Experimental tests of quantum nonlinear dynamics in atom optics

Cold atoms in optical potentials provide an ideal test bed to explore quantum nonlinear dynamics. Atoms are prepared in a magneto-optic trap or as a dilute Bose-Einstein condensate and subjected to a far detuned optical standing wave that is modulated. They exhibit a wide range of dynamics, some of which can be explained by classical theory while other aspects show the underlying quantum nature of the system. The atoms have a mixed phase space containing regions of regular motion which appear as distinct peaks in the atomic momentum distribution embedded in a sea of chaos. The action of the atoms is of the order of Planck's constant, making quantum effects significant. This tutorial presents a detailed description of experiments measuring the evolution of atoms in time-dependent optical potentials. Experimental methods are developed providing means for the observation and selective loading of regions of regular motion. The dependence of the atomic dynamics on the system parameters is explored and distinct changes in the atomic momentum distribution are observed which are explained by the applicable quantum and classical theory. The observation of a bifurcation sequence is reported and explained using classical perturbation theory. Experimental methods for the accurate control of the momentum of an ensemble of atoms are developed. They use phase space resonances and chaotic transients providing novel ensemble atomic beamsplitters. The divergence between quantum and classical nonlinear dynamics is manifest in the experimental observation of dynamical tunnelling. It involves no potential barrier. However a constant of motion other than energy still forbids classically this quantum allowed motion. Atoms coherently tunnel back and forth between their initial state of oscillatory motion and the state 180 out of phase with the initial state.

On the Dynamics of Mining Operations in Open Pit Mines

In this paper, mining dynamics is defined as the relationship between the mining rate and movement of mining operations conducted on the benches of a surface mine. This relationship describes the intensity of the pit development in space, in order to meet ore demand at the mill over time. Meeting the mill ore demand is a key factor in optimizing production scheduling in surface mines. Displacement velocity of mining operations within cutbacks, or independent pit units, is introduced in the context of long-term mine planning. Displacement velocity allows the place and time of transition of the mining operations from one independent pit unit to another to be determined as the condition for meeting the mill ore demand. An application using data from Mt Keith Nickel Operations in Western Australia is used to elaborate on the methods presented.

Quantum dynamics with stochastic gauge simulations

The general idea of a stochastic gauge representation is introduced and compared with more traditional phase-space expansions, like the Wigner expansion. Stochastic gauges can be used to obtain an infinite class of positive-definite stochastic time-evolution equations, equivalent to master equations, for many systems including quantum time evolution. The method is illustrated with a variety of simple examples ranging from astrophysical molecular hydrogen production, through to the topical problem of Bose-Einstein condensation in an optical trap and the resulting quantum dynamics.

A Lanczos-powered implementation of the Faber polynomial quantum time propagator for reaction probabilities

Complementing our recent work on subspace wavepacket propagation [Chem. Phys. Lett. 336 (2001) 149], we introduce a Lanczos-based implementation of the Faber polynomial quantum long-time propagator. The original version [J. Chem. Phys. 101 (1994) 10493] implicitly handles non-Hermitian Hamiltonians, that is, those perturbed by imaginary absorbing potentials to handle unwanted reflection effects. However, like many wavepacket propagation schemes, it encounters a bottleneck associated with dense matrix-vector multiplications. Our implementation seeks to reduce the quantity of such costly operations without sacrificing numerical accuracy. For some benchmark scattering problems, our approach compares favourably with the original. (C) 2004 Elsevier B.V. All rights reserved.

Fungible dynamics: There are only two types of entangling multiple-qubit interactions

What interactions are sufficient to simulate arbitrary quantum dynamics in a composite quantum system? It has been shown that all two-body Hamiltonian evolutions can be simulated using any fixed two-body entangling n-qubit Hamiltonian and fast local unitaries. By entangling we mean that every qubit is coupled to every other qubit, if not directly, then indirectly via intermediate qubits. We extend this study to the case where interactions may involve more than two qubits at a time. We find necessary and sufficient conditions for an arbitrary n-qubit Hamiltonian to be dynamically universal, that is, able to simulate any other Hamiltonian acting on n qubits, possibly in an inefficient manner. We prove that an entangling Hamiltonian is dynamically universal if and only if it contains at least one coupling term involving an even number of interacting qubits. For odd entangling Hamiltonians, i.e., Hamiltonians with couplings that involve only an odd number of qubits, we prove that dynamic universality is possible on an encoded set of n-1 logical qubits. We further prove that an odd entangling Hamiltonian can simulate any other odd Hamiltonian and classify the algebras that such Hamiltonians generate. Thus, our results show that up to local unitary operations, there are only two fundamentally different types of entangling Hamiltonian on n qubits. We also demonstrate that, provided the number of qubits directly coupled by the Hamiltonian is bounded above by a constant, our techniques can be made efficient.

