Effect of an atom on a quantum guided field in a weakly driven fiber-Bragg-grating cavity

We study the interaction of an atom with a quantum guided field in a weakly driven fiber-Bragg-grating (FBG) cavity. We present an effective Hamiltonian and derive the density-matrix equations for the combined atom-cavity system. We calculate the mean photon number, the second-order photon correlation function, and the atomic excited-state population. We show that, due to the confinement of the guided cavity field in the fiber cross-section plane and in the space between the FBG mirrors, the presence of the atom in the FBG cavity can significantly affect the mean photon number and the photon statistics even though the cavity finesse is moderate, the cavity is long, and the probe field is weak.Comment: Accepted for Phys. Rev.

Continuation Sheaves in Dynamics: Sheaf Cohomology and Bifurcation

Continuation of algebraic structures in families of dynamical systems is described using category theory, sheaves, and lattice algebras. Well-known concepts in dynamics, such as attractors or invariant sets, are formulated as functors on appropriate categories of dynamical systems mapping to categories of lattices, posets, rings or abelian groups. Sheaves are constructed from such functors, which encode data about the continuation of structure as system parameters vary. Similarly, morphisms for the sheaves in question arise from natural transformations. This framework is applied to a variety of lattice algebras and ring structures associated to dynamical systems, whose algebraic properties carry over to their respective sheaves. Furthermore, the cohomology of these sheaves are algebraic invariants which contain information about bifurcations of the parametrized systems

The time-reversal test for stochastic quantum dynamics

The calculation of quantum dynamics is currently a central issue in theoretical physics, with diverse applications ranging from ultra-cold atomic Bose-Einstein condensates (BEC) to condensed matter, biology, and even astrophysics. Here we demonstrate a conceptually simple method of determining the regime of validity of stochastic simulations of unitary quantum dynamics by employing a time-reversal test. We apply this test to a simulation of the evolution of a quantum anharmonic oscillator with up to $6.022\times10^{23}$ (Avogadro's number) of particles. This system is realisable as a Bose-Einstein condensate in an optical lattice, for which the time-reversal procedure could be implemented experimentally.Comment: revtex4, two figures, four page

Quantum Clock Synchronization Based on Shared Prior Entanglement

We demonstrate that two spatially separated parties (Alice and Bob) can utilize shared prior quantum entanglement, and classical communications, to establish a synchronized pair of atomic clocks. In contrast to classical synchronization schemes, the accuracy of our protocol is independent of Alice or Bob's knowledge of their relative locations or of the properties of the intervening medium.Comment: 4 page

Putting the "I" in Interaction: interactive interfaces personalized to the individual

Interactive data exploration and analysis is an inherently personal process. One's background, experience, interests, cognitive style, personality, and other sociotechnical factors often shape such a process, as well as the provenance of exploring, analyzing, and interpreting data. This viewpoint posits both what personal information and how such personal information could be taken into account to design more effective visual analytic systems, a valuable and under-explored direction

Quantum States of Light Produced by a High-Gain Optical Parametric Amplifier for Use in Quantum Lithography

We present a theoretical analysis of the properties of an unseeded optical parametic amplifier (OPA) used as the source of entangled photons for applications in quantum lithography. We first study the dependence of the excitation rate of a two-photon absorber on the intensity of the light leaving the OPA. We find that the rate depends linearly on intensity only for output beams so weak that they contain fewer than one photon per mode. We also study the use of an N-photon absorber for arbitrary N as the recording medium to be used with such a light source. We find that the contrast of the interference pattern and the sharpness of the fringe maxima tend to increase with increasing values of N, but that the density of fringes and thus the limiting resolution does not increase with N. We conclude that the output of an unseeded OPA exciting an N-photon absorber provides an attractive system in which to perform quantum lithography

From Linear Optical Quantum Computing to Heisenberg-Limited Interferometry

The working principles of linear optical quantum computing are based on photodetection, namely, projective measurements. The use of photodetection can provide efficient nonlinear interactions between photons at the single-photon level, which is technically problematic otherwise. We report an application of such a technique to prepare quantum correlations as an important resource for Heisenberg-limited optical interferometry, where the sensitivity of phase measurements can be improved beyond the usual shot-noise limit. Furthermore, using such nonlinearities, optical quantum nondemolition measurements can now be carried out at the single-photon level.Comment: 10 pages, 5 figures; Submitted to a Special Issue of J. Opt. B on "Fluctuations and Noise in Photonics and Quantum Optics" (Herman Haus Memorial Issue); v2: minor change

Two-Photon Interferometry for High-Resolution Imaging

We discuss advantages of using non-classical states of light for two aspects of optical imaging: creating of miniature images on photosensitive substrates, which constitutes the foundation for optical lithography, and imaging of micro objects. In both cases, the classical resolution limit given by the Rayleigh criterion is approximately a half of the optical wavelength. It has been shown, however, that by using multi-photon quantum states of the light field, and multi-photon sensitive material or detector, this limit can be surpassed. We give a rigorous quantum mechanical treatment of this problem, address some particularly widespread misconceptions and discuss the requirements for turning the research on quantum imaging into a practical technology.Comment: Presented at PQE 2001. To appear in Special Issue of Journal of Modern Optic