Characterization of high finesse mirrors: loss, phase shifts and mode structure in an optical cavity

An extensive characterization of high finesse optical cavities used in cavity QED experiments is described. Different techniques in the measurement of the loss and phase shifts associated with the mirror coatings are discussed and their agreement shown. Issues of cavity field mode structure supported by the dielectric coatings are related to our effort to achieve the strongest possible coupling between an atom and the cavity.Comment: 8 pages, 4 figure

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

Young people's attitudes to religious diversity : quantitative approaches from social psychology and empirical theology

This essay discusses the design of the quantitative component of the ‘Young People’s Attitudes to Religious Diversity’ project, conceived by Professor Robert Jackson within the Warwick Religions and Education Research Unit, and presents some preliminary findings from the data. The quantitative component followed and built on the qualitative component within a mixed method design. The argument is advanced in seven steps: introducing the major sources of theory on which the quantitative approach builds from the psychology of religion and from empirical theology; locating the empirical traditions of research among young people that have shaped the study; clarifying the notions and levels of measurement employed in the study anticipating the potential for various forms of data analysis; discussing some of the established measures incorporated in the survey; defining the ways in which the sample was structured to reflect the four nations of the UK, and London; illustrating the potential within largely descriptive cross-tabulation forms of analysis; and illustrating the potential within more sophisticated multivariate analytic models

Trapping of Single Atoms with Single Photons in Cavity QED

Two recent experiments have reported the trapping of individual atoms inside optical resonators by the mechanical forces associated with single photons [Hood et al., Science 287, 1447 (2000) and Pinkse et al., Nature 404, 365 (2000)]. Here we analyze the trapping dynamics in these settings, focusing on two points of interest. Firstly, we investigate the extent to which light-induced forces in these experiments are distinct from their free-space counterparts. Secondly, we explore the quantitative features of the resulting atomic motion and how these dynamics are mapped onto variations of the intracavity field. Not surprisingly, qualitatively distinct atomic dynamics arise as the coupling and dissipative rates are varied. For the experiment of Hood et al., we show that atomic motion is largely conservative and is predominantly in radial orbits transverse to the cavity axis. A comparison with the free-space theory demonstrates that the fluctuations of the dipole force are suppressed by an order of magnitude. This effect is based upon the Jaynes-Cummings eigenstates of the atom-cavity system and represents qualitatively new physics for optical forces at the single-photon level. By contrast, even in a regime of strong coupling in the experiment of Pinkse et al., there are only small quantitative distinctions between the free-space theory and the quantum theory, so it is not clear that description of this experiment as a novel single-quantum trapping effect is necessary. The atomic motion is strongly diffusive, leading to an average localization time comparable to the time for an atom to transit freely through the cavity and to a reduction in the ability to infer aspects of the atomic motion from the intracavity photon number.Comment: 19 pages, 22 figure files, REVTEX, corrected spelling, LaTeX now produces postscript which includes figures, minor changes to figures. Final version to be published in Physical Review A, expanded summary of results in introduction, minor changes to figures and tex

Continuous Quantum Measurement and the Quantum to Classical Transition

While ultimately they are described by quantum mechanics, macroscopic mechanical systems are nevertheless observed to follow the trajectories predicted by classical mechanics. Hence, in the regime defining macroscopic physics, the trajectories of the correct classical motion must emerge from quantum mechanics, a process referred to as the quantum to classical transition. Extending previous work [Bhattacharya, Habib, and Jacobs, Phys. Rev. Lett. {\bf 85}, 4852 (2000)], here we elucidate this transition in some detail, showing that once the measurement processes which affect all macroscopic systems are taken into account, quantum mechanics indeed predicts the emergence of classical motion. We derive inequalities that describe the parameter regime in which classical motion is obtained, and provide numerical examples. We also demonstrate two further important properties of the classical limit. First, that multiple observers all agree on the motion of an object, and second, that classical statistical inference may be used to correctly track the classical motion.Comment: 12 pages, 4 figures, Revtex

Dynamic generation of maximally entangled photon multiplets by adiabatic passage

The adiabatic passage scheme for quantum state synthesis, in which atomic Zeeman coherences are mapped to photon states in an optical cavity, is extended to the general case of two degenerate cavity modes with orthogonal polarization. Analytical calculations of the dressed-state structure and Monte Carlo wave-function simulations of the system dynamics show that, for a suitably chosen cavity detuning, it is possible to generate states of photon multiplets that are maximally entangled in polarization. These states display nonclassical correlations of the type described by Greenberger, Horne, and Zeilinger (GHZ). An experimental scheme to realize a GHZ measurement using coincidence detection of the photons escaping from the cavity is proposed. The correlations are found to originate in the dynamics of the adiabatic passage and persist even if cavity decay and GHZ state synthesis compete on the same time scale. Beyond entangled field states, it is also possible to generate entanglement between photons and the atom by using a different atomic transition and initial Zeeman state.Comment: 22 pages (RevTeX), including 23 postscript figures. To be published in Physical Review

Experimental Proposal for Achieving Superadditive Communication Capacities with a Binary Quantum Alphabet

We demonstrate superadditivity in the communication capacity of a binary alphabet consisting of two nonorthogonal quantum states. For this scheme, collective decoding is performed two transmissions at a time. This improves upon the previous schemes of Sasaki et al. [Phys. Rev. A 58, 146 (1998)] where superadditivity was not achieved until a decoding of three or more transmissions at a time. This places superadditivity within the regime of a near-term laboratory demonstration. We propose an experimental test based upon an alphabet of low photon-number coherent states where the signal decoding is done with atomic state measurements on a single atom in a high-finesse optical cavity.Comment: 7 pages, 5 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

Multipartite Entanglement and Quantum State Exchange

We investigate multipartite entanglement in relation to the theoretical process of quantum state exchange. In particular, we consider such entanglement for a certain pure state involving two groups of N trapped atoms. The state, which can be produced via quantum state exchange, is analogous to the steady-state intracavity state of the subthreshold optical nondegenerate parametric amplifier. We show that, first, it possesses some 2N-way entanglement. Second, we place a lower bound on the amount of such entanglement in the state using a novel measure called the entanglement of minimum bipartite entropy.Comment: 12 pages, 4 figure