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).

Positive-P and Wigner representations for quantum-optical systems with nonorthogonal modes

We generalize the basic concepts of the positive-P and Wigner representations to unstable quantum-optical systems that are based on nonorthogonal quasimodes. This lays the foundation for a quantum description of such systems, such as, for example an unstable cavity laser. We compare both representations by calculating the tunneling times for an unstable resonator optical parametric oscillator.

Bayesian feedback versus Markovian feedback in a two-level atom

We compare two different approaches to the control of the dynamics of a continuously monitored open quantum system. The first is Markovian feedback, as introduced in quantum optics by Wiseman and Milburn [Phys. Rev. Lett. 70, 548 (1993)]. The second is feedback based on an estimate of the system state, developed recently by Doherty and Jacobs [Phys. Rev. A 60, 2700 (1999)]. Here we choose to call it, for brevity, Bayesian feedback. For systems with nonlinear dynamics, we expect these two methods of feedback control to give markedly different results. The simplest possible nonlinear system is a driven and damped two-level atom, so we choose this as our model system. The monitoring is taken to be homodyne detection of the atomic fluorescence, and the control is by modulating the driving. The aim of the feedback in both cases is to stabilize the internal state of the atom as close as possible to an arbitrarily chosen pure state, in the presence of inefficient detection and other forms of decoherence. Our results (obtained without recourse to stochastic simulations) prove that Bayesian feedback is never inferior, and is usually superior, to Markovian feedback. However, it would be far more difficult to implement than Markovian feedback and it loses its superiority when obvious simplifying approximations are made. It is thus not clear which form of feedback would be better in the face of inevitable experimental imperfections.

Controlling the complex Lorenz equations by modulation

We demonstrate that a system obeying the complex Lorenz equations in the deep chaotic regime can be controlled to periodic behavior by applying a modulation to the pump parameter. For arbitrary modulation frequency and amplitude there is no obvious simplification of the dynamics. However, we find that there are numerous windows where the chaotic system has been controlled to different periodic behaviors. The widths of these windows in parameter space are narrow, and the positions are related to the ratio of the modulation frequency of the pump to the average pulsation frequency of the output variable. These results are in good agreement with observations previously made in a far-infrared laser system.

The damped and coherently-driven Jaynes-Cummings model

We investigate the influence of a single-mode cavity on the Autler-Townes doublet that arises when a three-level atom is strongly driven by a laser field tuned to one of the atomic transitions and probed by a tunable, weak field coupled to the other transition. We assume that the cavity mode is coupled to the driven transition and the cavity and laser frequencies are equal to the atomic transition frequency. We find that the Autler-Townes spectrum can have one, two or three peaks depending on the relative magnitudes of the Rabi frequencies of the cavity and driving fields. We show that, in order to understand the three-peaked spectrum, it is necessary to go beyond the secular approximation, leading to interesting quantum interference effects. We find that the positions and relative intensities of the three spectral components are affected strongly by the atom-cavity coupling strength g and the cavity damping K. For an increasing g and/or decreasing K the triplet evolves into a single peak. This results in 'undressing' of the system such that the atom collapses into its ground state. We interpret the spectral features in terms of the semiclassical dressed-atom model, and also provide complementary views of the cavity effects in terms of quantum Langevin equations and the fully quantized, 'double -dressing' model.

Behavior of argon gas release from manganese oxide minerals as revealed by Ar-40/Ar-39 laser incremental heating analysis

Manganese oxides in association with paleo-weathering may provide significant insights into the multiple factors affecting the formation and evolution of weathering profiles, such as temperature, precipitation, and biodiversity. Laser probe step-heating analysis of supergene hollandite and cryptomelane samples collected from central Queensland, Australia, yield well-defined plateaus and consistent isochron ages, confirming the feasibility, dating very-fined supergene manganese oxides by Ar-40/(39) Ar technique. Two distinct structural sites hosting Ar isotopes can be identified in light of their degassing behaviors obtained by incremental heating analyses. The first site, releasing its gas fraction at the laser power 0.2-0.4 W, yields primarily Ar-40(atm), Ar-38(atm), and Ar-36(atm), (atmospheric Ar isotopes). The second sites yield predominantly Ar-40* (radiogenic Ar-40), Ar-39(K), and Ar-38(K) (nucleogenic components), at similar to0.5-1.0 W. There is no significant Ar gas released at the laser power higher than 1.0 W, indicating the breakdown of the tunnel sites hosting the radiogenic and nucleogenic components. The excellent match between the degassing behaviors of Ar-40*, Ar-39(K), and Ar-38(K) suggests that these isotopes occupy the same crystallographic sites and that Ar-39(K) loss from the tunnel site by recoil during neutron irradiation and/or bake-out procedure preceding isotopic analysis does not occur. Present investigation supports that neither the overwhelming atmospheric Ar-40 nor the very-fined nature of the supergene manganese oxides poses problems in extracting meaningful weathering geo-chronological information by analyzing supergene manganese oxides minerals.

Modelling the activated sludge flocculation process combining laser light diffraction particle sizing and population balance modelling (PBM)

A technique based on laser light diffraction is shown to be successful in collecting on-line experimental data. Time series of floc size distributions (FSD) under different shear rates (G) and calcium additions were collected. The steady state mass mean diameter decreased with increasing shear rate G and increased when calcium additions exceeded 8 mg/l. A so-called population balance model (PBM) was used to describe the experimental data, This kind of model describes both aggregation and breakage through birth and death terms. A discretised PBM was used since analytical solutions of the integro-partial differential equations are non-existing. Despite the complexity of the model, only 2 parameters need to be estimated: the aggregation rate and the breakage rate. The model seems, however, to lack flexibility. Also, the description of the floc size distribution (FSD) in time is not accurate.