Of sheep and rain: large-scale population dynamics of the red kangaroo

1. We analysed time-series data from populations of red kangaroos (Macropus rufus, Desmarest) inhabiting four areas in the pastoral zone of South Australia. We formulated a set of a priori models to disentangle the relative effects of the covariates: rainfall, harvesting, intraspecific competition, and domestic herbivores, on kangaroo population-growth rate. 2. The statistical framework allowed for spatial variation in the growth-rate parameters, response to covariates, and environmental variability, as well as spatially correlated error terms due to shared environment. 3. The most parsimonious model included all covariates but no area-specific parameter values, suggesting that kangaroo densities respond in the same way to the covariates across the areas. 4. The temporal dynamics were spatially correlated, even after taking into account the potentially synchronizing effect of rainfall, harvesting and domestic herbivores. 5. Counter-intuitively, we found a positive rather than negative effect of domestic herbivore density on the population-growth rate of kangaroos. We hypothesize that this effect is caused by sheep and cattle acting as a surrogate for resource availability beyond rainfall. 6. Even though our system is well studied, we must conclude that approximating resources by surrogates such as rainfall is more difficult than previously thought. This is an important message for studies of consumer-resource systems and highlights the need to be explicit about population processes when analysing population patterns.

Auxin dynamics after decapitation are not correlated with the initial growth of axillary buds

One of the first and most enduring roles identified for the plant hormone auxin is the mediation of apical dominance. Many reports have claimed that reduced stem indole-3-acetic acid (IAA) levels and/ or reduced basipetal IAA transport directly or indirectly initiate bud growth in decapitated plants. We have tested whether auxin inhibits the initial stage of bud release, or subsequent stages, in garden pea (Pisum sativum) by providing a rigorous examination of the dynamics of auxin level, auxin transport, and axillary bud growth. We demonstrate that after decapitation, initial bud growth occurs prior to changes in IAA level or transport in surrounding stem tissue and is not prevented by an acropetal supply of exogenous auxin. We also show that auxin transport inhibitors cause a similar auxin depletion as decapitation, but do not stimulate bud growth within our experimental time- frame. These results indicate that decapitation may trigger initial bud growth via an auxin-independent mechanism. We propose that auxin operates after this initial stage, mediating apical dominance via autoregulation of buds that are already in transition toward sustained growth.

Time-resolved spectroscopy of the metal-to-metal charge transfer excited state in dinuclear cyano-bridged mixed-valence complexes

Visible pump-probe spectroscopy has been used to identify and characterize short-lived metal-to-metal charge transfer (MMCT) excited states in a group of cyano-bridged mixed-valence complexes of the formula [(LCoNCMII)-N-III(CN)(5)](-), where L is a pentadentate macrocyclic pentaamine (L-14) or triamine-dithiaether (L-14S) and M is Fe or Ru. Nanosecond pump-probe spectroscopy on frozen solutions of [(LCoNCFeII)-Co-14-N-III(CN)(5)](-) and [(LCoNCFeII)-Co-14S-N-III(CN)(5)](-) at 11 K enabled the construction of difference transient absorption spectra that featured a rise in absorbance in the region of 350-400 nm consistent with the generation of the ferricyanide chromophore of the photoexcited complex. The MMCT excited state of the Ru analogue [(LCoNCRuII)-Co-14-N-III(CN)(5)](-) was too short-lived to allow its detection. Femtosecond pump-probe spectroscopy on aqueous solutions of [(LCoNCFeII)-Co-14-N-III(CN)(5)](-) and [(LCoNCFeII)-Co-14S-N-III(CN)(5)](-) at room temperature enabled the lifetimes of their Co-II-Fe-III MMCT excited states to be determined as 0.8 and 1.3 ps, respectively.

Quantum dynamics of a model for two Josephson-coupled Bose-Einstein condensates

In this work, we investigate the quantum dynamics of a model for two singlemode Bose-Einstein condensates which are coupled via Josephson tunnelling. Using direct numerical diagonalization of the Hamiltonian, we compute the time evolution of the expectation value for the relative particle number across a wide range of couplings. Our analysis shows that the system exhibits rich and complex behaviours varying between harmonic and non-harmonic oscillations, particularly around the threshold coupling between the delocalized and selftrapping phases. We show that these behaviours are dependent on both the initial state of the system and regime of the coupling. In addition, a study of the dynamics for the variance of the relative particle number expectation and the entanglement for different initial states is presented in detail.

FRAP analysis of nucleocytoplasmic dynamics of the vitamin D receptor splice variant VDRB1: preferential targeting to nuclear speckles

Although the key components of the cellular nuclear transport machinery have largely been characterized through extensive efforts in recent years, in vivo measurements of the kinetics of nuclear protein import/export are patently few. The present study applies the approach of FRAP (fluorescence recovery after photobleaching) to examine the nucleocytoplasmic flux of a novel human VDRB1 (vitamin D receptor B I) isoform in living cells. Through an N-terminal extension containing a consensus nuclear targeting sequence, VDRB1 is capable of localizing in nuclear speckles adjacent to SC-35 (35 kDa splicing component)containing speckles as well as in the nucleoplasm, dependent on ligand. Investigation of VDRB1 nucleocytoplasmic transport using FRAP indicates for the first time that the VDRB1 has a serum-modulated, active nuclear-import mechanism. There is no evidence of an efficient, active export mechanism for VDRB1, probably as a result of nuclear retention. VDRB1 nuclear import in the absence of serum occurred more rapidly and to a greater extent to nuclear speckles compared with import to other nuclear sites. This preferential transport from the cytoplasm to and accumulation within nuclear speckles is consistent with the idea that the latter represent dynamic centres of VDRB1 interaction with other nuclear proteins. The results are consistent with the existence of specialized pathways to target proteins to nuclear subdomains.

