Atom lasers, coherent states, and coherence II. Maximally robust ensembles of pure states

As discussed in the preceding paper [Wiseman and Vaccaro, preceding paper, Phys. Rev. A 65, 043605 (2002)], the stationary state of an optical or atom laser far above threshold is a mixture of coherent field states with random phase, or, equivalently, a Poissonian mixture of number states. We are interested in which, if either, of these descriptions of rho(ss) as a stationary ensemble of pure states, is more natural. In the preceding paper we concentrated upon the question of whether descriptions such as these are physically realizable (PR). In this paper we investigate another relevant aspect of these ensembles, their robustness. A robust ensemble is one for which the pure states that comprise it survive relatively unchanged for a long time under the system evolution. We determine numerically the most robust ensembles as a function of the parameters in the laser model: the self-energy chi of the bosons in the laser mode, and the excess phase noise nu. We find that these most robust ensembles are PR ensembles, or similar to PR ensembles, for all values of these parameters. In the ideal laser limit (nu=chi=0), the most robust states are coherent states. As the phase noise or phase dispersion is increased through nu or the self-interaction of the bosons chi, respectively, the most robust states become more and more amplitude squeezed. We find scaling laws for these states, and give analytical derivations for them. As the phase diffusion or dispersion becomes so large that the laser output is no longer quantum coherent, the most robust states become so squeezed that they cease to have a well-defined coherent amplitude. That is, the quantum coherence of the laser output is manifest in the most robust PR ensemble being an ensemble of states with a well-defined coherent amplitude. This lends support to our approach of regarding robust PR ensembles as the most natural description of the state of the laser mode. It also has interesting implications for atom lasers in particular, for which phase dispersion due to self-interactions is expected to be large.

Atom lasers, coherent states, and coherence. I. Physically realizable ensembles of pure states

A laser, be it an optical laser or an atom laser, is an open quantum system that produces a coherent beam of bosons (photons or atoms, respectively). Far above threshold, the stationary state rho(ss) of the laser mode is a mixture of coherent-field states with random phase, or, equivalently, a Poissonian mixture of number states. This paper answers the question: can descriptions such as these, of rho(ss) as a stationary ensemble of pure states, be physically realized? Here physical realization is as defined previously by us [H. M. Wiseman and J. A. Vaccaro, Phys. Lett. A 250, 241 (1998)]: an ensemble of pure states for a particular system can be physically realized if, without changing the dynamics of the system, an experimenter can (in principle) know at any time that the system is in one of the pure-state members of the ensemble. Such knowledge can be obtained by monitoring the baths to which the system is coupled, provided that coupling is describable by a Markovian master equation. Using a family of master equations for the (atom) laser, we solve for the physically realizable (PR) ensembles. We find that for any finite self-energy chi of the bosons in the laser mode, the coherent-state ensemble is not PR; the closest one can come to it is an ensemble of squeezed states. This is particularly relevant for atom lasers, where the self-energy arising from elastic collisions is expected to be large. By contrast, the number-state ensemble is always PR. As the self-energy chi increases, the states in the PR ensemble closest to the coherent-state ensemble become increasingly squeezed. Nevertheless, there are values of chi for which states with well-defined coherent amplitudes are PR, even though the atom laser is not coherent (in the sense of having a Bose-degenerate output). We discuss the physical significance of this anomaly in terms of conditional coherence (and hence conditional Bose degeneracy).

Nondeterministic gates for photonic single-rail quantum logic

We discuss techniques for producing, manipulating, and measuring qubits encoded optically as vacuum- and single-photon states. We show that a universal set of nondeterministic gates can be constructed using linear optics and photon counting. We investigate the efficacy of a test gate given realistic detector efficiencies.

Synthesis of optically complex core-shell colloidal suspensions: Pathways to multiplexed biological screening

The ability to generate enormous random libraries of DNA probes via split-and-mix synthesis on solid supports is an important biotechnological application of colloids that has not been fully utilized to date. To discriminate between colloid-based DNA probes each colloidal particle must be 'encoded' so it is distinguishable from all other particles. To this end, we have used novel particle synthesis strategies to produce large numbers of optically encoded particle suitable for DNA library synthesis. Multifluorescent particles with unique and reproducible optical signatures (i.e., fluorescence and light-scattering attributes) suitable for high-throughput flow cytometry have been produced. In the spectroscopic study presented here, we investigated the optical characteristics of multi-fluorescent particles that were synthesized by coating silica 'core' particles with up to six different fluorescent dye shells alternated with non-fluorescent silica 'spacer' shells. It was observed that the diameter of the particles increased by up to 20% as a result of the addition of twelve concentric shells and that there was a significant reduction in fluorescence emission intensities from inner shells as an increasing number of shells were deposited.

Mapping water quality and substrate cover in optically complex coastal and reef waters: an integrated approach

Sustainable management of coastal and coral reef environments requires regular collection of accurate information on recognized ecosystem health indicators. Satellite image data and derived maps of water column and substrate biophysical properties provide an opportunity to develop baseline mapping and monitoring programs for coastal and coral reef ecosystem health indicators. A significant challenge for satellite image data in coastal and coral reef water bodies is the mixture of both clear and turbid waters. A new approach is presented in this paper to enable production of water quality and substrate cover type maps, linked to a field based coastal ecosystem health indicator monitoring program, for use in turbid to clear coastal and coral reef waters. An optimized optical domain method was applied to map selected water quality (Secchi depth, Kd PAR, tripton, CDOM) and substrate cover type (seagrass, algae, sand) parameters. The approach is demonstrated using commercially available Landsat 7 Enhanced Thematic Mapper image data over a coastal embayment exhibiting the range of substrate cover types and water quality conditions commonly found in sub-tropical and tropical coastal environments. Spatially extensive and quantitative maps of selected water quality and substrate cover parameters were produced for the study site. These map products were refined by interactions with management agencies to suit the information requirements of their monitoring and management programs. (c) 2004 Elsevier Ltd. All rights reserved.

Lasers - An effective artificial source of radiation for the cultivation of anoxygenic photosynthetic bacteria

The laser diode (LD) is a unique light source that can efficiently produce all radiant energy within the narrow wavelength range used most effectively by a photosynthetic microorganism. We have investigated the use of a single type of LID for the cultivation of the well-studied anoxygenic photosynthetic bacterium, Rhodobacter capsulatus (Rb. capsulatus). An array of vertical-cavity surface-emitting lasers (VCSELs) was driven with a current of 25 mA, and delivered radiation at 860 nm with 0.4 nm linewidth. The emitted light was found to be a suitable source of radiant energy for the cultivation of Rb. capsulatus. The dependence of growth rate on incident irradiance was quantified. Despite the unusual nearly monochromatic light source used in these experiments, no significant changes in the pigment composition and in the distribution of bacteriochlorophyll between LHII and LHI-RC were detected in bacterial cells transferred from incandescent light to laser light. We were also able to show that to achieve a given growth rate in a light-limited culture, the VCSEL required only 30% of the electricity needed by an incandescent bulb, which is of great significance for the potential use of laser-devices in biotechnological applications and photobioreactor construction. (c) 2006 Wiley Periodicals, Inc.