Four wave mixing with self-phase matching due to collective atomic recoil

We describe a method for non-degenerate four-wave mixing in a cold sample of 4-level atoms. An integral part of the four-wave mixing process is a collective instability which spontaneously generates a periodic density modulation in the cold atomic sample with a period equal to half of the wavelength of the generated high-frequency optical field. Due to the generation of this density modulation, phase-matching between the pump and scattered fields is not a necessary initial condition for this wave-mixing process to occur, rather the density modulation acts to "self phase-match" the fields during the course of the wave-mixing process. We describe a one-dimensional model of this process, and suggest a proof-of-principle experiment which would involve pumping a sample of cold Cs atoms with three infra-red pump fields to produce blue light.Comment: to appear in Physical Review Letter

The Semiclassical and Quantum Regimes of Superradiant Light Scattering from a Bose-Einstein Condensate

We show that many features of the recent experiments of Schneble et al. [D. Schneble, Y. Torii, M. Boyd, E.W. Streed, D.E. Pritchard and W. Ketterle, Science vol. 300, p. 475 (2003)], which demonstrate two different regimes of light scattering by a Bose-Einstein condensate, can be described using a one-dimensional mean-field quantum CARL model, where optical amplification occurs simultaneously with the production of a periodic density modulation in the atomic medium. The two regimes of light scattering observed in these experiments, originally described as ``Kapiza-Dirac scattering'' and ``Superradiant Rayleigh scattering'', can be interpreted as the semiclassical and quantum limits respectively of CARL lasing.Comment: 10 pages, 5 figures - to appear in Journal of Optics

Inducing strong density modulation with small energy dispersion in particle beams and the harmonic amplifier free electron laser

We present a possible method of inducing a periodic density modulation in a particle beam with little increase in the energy dispersion of the particles. The flow of particles in phase space does not obey Liouville's Theorem. The method relies upon the Kuramoto-like model of collective synchronism found in free electron generators of radiation, such as Cyclotron Resonance Masers and the Free Electron Laser. For the case of an FEL interaction, electrons initially begin to bunch and emit radiation energy with a correlated energy dispersion which is periodic with the FEL ponderomotive potential. The relative phase between potential and particles is then changed by approximately 180 degrees. The particles continue to bunch, however, there is now a correlated re-absorption of energy from the field. We show that, by repeating this relative phase change many times, a significant density modulation of the particles may be achieved with only relatively small energy dispersion. A similar method of repeated relative electron/radiation phase changes is used to demonstrate supression of the fundamental growth in a high gain FEL so that the FEL lases at the harmonic only

Mode-locked Bloch oscillations in a ring cavity

We present a new technique for stabilizing and monitoring Bloch oscillations of ultracold atoms in an optical lattice under the action of a constant external force. In the proposed scheme, the atoms also interact with a unidirectionally pumped optical ring cavity whose one arm is collinear with the optical lattice. For weak collective coupling, Bloch oscillations dominate over the collective atomic recoil lasing instability and develop a synchronized regime in which the atoms periodically exchange momentum with the cavity field.Comment: 7 pages, 5 figure

Optical pattern formation with a 2-level nonlinearity

We present an experimental and theoretical investigation of spontaneous pattern formation in the transverse section of a single retro-reflected laser beam passing through a cloud of cold Rubidium atoms. In contrast to previously investigated systems, the nonlinearity at work here is that of a 2-level atom, which realizes the paradigmatic situation considered in many theoretical studies of optical pattern formation. In particular, we are able to observe the disappearance of the patterns at high intensity due to the intrinsic saturable character of 2-level atomic transitions.Comment: 5 pages, 4 figure

Two-stream instability in quasi-one-dimensional Bose-Einstein condensates

We apply a kinetic model to predict the existence of an instability mechanism in elongated Bose-Einstein condensates. Our kinetic description, based on the Wigner formalism, is employed to highlight the existence of unstable Bogoliubov waves that may be excited in the counterpropagation configuration. We identify a dimensionless parameter, the Mach number at T=0, that tunes different regimes of stability. We also estimate the magnitude of the main parameters at which two-stream instability is expected to be observed under typical experimental conditions

Chaotic resonances of a Bose-Einstein condensate in a cavity pumped by a modulated optical field

We present a theoretical analysis of a Bose-Einstein condensate (BEC) enclosed in an optical cavity driven by a modulated external laser beam where the cavity-field variable is adiabatically eliminated. The modulation of the amplitude of the pump laser induces nonlinear resonances and the widespread presence of chaotic oscillations even when repulsive atom-atom interactions are negligible. Close to resonance, varying the modulation amplitude by just a few percent causes abrupt and erratic changes to the output laser intensity with peak power increasing by almost an order of magnitude. We also use a simplified model of the BEC-cavity system that considers only a small number of spatial modes of the BEC to show that, despite the disruptive presence of a modulation in the pump beam, the system can still be considered to be low-dimensional

Ground-state degeneracies leave recognizable topological scars in the one-particle density

In Kohn-Sham density functional theory (KS-DFT) a fictitious system of non-interacting particles is constructed having the same ground-state (GS) density as the physical system of interest. A fundamental open question in DFT concerns the ability of an exact KS calculation to spot and characterize the GS degeneracies in the physical system. In this article we provide theoretical evidence suggesting that the GS density, as a function of position on a 2D manifold of parameters affecting the external potential, is "topologically scarred" in a distinct way by degeneracies. These scars are sufficiently detailed to enable determination of the positions of degeneracies and even the associated Berry phases. We conclude that an exact KS calculation can spot and characterize the degeneracies of the physical system

The detrimental effect of spontaneous emission in quantum free electron lasers : a discrete Wigner model

We study the spontaneous emission in high-gain free-electron lasers operating in the quantum regime and its detrimental effect on coherent emission. A quantum model describing the coherent and spontaneous emission in free electron lasers has been recently proposed and investigated [G. R. M. Robb and R. Bonifacio, Phys. Plasmas 19, 073101 (2012)]. The model is based on a Wigner distribution describing the electron beam dynamics, coupled to Maxwell equations for the emitted radiation field. Here, we rephrase the model in a more rigorous way, considering a discrete Wigner distribution defined for a periodic space coordinate for which the electron momentum is discrete. From its numerical solution, we find good agreement with the approximate continuous model. In the quantum regime of the free-electron laser, we obtain a simple density matrix equation for two momentum states, where the role of the spontaneous emission has a clear interpretation in terms of coherence decay and population transfer