Non-Markovian homodyne-mediated feedback on a two-level atom: a quantum trajectory treatment

Quantum feedback can stabilize a two-level atom against decoherence (spontaneous emission), putting it into an arbitrary (specified) pure state. This requires perfect homodyne detection of the atomic emission, and instantaneous feedback. Inefficient detection was considered previously by two of us. Here we allow for a non-zero delay time tau in the feedback circuit. Because a two-level atom is a non-linear optical system, an analytical solution is not possible. However, quantum trajectories allow a simple numerical simulation of the resulting non-Markovian process. We find the effect of the time delay to be qualitatively similar to chat of inefficient detection. The solution of the non-Markovian quantum trajectory will not remain fixed, so that the time-averaged state will be mixed, not pure. In the case where one tries to stabilize the atom in the excited state, an approximate analytical solution to the quantum trajectory is possible. The result, that the purity (P = 2Tr[rho (2)] - 1) of the average state is given by P = 1 - 4y tau (where gamma is the spontaneous emission rate) is found to agree very well with the numerical results. (C) 2001 Elsevier Science B.V. All rights reserved.

The programming language python in earth system simulations

-scale vary from a planetary scale and million years for convection problems to 100km and 10 years for fault systems simulations. Various techniques are in use to deal with the time dependency (e.g. Crank-Nicholson), with the non-linearity (e.g. Newton-Raphson) and weakly coupled equations (e.g. non-linear Gauss-Seidel). Besides these high-level solution algorithms discretization methods (e.g. finite element method (FEM), boundary element method (BEM)) are used to deal with spatial derivatives. Typically, large-scale, three dimensional meshes are required to resolve geometrical complexity (e.g. in the case of fault systems) or features in the solution (e.g. in mantel convection simulations). The modelling environment escript allows the rapid implementation of new physics as required for the development of simulation codes in earth sciences. Its main object is to provide a programming language, where the user can define new models and rapidly develop high-level solution algorithms. The current implementation is linked with the finite element package finley as a PDE solver. However, the design is open and other discretization technologies such as finite differences and boundary element methods could be included. escript is implemented as an extension of the interactive programming environment python (see www.python.org). Key concepts introduced are Data objects, which are holding values on nodes or elements of the finite element mesh, and linearPDE objects, which are defining linear partial differential equations to be solved by the underlying discretization technology. In this paper we will show the basic concepts of escript and will show how escript is used to implement a simulation code for interacting fault systems. We will show some results of large-scale, parallel simulations on an SGI Altix system. Acknowledgements: Project work is supported by Australian Commonwealth Government through the Australian Computational Earth Systems Simulator Major National Research Facility, Queensland State Government Smart State Research Facility Fund, The University of Queensland and SGI.

A scheme for efficient quantum computation wtih linear optics

Quantum computers promise to increase greatly the efficiency of solving problems such as factoring large integers, combinatorial optimization and quantum physics simulation. One of the greatest challenges now is to implement the basic quantum-computational elements in a physical system and to demonstrate that they can be reliably and scalably controlled. One of the earliest proposals for quantum computation is based on implementing a quantum bit with two optical modes containing one photon. The proposal is appealing because of the ease with which photon interference can be observed. Until now, it suffered from the requirement for non-linear couplings between optical modes containing few photons. Here we show that efficient quantum computation is possible using only beam splitters, phase shifters, single photon sources and photo-detectors. Our methods exploit feedback from photo-detectors and are robust against errors from photon loss and detector inefficiency. The basic elements are accessible to experimental investigation with current technology.

Searching oligo sets of human chromosome 12 using evolutionary strategies

DNA Microarray is a powerful tool to measure the level of a mixed population of nucleic acids at one time, which has great impact in many aspects of life sciences research. In order to distinguish nucleic acids with very similar composition by hybridization, it is necessary to design microarray probes with high specificities and sensitivities. Highly specific probes correspond to probes having unique DNA sequences; whereas highly sensitive probes correspond to those with melting temperature within a desired range and having no secondary structure. The selection of these probes from a set of functional DNA sequences (exons) constitutes a computationally expensive discrete non-linear search problem. We delegate the search task to a simple yet effective Evolution Strategy algorithm. The computational efficiency is also greatly improved by making use of an available bioinformatics tool.

Adaptive phase measurements in linear optical quantum computation

Photon counting induces an effective non-linear optical phase shift in certain states derived by linear optics from single photons. Although this non-linearity is non-deterministic, it is sufficient in principle to allow scalable linear optics quantum computation (LOQC). The most obvious way to encode a qubit optically is as a superposition of the vacuum and a single photon in one mode-so-called 'single-rail' logic. Until now this approach was thought to be prohibitively expensive (in resources) compared to 'dual-rail' logic where a qubit is stored by a photon across two modes. Here we attack this problem with real-time feedback control, which can realize a quantum-limited phase measurement on a single mode, as has been recently demonstrated experimentally. We show that with this added measurement resource, the resource requirements for single-rail LOQC are not substantially different from those of dual-rail LOQC. In particular, with adaptive phase measurements an arbitrary qubit state a alpha/0 > + beta/1 > can be prepared deterministically.