The current status of laser applications in dentistry

A range of lasers. is now available for use in dentistry. This paper summarizes key current and emerging applications, for lasers in clinical practice. A major diagnostic application of low power lasers is the detection of caries, using fluorescence elicited from hydroxyapatite or from bacterial by-products. Laser fluorescence is an effective method for detecting and quantifying incipient occlusal and cervical,carious lesions, and with further refinement could be used in the, same manner for proximal lesions. Photoactivated dye techniques have been developed which use low power lasers to elicit a photochemical reaction, Photoactivated dye techniques' can be used to disinfect root canals, periodontal pockets, cavity preparations and sites of peri-implantitis. Using similar principles, more powerful lasers tan be used for photodynamic therapy in the treatment of malignancies of the oral mucosa. Laser-driven photochemical reactions can also be used for tooth whitening. In combination with fluoride, laser irradiation can improve the resistance of tooth structure to demineralization, and this application is of particular benefit for susceptible sites in high caries risk patients. Laser technology for caries' removal, cavity preparation and soft tissue surgery is at a high state of refinement, having had several decades of development up to the present time. Used in conjunction with or as a replacement for traditional methods, it is expected that specific laser technologies will become an essential component of contemporary dental practice over the next decade.

Modeling diffraction in free-space optical interconnects by the mode expansion method

Free-space optical interconnects (FSOIs), made up of dense arrays of vertical-cavity surface-emitting lasers, photodetectors and microlenses can be used for implementing high-speed and high-density communication links, and hence replace the inferior electrical interconnects. A major concern in the design of FSOIs is minimization of the optical channel cross talk arising from laser beam diffraction. In this article we introduce modifications to the mode expansion method of Tanaka et al. [IEEE Trans. Microwave Theory Tech. MTT-20, 749 (1972)] to make it an efficient tool for modelling and design of FSOIs in the presence of diffraction. We demonstrate that our modified mode expansion method has accuracy similar to the exact solution of the Huygens-Kirchhoff diffraction integral in cases of both weak and strong beam clipping, and that it is much more accurate than the existing approximations. The strength of the method is twofold: first, it is applicable in the region of pronounced diffraction (strong beam clipping) where all other approximations fail and, second, unlike the exact-solution method, it can be efficiently used for modelling diffraction on multiple apertures. These features make the mode expansion method useful for design and optimization of free-space architectures containing multiple optical elements inclusive of optical interconnects and optical clock distribution systems. (C) 2003 Optical Society of America.

Use of confocal scanning laser microscopy to measure the concentrations of aerial and penetrative hyphae during growth of Rhizopus oligosporus on a solid surface

In order to develop a method for use in investigations of spatial biomass distribution in solid-state fermentation systems, confocal scanning laser microscopy was used to determine the concentrations of aerial and penetrative biomass against height and depth above and below the substrate surface, during growth of Rhizopus oligosporus on potato dextrose agar. Penetrative hyphae had penetrated to a depth of 0.445 cm by 64 h and showed rhizoid morphology, in which the maximum biomass concentration, of 4.45 mg dry wt cm(-3), occurred at a depth of 0.075 cm. For aerial biomass the maximum density of 39.54 mg dry wt(-3) occurred at the substrate surface. For both aerial and penetrative biomass, there were two distinct regions in which the biomass concentration decayed exponentially with distance from the surface. For aerial biomass, the first exponential decay region was up to 0.1 cm height. The second region above the height of 0.1 cm corresponded to that in which sporangiophores dominated. This work lays the foundation for deeper studies into what controls the growth of fungal hyphae above and below the surfaces of solid substrates. (C) Wiley Periodicals, Inc.

Stokes-operator-squeezed continuous-variable polarization states

We investigate nonclassical Stokes-operator variances in continuous-wave polarization-squeezed laser light generated from one and two optical parametric amplifiers. A general expression of how Stokes-operator variances decompose into two-mode quadrature operator variances is given. Stokes parameter variance spectra for four different polarization-squeezed states have been measured and compared with a coherent state. Our measurement results are visualized by three-dimensional Stokes-operator noise volumes mapped on the quantum Poincare sphere. We quantitatively compare the channel capacity of the different continuous-variable polarization states for communication protocols. It is shown that squeezed polarization states provide 33% higher channel capacities than the optimum coherent beam protocol.

Continuous variable polarization entanglement, experiment and analysis

We generate and characterize continuous variable polarization entanglement between two optical beams. We first produce quadrature entanglement, and by performing local operations we transform it into a polarization basis. We extend two entanglement criteria, the inseparability criteria proposed by Duan et al (2000 Phys. Rev. Lett. 84 2722) and the Einstein–Podolsky–Rosen (EPR) paradox criteria proposed by Reid and Drummond (1988 Phys. Rev. Lett. 60 2731), to Stokes operators; and use them to characterize the entanglement. Our results for the EPR paradox criteria are visualized in terms of uncertainty balls on the Poincaré sphere. We demonstrate theoretically that using two quadrature entangled pairs it is possible to entangle three orthogonal Stokes operators between a pair of beams, although with a bound √3 times more stringent than for the quadrature entanglement.