Energy transfer dynamics of nanocrystal-polymer composites

Steady-state and time-resolved photoluminescence spectroscopy are used to examine the photoluminescent properties of nanocrystal-polymer composites consisting of colloidal PbS nanocrystals blended with poly(2-methoxy-5(2-ethylhexyloxy)-p-phenylene vinylene). Quenching of the emission from the conjugated polymer due to the PbS nanocrystals is observed along with band edge emission from the ligand capped PbS nanocrystals. A decrease in the photoluminescence lifetime of MEH-PPV is also observed in the thin film nanocrystal-polymer composite materials. Photoluminescence excitation spectroscopy of the PbS nanocrystal emission from the composite shows features attributed to MEH-PPV providing evidence of a Forster transfer process.

A stochastic metapopulation model accounting for habitat dynamics

A stochastic metapopulation model accounting for habitat dynamics is presented. This is the stochastic SIS logistic model with the novel aspect that it incorporates varying carrying capacity. We present results of Kurtz and Barbour, that provide deterministic and diffusion approximations for a wide class of stochastic models, in a form that most easily allows their direct application to population models. These results are used to show that a suitably scaled version of the metapopulation model converges, uniformly in probability over finite time intervals, to a deterministic model previously studied in the ecological literature. Additionally, they allow us to establish a bivariate normal approximation to the quasi-stationary distribution of the process. This allows us to consider the effects of habitat dynamics on metapopulation modelling through a comparison with the stochastic SIS logistic model and provides an effective means for modelling metapopulations inhabiting dynamic landscapes.

Evolutionary dynamics of wAu-Like Wolbachia variants in neotropical Drosophila spp.

Wolbachia bacteria are common intracellular symbionts of arthropods and have been extensively studied in Drosophila. Most research focuses on two Old Word hosts, Drosophila melanogaster and Drosophila simulans, and does not take into account that some of the Wolbachia associations in these species may have evolved only after their fast global expansion and after the exposure to Wolbachia of previously isolated habitats. Here we looked at Wolbachia of Neotropical Drosophila species. Seventy-one lines of 16 Neotropical Drosophild species sampled in different regions and at different time points were analyzed. Wolbachia is absent in lines of Drosophild willistoni collected before the 1970s, but more recent samples are infected with a strain designated wWiL Wolbachia is absent in all other species of the willistoni group. Polymorphic wWil-related strains were detected in some saltans group species, with D. septentriosaltans being coinfected with at least four variants. Based on wsp and ftsZ sequence data, wWil of D. willistoni is identical to wAu, a strain isolated from D. simulans, but can be discriminated when using a polymorphic minisatellite marker. In contrast to wAu, which infects both germ line and somatic tissues of D. simulans, wWil is found exclusively in the primordial germ line cells of D. willistoni embryos. We report on a pool of closely related Wolbachia strains in Neotropical Drosophila species as a potential source for the wAu strain in D. simulans. Possible evolutionary scenarios reconstructing the infection history of wAu-like Wolbachia in Neotropical Drosophild species and the Old World species D. simulans are discussed.

First-principles quantum dynamics in interacting Bose gases II: stochastic gauges

First principles simulations of the quantum dynamics of interacting Bose gases using the stochastic gauge representation are analysed. In a companion paper, we showed how the positive-P representation can be applied to these problems using stochastic differential equations. That method, however, is limited by increased sampling error as time evolves. Here, we show how the sampling error can be greatly reduced and the simulation time significantly extended using stochastic gauges. In particular, local stochastic gauges (a subset) are investigated. Improvements are confirmed in numerical calculations of single-, double- and multi-mode systems in the weak-mode coupling regime. Convergence issues are investigated, including the recognition of two modes by which stochastic equations produced by phase-space methods in general can diverge: movable singularities and a noise-weight relationship. The example calculated here displays wave-like behaviour in spatial correlation functions propagating in a uniform 1D gas after a sudden change in the coupling constant. This could in principle be tested experimentally using Feshbach resonance methods.

First-principles quantum dynamics in interacting Bose gases: I. The positive P representation

The performance of the positive P phase-space representation for exact many- body quantum dynamics is investigated. Gases of interacting bosons are considered, where the full quantum equations to simulate are of a Gross-Pitaevskii form with added Gaussian noise. This method gives tractable simulations of many-body systems because the number of variables scales linearly with the spatial lattice size. An expression for the useful simulation time is obtained, and checked in numerical simulations. The dynamics of first-, second- and third-order spatial correlations are calculated for a uniform interacting 1D Bose gas subjected to a change in scattering length. Propagation of correlations is seen. A comparison is made with other recent methods. The positive P method is particularly well suited to open systems as no conservation laws are hard-wired into the calculation. It also differs from most other recent approaches in that there is no truncation of any kind.