Analytical solutions of linear finite- and small-strain one-dimensional consolidation

Analytical solutions are presented for linear finite-strain one-dimensional consolidation of initially unconsolidated soil layers with surcharge loading for both one- and two-way drainage. These solutions complement earlier solutions for initially unconsolidated soil layers without surcharge and initially normally consolidated soil layers with surcharge. Small-strain solutions for the consolidation of initially unconsolidated soil layers with surcharge loading are also presented, and the relationship between the earlier solutions for initially unconsolidated soil without surcharge and the corresponding small-strain solutions, which was not addressed in the earlier work, is clarified. The new solutions for initially unconsolidated soil with surcharge loading can be applied to the analysis of low stress consolidation tests and to the partial validation of numerical solutions of non-linear finite-strain consolidation. They also clarify a formerly perplexing aspect of finite-strain solution charts first noted in numerical solutions. Copyright (C) 2004 John Wiley Sons, Ltd.

A D-optimal designed population pharmacokinetic study of itraconazole capsules and solution in adults with cystic fibrosis

Background: Oral itraconazole (ITRA) is used for the treatment of allergic bronchopulmonary aspergillosis in patients with cystic fibrosis (CF) because of its antifungal activity against Aspergillus species. ITRA has an active hydroxy-metabolite (OH-ITRA) which has similar antifungal activity. ITRA is a highly lipophilic drug which is available in two different oral formulations, a capsule and an oral solution. It is reported that the oral solution has a 60% higher relative bioavailability. The influence of altered gastric physiology associated with CF on the pharmacokinetics (PK) of ITRA and its metabolite has not been previously evaluated. Objectives: 1) To estimate the population (pop) PK parameters for ITRA and its active metabolite OH-ITRA including relative bioavailability of the parent after administration of the parent by both capsule and solution and 2) to assess the performance of the optimal design. Methods: The study was a cross-over design in which 30 patients received the capsule on the first occasion and 3 days later the solution formulation. The design was constrained to have a maximum of 4 blood samples per occasion for estimation of the popPK of both ITRA and OH-ITRA. The sampling times for the population model were optimized previously using POPT v.2.0.[1] POPT is a series of applications that run under MATLAB and provide an evaluation of the information matrix for a nonlinear mixed effects model given a particular design. In addition it can be used to optimize the design based on evaluation of the determinant of the information matrix. The model details for the design were based on prior information obtained from the literature, which suggested that ITRA may have either linear or non-linear elimination. The optimal sampling times were evaluated to provide information for both competing models for the parent and metabolite and for both capsule and solution simultaneously. Blood samples were assayed by validated HPLC.[2] PopPK modelling was performed using FOCE with interaction under NONMEM, version 5 (level 1.1; GloboMax LLC, Hanover, MD, USA). The PK of ITRA and OH‑ITRA was modelled simultaneously using ADVAN 5. Subsequently three methods were assessed for modelling concentrations less than the LOD (limit of detection). These methods (corresponding to methods 5, 6 & 4 from Beal[3], respectively) were (a) where all values less than LOD were assigned to half of LOD, (b) where the closest missing value that is less than LOD was assigned to half the LOD and all previous (if during absorption) or subsequent (if during elimination) missing samples were deleted, and (c) where the contribution of the expectation of each missing concentration to the likelihood is estimated. The LOD was 0.04 mg/L. The final model evaluation was performed via bootstrap with re-sampling and a visual predictive check. The optimal design and the sampling windows of the study were evaluated for execution errors and for agreement between the observed and predicted standard errors. Dosing regimens were simulated for the capsules and the oral solution to assess their ability to achieve ITRA target trough concentration (Cmin,ss of 0.5-2 mg/L) or a combined Cmin,ss for ITRA and OH-ITRA above 1.5mg/L. Results and Discussion: A total of 241 blood samples were collected and analysed, 94% of them were taken within the defined optimal sampling windows, of which 31% where taken within 5 min of the exact optimal times. Forty six per cent of the ITRA values and 28% of the OH-ITRA values were below LOD. The entire profile after administration of the capsule for five patients was below LOD and therefore the data from this occasion was omitted from estimation. A 2-compartment model with 1st order absorption and elimination best described ITRA PK, with 1st order metabolism of the parent to OH-ITRA. For ITRA the clearance (ClItra/F) was 31.5 L/h; apparent volumes of central and peripheral compartments were 56.7 L and 2090 L, respectively. Absorption rate constants for capsule (kacap) and solution (kasol) were 0.0315 h-1 and 0.125 h-1, respectively. Comparative bioavailability of the capsule was 0.82. There was no evidence of nonlinearity in the popPK of ITRA. No screened covariate significantly improved the fit to the data. The results of the parameter estimates from the final model were comparable between the different methods for accounting for missing data, (M4,5,6)[3] and provided similar parameter estimates. The prospective application of an optimal design was found to be successful. Due to the sampling windows, most of the samples could be collected within the daily hospital routine, but still at times that were near optimal for estimating the popPK parameters. The final model was one of the potential competing models considered in the original design. The asymptotic standard errors provided by NONMEM for the final model and empirical values from bootstrap were similar in magnitude to those predicted from the Fisher Information matrix associated with the D-optimal design. Simulations from the final model showed that the current dosing regimen of 200 mg twice daily (bd) would provide a target Cmin,ss (0.5-2 mg/L) for only 35% of patients when administered as the solution and 31% when administered as capsules. The optimal dosing schedule was 500mg bd for both formulations. The target success for this dosing regimen was 87% for the solution with an NNT=4 compared to capsules. This means, for every 4 patients treated with the solution one additional patient will achieve a target success compared to capsule but at an additional cost of AUD $220 per day. The therapeutic target however is still doubtful and potential risks of these dosing schedules need to be assessed on an individual basis. Conclusion: A model was developed which described the popPK of ITRA and its main active metabolite OH-ITRA in adult CF after administration of both capsule and solution. The relative bioavailability of ITRA from the capsule was 82% that of the solution, but considerably more variable. To incorporate missing data, using the simple Beal method 5 (using half LOD for all samples below LOD) provided comparable results to the more complex but theoretically better Beal method 4 (integration method). The optimal sparse design performed well for estimation of model parameters and provided a good fit to the data.

