferred scattering path arises along the major axis of the atomic cloud. We derive a full vectorial model for multimode collective atomic recoil lasing in free space. Such a model consists of multi-particle equations capable of describing the motion of each atom in a 2D/3D cloud. These equations are numerically solved by means of molecular dynamic algorithms, usually employed in other scientific fields. The numerical results show that both atomic density and collective scattering patterns are applicable to the cloud’s orientation and shape and to the polarization of the incident light.
We analyze the collective light scattering by cold atoms in free space of a pump-laser beam possessing orbital angular momentum. We derive a set of coupled multiparticle equations for the atomic motion in which the vacuum-mode field is adiabatically eliminated. The resulting equations describe collective recoil as due to either transfer of linear momentum or orbital angular momentum. For a transverse annular atomic distribution the initial equilibrium with uniform atomic phases and no scattered field is unstable. The atoms are set in rotation and bunched in phase at different harmonics depending on the pump azimuthal index $\ensuremath{\ell}$ and on the ring radius.
Collective scattering of light due to atomic recoil, also known as collective atomic recoil lasing (CARL), occurs when a gas of atoms coherently scatters light from a pump laser via a collective instability. The scattering process can become unstable due to the atoms in the gas recoiling under the influence of the dynamic optical forces which arise due to the interference of the pump and scattered fields. The atoms move to form a spatially periodic density grating, which in turn amplifies the scattered field. This paper presents a theoretical analysis of CARL phenomena in degenerate ultracold gases of bosons and fermions. In the case of bosons i.e. in a Bose-Einstein Condensate (BEC),the effect of atom-atom interactions due to collisions on the CARL instability in the case of both attractive and repulsive condensates, is investigated. In the case of fermionic gases, the effect of Fermi pressure, is also presented. The linear and nonlinear evolution of the optical field and the atomic momentum distribution are considered for both cases.
A semi-classical theory of coherent light scattering from an elongated sample of cold atoms exposed to an off-resonant laser beam is presented. The model, which is a direct extension of that of the collective atomic recoil laser (CARL), describes the emission of two superradiant pulses along the sample's major axis simultaneous with the formation of a bidimensional atomic grating inside the sample. It provides a simple physical picture of the recent observation of collective light scattering from a Bose-Einstein condensate [S. Inouye et al., Science N.285, p. 571 (1999)]. In addition, the model provides an analytical description of the temporal evolution of the scattered light intensity which shows good quantitative agreement with the experimental results of Inouye et al.
Cold atoms in optical high‐Q cavities are an ideal model system for long‐range interacting particles. The position of two arbitrary atoms is, independent on their distance, coupled by the back‐scattering of photons within the cavity. This mutual coupling can lead to collective instability and self‐organization of a cloud of cold atoms interacting with the cavity fields. This phenomenon (CARL, i.e. Collective Atomic Recoil Lasing) has been discussed theoretically for years, but was observed only recently in our lab. The CARL‐effect is closely linked to superradiant Rayleigh scattering, which has been intensely studied with Bose‐Einstein condensates in free space. By adding a resonator the coherence time of the system, in which the instability occurs, can be strongly enhanced. This enables us to observe cavity‐enhanced superradiance with both Bose‐Einstein condensates and thermal clouds and allows us to close the discussion about the role of quantum statistics in superradiant scattering.
We report on the observation of collective atomic recoil lasing and superradiant Rayleigh scattering with ultracold and Bose-Einstein condensed atoms in an optical ring cavity. Both phenomena are based on instabilities evoked by the collective interaction of light with cold atomic gases. This publication clarifies the link between the two effects. The observation of superradiant behavior with thermal clouds as hot as several tens of $\ensuremath{\mu}\mathrm{K}$ proves that the phenomena are driven by the cooperative dynamics of the atoms, which is strongly enhanced by the presence of the ring cavity.