Coupled dynamics of atoms and radiation pressure driven interferometers

We consider the motion of the end mirror of a cavity in whose standing wave mode pattern atoms are trapped. The atoms and the light field strongly couple to each other because the atoms form a distributed Bragg mirror with a reflectivity that can be fairly high. We analyze how the dipole potential in which the atoms move is modified due to this backaction of the atoms. We show that the position of the atoms can become bistable. These results are of a more general nature and can be applied to any situation where atoms are trapped in an optical lattice inside a cavity and where the backaction of the atoms on the light field cannot be neglected. We analyze the dynamics of the coupled system in the adiabatic limit where the light field adjusts to the position of the atoms and the light field instantaneously and where the atoms move much faster than the mirror. We calculate the side band spectrum of the light transmitted through the cavity and show that these spectra can be used to detect the coupled motion of the atoms and the mirror.Comment: 11 pages; 13 figures; two added references and other minor correction

Accurate and efficient spin integration for particle accelerators

Accurate spin tracking is a valuable tool for understanding spin dynamics in particle accelerators and can help improve the performance of an accelerator. In this paper, we present a detailed discussion of the integrators in the spin tracking code gpuSpinTrack. We have implemented orbital integrators based on drift-kick, bend-kick, and matrix-kick splits. On top of the orbital integrators, we have implemented various integrators for the spin motion. These integrators use quaternions and Romberg quadratures to accelerate both the computation and the convergence of spin rotations. We evaluate their performance and accuracy in quantitative detail for individual elements as well as for the entire RHIC lattice. We exploit the inherently data-parallel nature of spin tracking to accelerate our algorithms on graphics processing units.Comment: 43 pages, 17 figure

Fluctuations in the formation time of ultracold dimers from fermionic atoms

We investigate the temporal fluctuations characteristic of the formation of molecular dimers from ultracold fermionic atoms via Raman photoassociation. The quantum fluctuations inherent to the initial atomic state result in large fluctuations in the passage time from atoms to molecules. Assuming degeneracy of kinetic energies of atoms in the strong coupling limit we find that a heuristic classical stochastic model yields qualitative agreement with the full quantum treatment in the initial stages of the dynamics. We also show that in contrast to the association of atoms into dimers, the reverse process of dissociation from a condensate of bosonic dimers exhibits little passage time fluctuations. Finally we explore effects due to the non-degeneracy of atomic kinetic energies.Comment: 7 pages, 6 figure

Prospects for a mHz-linewidth laser

We propose a new light source based on having alkaline-earth atoms in an optical lattice collectively emit photons on an ultra-narrow clock transition into the mode of a high Q-resonator. The resultant optical radiation has an extremely narrow linewidth in the mHz range, even smaller than that of the clock transition itself due to collective effects. A power level of order $10^{-12}W$ is possible, sufficient for phase-locking a slave optical local oscillator. Realizing this light source has the potential to improve the stability of the best clocks by two orders of magnitude.Comment: minor revisions + shortening; factor 2 algebra mistake correcte

Molecule formation as a diagnostic tool for second order correlations of ultra-cold gases

We calculate the momentum distribution and the second-order correlation function in momentum space, $g^{(2)}({\bf p},{\bf p}',t)$ for molecular dimers that are coherently formed from an ultracold atomic gas by photoassociation or a Feshbach resonance. We investigate using perturbation theory how the quantum statistics of the molecules depend on the initial state of the atoms by considering three different initial states: a Bose-Einstein condensate (BEC), a normal Fermi gas of ultra-cold atoms, and a BCS-type superfluid Fermi gas. The cases of strong and weak coupling to the molecular field are discussed. It is found that BEC and BCS states give rise to an essentially coherent molecular field with a momentum distribution determined by the zero-point motion in the confining potential. On the other hand, a normal Fermi gas and the unpaired atoms in the BCS state give rise to a molecular field with a broad momentum distribution and thermal number statistics. It is shown that the first-order correlations of the molecules can be used to measure second-order correlations of the initial atomic state.Comment: revtex, 15 pages,8 figure

Full counting statistics of heteronuclear molecules from Feshbach-assisted photo association

We study the effects of quantum statistics on the counting statistics of ultracold heteronuclear molecules formed by Feshbach-assisted photoassociation [Phys. Rev. Lett. {\bf 93}, 140405 (2004)]. Exploiting the formal similarities with sum frequency generation and using quantum optics methods we consider the cases where the molecules are formed from atoms out of two Bose-Einstein condensates, out of a Bose-Einstein condensate and a gas of degenerate fermions, and out of two degenerate Fermi gases with and without superfluidity. Bosons are treated in a single mode approximation and fermions in a degenerate model. In these approximations we can numerically solve the master equations describing the system's dynamics and thus we find the full counting statistics of the molecular modes. The full quantum dynamics calculations are complemented by mean field calculations and short time perturbative expansions. While the molecule production rates are very similar in all three cases at this level of approximation, differences show up in the counting statistics of the molecular fields. The intermediate field of closed-channel molecules is for short times second-order coherent if the molecules are formed from two Bose-Einstein condensates or a Bose-Fermi mixture. They show counting statistics similar to a thermal field if formed from two normal Fermi gases. The coherence properties of molecule formation in two superfluid Fermi gases are intermediate between the two previous cases. In all cases the final field of deeply-bound molecules is found to be twice as noisy as that of the intermediate state. This is a consequence of its coupling to the lossy optical cavity in our model, which acts as an input port for quantum noise, much like the situation in an optical beam splitter.Comment: replacement of earlier manuscript cond-mat/0508080 ''Feshbach-assisted photoassociation of ultracold heteronuclear molecules'' with minor revision

A multiphase model for the cross‐linking of ultra‐high viscous alginate hydrogels

In this study, a model for the cross-linking of ultra-high viscous alginate hydrogels is provided. The model consists of four kinetic equations describing the process, including the local accumulation and the depletion of mobile alginate, cross-linked alginate and cross-linking cations. For an efficient simulation, finite difference schemes with predictor-corrector algorithms were implemente

Decoherence due to elastic Rayleigh scattering

We present theoretical and experimental studies of the decoherence of hyperfine ground-state superpositions due to elastic Rayleigh scattering of light off-resonant with higher lying excited states. We demonstrate that under appropriate conditions, elastic Rayleigh scattering can be the dominant source of decoherence, contrary to previous discussions in the literature. We show that the elastic-scattering decoherence rate of a two-level system is given by the square of the difference between the elastic-scattering \textit{amplitudes} for the two levels, and that for certain detunings of the light, the amplitudes can interfere constructively even when the elastic scattering \textit{rates} from the two levels are equal. We confirm this prediction through calculations and measurements of the total decoherence rate for a superposition of the valence electron spin levels in the ground state of $^9$Be$^+$ in a 4.5 T magnetic field.Comment: 5 pages, 3 figure

Atomic physics: An almost lightless laser

Lasers are often described in terms of a light field circulating in an optical resonator system. Now a laser has been demonstrated in which the field resides primarily in the atomic medium that is used to generate the light