Bifurcations in the non-dissipative dynamics of ultra cold atoms

We present the first experimental observation of several bifurcations in a controllable non-linear Hamiltonian system. Dynamics of cold atoms are used to test predictions of non-linear, non-dissipative Hamiltonian dynamics.

Computationally efficient solution techniques for adsorption problems involving steep gradients in bidisperse particles

A piecewise uniform fitted mesh method turns out to be sufficient for the solution of a surprisingly wide variety of singularly perturbed problems involving steep gradients. The technique is applied to a model of adsorption in bidisperse solids for which two fitted mesh techniques, a fitted-mesh finite difference method (FMFDM) and fitted mesh collocation method (FMCM) are presented. A combination (FMCMD) of FMCM and the DASSL integration package is found to be most effective in solving the problems. Numerical solutions (FMFDM and FMCMD) were found to match the analytical solution when the adsorption isotherm is linear, even under conditions involving steep gradients for which global collocation fails. In particular, FMCMD is highly efficient for macropore diffusion control or micropore diffusion control. These techniques are simple and there is no limit on the range of the parameters. The techniques can be applied to a variety of adsorption and desorption problems in bidisperse solids with non-linear isotherm and for arbitrary particle geometry.

Relative dispersions of intra-albumin transit times across rat and elasmobranch perfused livers, and implications for intra- and inter-species scaling of hepatic clearance using microsomal data

It is recognized that vascular dispersion in the liver is a determinant of high first-pass extraction of solutes by that organ. Such dispersion is also required for translation of in-vitro microsomal activity into in-vivo predictions of hepatic extraction for any solute. We therefore investigated the relative dispersion of albumin transit times (CV2) in the livers of adult and weanling rats and in elasmobranch livers. The mean and normalized variance of the hepatic transit time distribution of albumin was estimated using parametric non-linear regression (with a correction for catheter influence) after an impulse (bolus) input of labelled albumin into a single-pass liver perfusion. The mean +/- s.e. of CV2 for albumin determined in each of the liver groups were 0.85 +/- 0.20 (n = 12), 1.48 +/- 0.33 (n = 7) and 0.90 +/- 0.18 (n = 4) for the livers of adult and weanling rats and elasmobranch livers, respectively. These CV2 are comparable with that reported previously for the dog and suggest that the CV2 Of the liver is of a similar order of magnitude irrespective of the age and morphological development of the species. It might, therefore, be justified, in the absence of other information, to predict the hepatic clearances and availabilities of highly extracted solutes by scaling within and between species livers using hepatic elimination models such as the dispersion model with a CV2 of approximately unity.

Quantum chaos in atom optics

I shall discuss the quantum and classical dynamics of a class of nonlinear Hamiltonian systems. The discussion will be restricted to systems with one degree of freedom. Such systems cannot exhibit chaos, unless the Hamiltonians are time dependent. Thus we shall consider systems with a potential function that has a higher than quadratic dependence on the position and, furthermore, we shall allow the potential function to be a periodic function of time. This is the simplest class of Hamiltonian system that can exhibit chaotic dynamics. I shall show how such systems can be realized in atom optics, where very cord atoms interact with optical dipole potentials of a far-off resonance laser. Such systems are ideal for quantum chaos studies as (i) the energy of the atom is small and action scales are of the order of Planck's constant, (ii) the systems are almost perfectly isolated from the decohering effects of the environment and (iii) optical methods enable exquisite time dependent control of the mechanical potentials seen by the atoms.