Optimal Sizes of Dielectric Microspheres for Cavity QED with Strong Coupling

The whispering gallery modes (WGMs) of quartz microspheres are investigated for the purpose of strong coupling between single photons and atoms in cavity quantum electrodynamics (cavity QED). Within our current understanding of the loss mechanisms of the WGMs, the saturation photon number, n, and critical atom number, N, cannot be minimized simultaneously, so that an "optimal" sphere size is taken to be the radius for which the geometric mean, (n x N)^(1/2), is minimized. While a general treatment is given for the dimensionless parameters used to characterize the atom-cavity system, detailed consideration is given to the D2 transition in atomic Cesium (852nm) using fused-silica microspheres, for which the maximum coupling coefficient g/(2*pi)=750MHz occurs for a sphere radius a=3.63microns corresponding to the minimum for n=6.06x10^(-6). By contrast, the minimum for N=9.00x10^(-6) occurs for a sphere radius of a=8.12microns, while the optimal sphere size for which (n x N)^(1/2) is minimized occurs at a=7.83microns. On an experimental front, we have fabricated fused-silica microspheres with radii a=10microns and consistently observed quality factors Q=0.8x10^(7). These results for the WGMs are compared with corresponding parameters achieved in Fabry-Perot cavities to demonstrate the significant potential of microspheres as a tool for cavity QED with strong coupling.Comment: 12 pages, 14 figure

Surface spin-flop and discommensuration transitions in antiferromagnets

Phase diagrams as a function of anisotropy $D$ and magnetic field $H$ are obtained for discommensurations and surface states for an antiferromagnet in which $H$ is parallel to the easy axis, by modeling it using the ground states of a one-dimensional chain of classical XY spins. A surface spin-flop phase exists for all $D$, but the interval in $H$ over which it is stable becomes extremely small as $D$ goes to zero. First-order transitions, separating different surface states and ending in critical points, exist inside the surface spin-flop region. They accumulate at a field $H'$ (depending on $D$) significantly less than the value $H_{SF}$ for a bulk spin-flop transition. For $H' < H < H_{SF}$ there is no surface spin-flop phase in the strict sense; instead, the surface restructures by, in effect, producing a discommensuration infinitely far away in the bulk. The results are used to explain in detail the phase transitions occurring in systems consisting of a finite, even number of layers.Comment: Revtex 17 pages, 15 figure

Quantum logic between atoms inside a high Q optical cavity

We propose a protocol for conditional quantum logic between two 4-state atoms inside a high Q optical cavity. The process detailed in this paper utilizes a direct 4-photon 2-atom resonant process and has the added advantage of commonly addressing the two atoms when they are inside the high Q optical cavity.Comment: 8 pages, 3 figs. submitte

Trapping atoms in the vacuum field of a cavity

The aim of this work is to find ways to trap an atom in a cavity. In contrast to other approaches we propose a method where the cavity is basically in the vacuum state and the atom in the ground state. The idea is to induce a spatial dependent AC Stark shift by irradiating the atom with a weak laser field, so that the atom experiences a trapping force. The main feature of our setup is that dissipation can be strongly suppressed. We estimate the lifetime of the atom as well as the trapping potential parameters and compare our estimations with numerical simulations.Comment: 8 pages, 8 figure

Resonance fluorescence of a trapped three-level atom

We investigate theoretically the spectrum of resonance fluorescence of a harmonically trapped atom, whose internal transitions are $\Lambda$--shaped and driven at two-photon resonance by a pair of lasers, which cool the center--of--mass motion. For this configuration, photons are scattered only due to the mechanical effects of the quantum interaction between light and atom. We study the spectrum of emission in the final stage of laser--cooling, when the atomic center-of-mass dynamics is quantum mechanical and the size of the wave packet is much smaller than the laser wavelength (Lamb--Dicke limit). We use the spectral decomposition of the Liouville operator of the master equation for the atomic density matrix and apply second order perturbation theory. We find that the spectrum of resonance fluorescence is composed by two narrow sidebands -- the Stokes and anti-Stokes components of the scattered light -- while all other signals are in general orders of magnitude smaller. For very low temperatures, however, the Mollow--type inelastic component of the spectrum becomes visible. This exhibits novel features which allow further insight into the quantum dynamics of the system. We provide a physical model that interprets our results and discuss how one can recover temperature and cooling rate of the atom from the spectrum. The behaviour of the considered system is compared with the resonance fluorescence of a trapped atom whose internal transition consists of two-levels.Comment: 11 pages, 4 Figure

