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Atoms

Classical and Quantum Collective Recoil Lasing: A Tutorial

N. Piovella, Angel T. Gisbert, Gordon R. M. Robb

Published Jul 6, 2021• 2 citations
Publisher

Abstract

Collective atomic recoil lasing (CARL) is a process during which an ensemble of cold atoms, driven by a far-detuned laser beam, spontaneously organize themselves in periodic structures on the scale of the optical wavelength. The principle was envisaged by R. Bonifacio in 1994 and, ten years later, observed in a series of experiments in Tübingen by C. Zimmermann and colleagues. Here, we review the basic model of CARL in the classical and in the quantum regime.

DOI
10.3390/atoms9030040

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Quantum Electronics and Laser Science Conference•Nov 13, 2002•0 citations
Collective atomic recoil lasing (CARL) is a process during which an ensemble of cold atoms, driven by a far-detuned laser beam, spontaneously organize themselves in periodic structures on the scale of the optical wavelength. The principle was envisaged by R. Bonifacio in 1994 and, ten years later, observed in a series of experiments in Tübingen by C. Zimmermann and colleagues. Here, we review the basic model of CARL in the classical and in the quantum regime.
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.
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 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.
A cloud of ultra-cold atoms is loaded into the attractive potential of a light wave that is generated by two counter-propagating modes of a high-finesse ring resonator. The two modes are coupled by the atoms due to coherent Rayleigh scattering and generate a potential which acts back on the motion of the atoms. This feedback leads to a new frequency component and can be described in terms of the long time proposed collective atomic recoil laser (CARL). This model is investigated experimentally and extended by introducing an optical friction force acting on the atoms. This allows for steady state operation of the CARL. Furthermore, it leads to a threshold behaviour of the CARL that translates into a novel type of phase transition: while passing the threshold the initially homogeneous atomic distribution is bunched in space and velocity. With this behaviour the system turns out to acquire some of the main features of the so-called Kuramoto model which provides a very general description of a network of limit cycle oscillators.
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.