A quantum model for collective recoil lasing

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 Schr\"{o}dinger equation coupled to a self-consistent radiation field. The model depends on a single collective parameter $\bar \rho$ which represents the maximum number of photons emitted per particle. We demonstrate that the classical model is recovered in the limit $\bar \rho\gg 1$, in which the Wigner function associated to the Schr\"{o}dinger equation obeys to the classical Vlasov equation. On the contrary, for $\bar \rho\le 1$, 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

Controlled generation of momentum states in a high-finesse ring cavity

A Bose-Einstein condensate in a high-finesse ring cavity scatters the photons of a pump beam into counterpropagating cavity modes, populating a bi-dimensional momentum lattice. A high-finesse ring cavity with a sub-recoil linewidth allows to control the quantized atomic motion, selecting particular discrete momentum states and generating atom-photon entanglement. The semiclassical and quantum model for the 2D collective atomic recoil lasing (CARL) are derived and the superradiant and good-cavity regimes discussed. For pump incidence perpendicular to the cavity axis, the momentum lattice is symmetrically populated. Conversely, for oblique pump incidence the motion along the two recoil directions is unbalanced and different momentum states can be populated on demand by tuning the pump frequency.Comment: Submitted to EPJ-ST Special Issue. 10 pages and 3 figure

Quantum optics in the phase space - A tutorial on Gaussian states

In this tutorial, we introduce the basic concepts and mathematical tools needed for phase-space description of a very common class of states, whose phase properties are described by Gaussian Wigner functions: the Gaussian states. In particular, we address their manipulation, evolution and characterization in view of their application to quantum information.Comment: Tutorial. 23 pages, 1 figure. Updated version accepted for publication in EPJ - ST devoted to the memory of Federico Casagrand

Propagation effects in the quantum description of collective recoil lasing

The free electron laser and collective atomic recoil laser (CARL) are examples of collective recoil lasing, where exponential amplification of a radiation field occurs simultaneously with self-bunching of an ensemble of particles (electrons in the case of the FEL and atoms in the case of the CARL). In this paper, we discuss quantum and propagation effects using a model where the particle dynamics are described quantum-mechanically in terms of a matter-wave field, which evolves self-consistently with the radiation field. The model shows that the scattered radiation evolves superradiantly both in the case where the particle ensemble is short compared to the cooperation length of the system, and where the ensemble is long compared to the cooperation length. In both short and long pulse cases there exist a classical and quantum regime of superradiant emission. For short samples in both quantum and classical regimes the superradiant pulse has a low peak intensity and is said to exhibit `weak' superradiance. For long pulses in both quantum and classical regimes of evolution, the dynamics at the rear edge of the sample is dominated by propagation. This produces a,strong' superradiant pulse with much higher peak intensity than that predicted by `mean-field' or `steady-state' models in which propagation effects are neglected. (c) 2005 Elsevier B.V. All rights reserved

Experimental requirements for X-ray compact free electron lasers with a laser wiggler

In this paper we specify the experimental parameters required to operate a Free Electron Laser with a laser wiggler in the Angstrom region. Both the quantum and the classical regimes are discussed. The quantum regime of SASE can be reached with more realistic parameters than the classical one. The fundamental feature of the quantum SASE is the extremely narrow single-line radiation spectrum, whose line width can be four orders of magnitude smaller than the bandwidth of the classical spiky SASE spectrum

A condensate in a lossy cavity: Collective atomic recoil and generation of entanglement

The interaction between a Bose-Einstein condensate and a single-mode quantized radiation field in the presence of a strong far-off-resonant pump laser generates, in proper regimes, atom-atom and atom-field entanglement. The effects of cavity losses are taken into account and an analytic solution of the corresponding master equation is given in terms of the Wigner function of the system

Entanglement in a Bose-Einstein condensate by collective atomic recoil

We address the interaction between a Bose-Einstein condensate and a single-mode quantized radiation field in the presence of a strong far off-resonant pump laser. The generation of atom-atom and atom-field entanglement is demonstrated in the linear regime. The effects of cavity losses are taken into account and an analytic solution of the corresponding master equation is given in terms of the Wigner function of the system

Three-dimensional free electron laser numerical simulations for a laser wiggler in the quantum regime

A compact tunable source of soft X-rays could be realized combining a state-of-the-art electron source with an intense counter-propagating laser pulse. If the source is operated in the quantum regime, the theoretical model predicts high monochromaticity (single-spike) and unprecedented temporal coherence for the emitted radiation. Here we present numerical simulations of the complete quantum model for an Free Electron Laser (FEL) with a laser wiggler in three spatial dimensions, based on a discrete Wigner function formalism taking into account the longitudinal momentum quantization. The numerical model includes the complete spatial and temporal evolution of the electron and radiation beams, with an explicit description of diffraction, propagation, laser wiggler profile and emittance effects. The contribution of each interaction term is studied independently, and the 3D results are contrasted with the 1D quantum FEL model neglecting transverse effects. Finally the parameter space for possible experiments is characterized, and a particular experimental case is discussed in detail

3D Wigner model for a quantum free electron laser with a laser wiggler

A three dimensional, time dependent, quantum model for an FEL with a laser wiggler, based on a discrete Wigner function formalism taking into account the longitudinal momentum quantization, is presented. Starting from the exact quantum treatment, a motion equation for the Wigner function coupled to the self-consistent radiation field is derived in the realistic limit in which the normalized electron beam emittance is much larger than the Compton wavelength quantum limit. The model describes the three-dimensional spatial and temporal evolution of the electron and radiation beams, including diffraction, propagation, laser wiggler, emittance and quantum recoil effects. It can be solved numerically and reduces to the three-dimensional Maxwell-VIasov model in the classical limit. We discuss the experimental requirements for a quantum X-ray FEL with a laser wiggler, presenting preliminary numerical results and parameters for a possible future experiment

Three-dimensional free electron laser numerical simulations for a laser wiggler in the quantum regime

A compact tunable source of soft X-rays could be realized combining a state-of-the-art electron source with an intense counter-propagating laser pulse. If the source is operated in the quantum regime, the theoretical model predicts high monochromaticity (single-spike) and unprecedented temporal coherence for the emitted radiation. Here we present numerical simulations of the complete quantum model for an Free Electron Laser (FEL) with a laser wiggler in three spatial dimensions, based on a discrete Wigner function formalism taking into account the longitudinal momentum quantization. The numerical model includes the complete spatial and temporal evolution of the electron and radiation beams, with an explicit description of diffraction, propagation, laser wiggler profile and emittance effects. The contribution of each interaction term is studied independently, and the 3D results are contrasted with the 1D quantum FEL model neglecting transverse effects. Finally the parameter space for possible experiments is characterized, and a particular experimental case is discussed in detail. (c) 2008 Elsevier B.V. All rights reserved