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Journal of Modern Optics

Optical gratings in the collective interaction between radiation and atoms, including recoil and collisions

M. Perrin, Gian Luca Lippi, Antonio Politi

Published Mar 1, 2002• 9 citations
Publisher

Abstract

The introduction of collisions and of a thermal distribution for the atomic momentum in the model for the Collective Atomic Recoil Laser (CARL) is at the origin of important modifications in the interpretation of the mechanisms that give rise to the amplification of the backreflected wave. It is shown that the atomic density grating, considered to be the cause of gain in CARL, disappears in the presence of collisions, while other gratings—in population and polarization phase—survive. While the population grating appears to be merely a consequence of the collective interaction, the latter is the likely cause for the instability. Finally, simulations show that models that make use of an exponential relaxation mechanism for the atomic momentum,rather than accounting for collisions explicitly, largely overestimate the strength of the interaction.

DOI
10.1080/09500340110087651

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The introduction of collisions and of a thermal distribution for the atomic momentum in the model for the Collective Atomic Recoil Laser (CARL) is at the origin of important modifications in the interpretation of the mechanisms that give rise to the amplification of the backreflected wave. It is shown that the atomic density grating, considered to be the cause of gain in CARL, disappears in the presence of collisions, while other gratings—in population and polarization phase—survive. While the population grating appears to be merely a consequence of the collective interaction, the latter is the likely cause for the instability. Finally, simulations show that models that make use of an exponential relaxation mechanism for the atomic momentum,rather than accounting for collisions explicitly, largely overestimate the strength of the interaction.
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.
An ensemble of periodically ordered atoms coherently scatters the light of an incident laser beam. The scattered and the incident light may interfere and give rise to a light intensity modulation and thus to optical dipole forces which, in turn, emphasize the atomic ordering. This positive feedback is at the origin of the collective atomic recoil laser (CARL). We demonstrate this dynamics using ultracold atoms confined by dipole forces in a unidirectionally pumped far red‐detuned high‐finesse optical ring cavity. Under the influence of an additional dissipative force exerted by an optical molasses the atoms, starting from an unordered distribution, spontaneously form a density grating moving at constant velocity. Additionally, steady state lasing is observed in the reverse direction if the pump laser power exceeds a certain threshold. We compare the dynamics of the atomic trajectories to the behavior of globally coupled oscillators, which exhibit phase transitions from incoherent to coherent states if the coupling strength exceeds a critical value.
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 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.