© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

arXiv:quant-ph/0407112 · Europhysics Letters (EPL)

A quantum model for collective recoil lasing

R. Bonifacio, Mary M. Cola, N. Piovella, Gordon R. M. Robb

Published Dec 7, 2004• 40 citations

Abstract

Free Electron Laser (FEL) and Collective Atomic Recoil Laser (CARL) are described by the same model of classical equations for properly defined scaled variables. These equations are extended to the quantum domain describing the particle's motion by a Schrödinger equation coupled to a self-consistent radiation field. The model depends on a single collective parameter which represents the maximum number of photons emitted per particle. We demonstrate that the classical model is recovered in the limit >> 1, in which the Wigner function associated to the Schrödinger equation obeys to the classical Vlasov equation. On the contrary, for ⩽ 1, a new quantum regime is obtained in which both FELs and CARLs behave as a two-state system coupled to the self-consistent radiation field and described by Maxwell-Bloch equations.

DOI: 10.1209/epl/i2004-10308-1

Related papers

Steady states and instabilities of collective atomic recoil laser

Hong Yuan Ling, Han Pu, Leslie O. Baksmaty +1 more

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.

Quantum Electronics and Laser Science Conference•Nov 13, 2002•0 citations

Theory of a collective atomic recoil laser

Hong Yuan Ling, Han Pu, Leslie O. Baksmaty +1 more

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.

Physical Review A•Apr 17, 2001•13 citations

Light Amplification in the Collective Atomic Recoil Laser(CARL)

Guojian Yang

We present a brief description of the collective atomic recoil laser, in contrast to the ordinary laser and free-electron laser. With a numerical solution to CARL equation, we reveal the amplification mechanism in CARL. Then we study the influence of some working parameters on CARL, which contributes to our later research.

Journal of Hunan University of Science and Engineering•Jan 1, 2005•0 citations

Classical and Quantum Collective Recoil Lasing: A Tutorial

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

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.

Atoms•Jul 6, 2021•2 citations

Collective atomic recoil lasing

Claus Zimmermann, Dietmar Kruse, C. von Cube +3 more

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.

Journal of Modern Optics•Apr 1, 2004•5 citations

Classical and quantum regimes in the collective atomic recoil laser from a Bose-Einstein condensate

N. Piovella, Mary M. Cola, R. Bonifacio

A collective atomic recoil laser (CARL) realized with a Bose-Einstein condensate offers the possibility to investigate new effects in the coherent interaction between optical and matter waves. This paper discusses some aspects of the nonlinear evolution of scattered radiation and the matter-wave field in the high-Q cavity and superradiant CARL regimes.

Journal of Modern Optics•Apr 1, 2004•1 citation

Free Electron Laser (FEL) and Collective Atomic Recoil Laser (CARL) are described by the same model of classical equations for properly defined scaled variables. These equations are extended to the quantum domain describing the particle's motion by a Schrödinger equation coupled to a self-consistent radiation field. The model depends on a single collective parameter which represents the maximum number of photons emitted per particle. We demonstrate that the classical model is recovered in the limit >> 1, in which the Wigner function associated to the Schrödinger equation obeys to the classical Vlasov equation. On the contrary, for ⩽ 1, a new quantum regime is obtained in which both FELs and CARLs behave as a two-state system coupled to the self-consistent radiation field and described by Maxwell-Bloch equations.

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.

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.