All-optical switching and strong coupling using tunable whispering-gallery-mode microresonators

We review our recent work on tunable, ultrahigh quality factor whispering-gallery-mode bottle microresonators and highlight their applications in nonlinear optics and in quantum optics experiments. Our resonators combine ultra-high quality factors of up to Q = 3.6 \times 10^8, a small mode volume, and near-lossless fiber coupling, with a simple and customizable mode structure enabling full tunability. We study, theoretically and experimentally, nonlinear all-optical switching via the Kerr effect when the resonator is operated in an add-drop configuration. This allows us to optically route a single-wavelength cw optical signal between two fiber ports with high efficiency. Finally, we report on progress towards strong coupling of single rubidium atoms to an ultra-high Q mode of an actively stabilized bottle microresonator.Comment: 20 pages, 24 figures. Accepted for publication in Applied Physics B. Changes according to referee suggestions: minor corrections to some figures and captions, clarification of some points in the text, added references, added new paragraph with results on atom-resonator interactio

Raman spectroscopy of a single ion coupled to a high-finesse cavity

We describe an ion-based cavity-QED system in which the internal dynamics of an atom is coupled to the modes of an optical cavity by vacuum-stimulated Raman transitions. We observe Raman spectra for different excitation polarizations and find quantitative agreement with theoretical simulations. Residual motion of the ion introduces motional sidebands in the Raman spectrum and leads to ion delocalization. The system offers prospects for cavity-assisted resolved-sideband ground-state cooling and coherent manipulation of ions and photons.Comment: 8 pages, 6 figure

Dynamical Coupling between a Bose-Einstein Condensate and a Cavity Optical Lattice

A Bose-Einstein condensate is dispersively coupled to a single mode of an ultra-high finesse optical cavity. The system is governed by strong interactions between the atomic motion and the light field even at the level of single quanta. While coherently pumping the cavity mode the condensate is subject to the cavity optical lattice potential whose depth depends nonlinearly on the atomic density distribution. We observe bistability already below the single photon level and strong back-action dynamics which tunes the system periodically out of resonance.Comment: 5 pages, 4 figure

Review article: MHD wave propagation near coronal null points of magnetic fields

We present a comprehensive review of MHD wave behaviour in the neighbourhood of coronal null points: locations where the magnetic field, and hence the local Alfven speed, is zero. The behaviour of all three MHD wave modes, i.e. the Alfven wave and the fast and slow magnetoacoustic waves, has been investigated in the neighbourhood of 2D, 2.5D and (to a certain extent) 3D magnetic null points, for a variety of assumptions, configurations and geometries. In general, it is found that the fast magnetoacoustic wave behaviour is dictated by the Alfven-speed profile. In a $\beta=0$ plasma, the fast wave is focused towards the null point by a refraction effect and all the wave energy, and thus current density, accumulates close to the null point. Thus, null points will be locations for preferential heating by fast waves. Independently, the Alfven wave is found to propagate along magnetic fieldlines and is confined to the fieldlines it is generated on. As the wave approaches the null point, it spreads out due to the diverging fieldlines. Eventually, the Alfven wave accumulates along the separatrices (in 2D) or along the spine or fan-plane (in 3D). Hence, Alfven wave energy will be preferentially dissipated at these locations. It is clear that the magnetic field plays a fundamental role in the propagation and properties of MHD waves in the neighbourhood of coronal null points. This topic is a fundamental plasma process and results so far have also lead to critical insights into reconnection, mode-coupling, quasi-periodic pulsations and phase-mixing.Comment: 34 pages, 5 figures, invited review in Space Science Reviews => Note this is a 2011 paper, not a 2010 pape

The delta-function-kicked rotor: Momentum diffusion and the quantum-classical boundary

We investigate the quantum-classical transition in the delta-kicked rotor and the attainment of the classical limit in terms of measurement-induced state-localization. It is possible to study the transition by fixing the environmentally induced disturbance at a sufficiently small value, and examining the dynamics as the system is made more macroscopic. When the system action is relatively small, the dynamics is quantum mechanical and when the system action is sufficiently large there is a transition to classical behavior. The dynamics of the rotor in the region of transition, characterized by the late-time momentum diffusion coefficient, can be strikingly different from both the purely quantum and classical results. Remarkably, the early time diffusive behavior of the quantum system, even when different from its classical counterpart, is stabilized by the continuous measurement process. This shows that such measurements can succeed in extracting essentially quantum effects. The transition regime studied in this paper is accessible in ongoing experiments.Comment: 8 pages, 4 figures, revtex4 (revised version contains much more introductory material