First-principles quantum simulations of dissociation of molecular condensates: Atom correlations in momentum space

We investigate the quantum many-body dynamics of dissociation of a Bose-Einstein condensate of molecular dimers into pairs of constituent bosonic atoms and analyze the resulting atom-atom correlations. The quantum fields of both the molecules and atoms are simulated from first principles in three dimensions using the positive-P representation method. This allows us to provide an exact treatment of the molecular field depletion and s-wave scattering interactions between the particles, as well as to extend the analysis to nonuniform systems. In the simplest uniform case, we find that the major source of atom-atom decorrelation is atom-atom recombination which produces molecules outside the initially occupied condensate mode. The unwanted molecules are formed from dissociated atom pairs with nonopposite momenta. The net effect of this process-which becomes increasingly significant for dissociation durations corresponding to more than about 40% conversion-is to reduce the atom-atom correlations. In addition, for nonuniform systems we find that mode mixing due to inhomogeneity can result in further degradation of the correlation signal. We characterize the correlation strength via the degree of squeezing of particle number-difference fluctuations in a certain momentum-space volume and show that the correlation strength can be increased if the signals are binned into larger counting volumes.

Gaussian phase-space representations for fermions

We introduce a positive phase-space representation for fermions, using the most general possible multimode Gaussian operator basis. The representation generalizes previous bosonic quantum phase-space methods to Fermi systems. We derive equivalences between quantum and stochastic moments, as well as operator correspondences that map quantum operator evolution onto stochastic processes in phase space. The representation thus enables first-principles quantum dynamical or equilibrium calculations in many-body Fermi systems. Potential applications are to strongly interacting and correlated Fermi gases, including coherent behavior in open systems and nanostructures described by master equations. Examples of an ideal gas and the Hubbard model are given, as well as a generic open system, in order to illustrate these ideas.

On the distributed compression of quantum information

The problem of distributed compression for correlated quantum sources is considered. The classical version of this problem was solved by Slepian and Wolf, who showed that distributed compression could take full advantage of redundancy in the local sources created by the presence of correlations. Here it is shown that, in general, this is not the case for quantum sources, by proving a lower bound on the rate sum for irreducible sources of product states which is stronger than the one given by a naive application of Slepian-Wolf. Nonetheless, strategies taking advantage of correlation do exist for some special classes of quantum sources. For example, Devetak and Winter demonstrated the existence of such a strategy when one of the sources is classical. Optimal nontrivial strategies for a different extreme, sources of Bell states, are presented here. In addition, it is explained how distributed compression is connected to other problems in quantum information theory, including information-disturbance questions, entanglement distillation and quantum error correction.

Optimal control, geometry, and quantum computing

We prove upper and lower bounds relating the quantum gate complexity of a unitary operation, U, to the optimal control cost associated to the synthesis of U. These bounds apply for any optimal control problem, and can be used to show that the quantum gate complexity is essentially equivalent to the optimal control cost for a wide range of problems, including time-optimal control and finding minimal distances on certain Riemannian, sub-Riemannian, and Finslerian manifolds. These results generalize the results of [Nielsen, Dowling, Gu, and Doherty, Science 311, 1133 (2006)], which showed that the gate complexity can be related to distances on a Riemannian manifold.

Phytotoxicity of surface waters of the Thames and Brisbane River Estuaries: A combined chemical analysis and bioassay approach for the comparison of two systems

The Thames Estuary, UK, and the Brisbane River, Australia, are comparable in size and catchment area. Both are representative of the large and growing number of the world's estuaries associated with major cities. Principle differences between the two systems relate to climate and human population pressures. In order to assess the potential phytotoxic impact of herbicide residues in the estuaries, surface waters were analysed with a PAM fluorometry-based bioassay that employs the photosynthetic efficiency (photosystem II quantum yield) of laboratory cultured microalgae, as an endpoint measure of phytotoxicity. In addition, surface waters were chemically analysed for a limited number of herbicides. Diuron atrazine and simazine were detected in both systems at comparable concentrations. In contrast, bioassay results revealed that whilst detected herbicides accounted for the observed phytotoxicity of Brisbane River extracts with great accuracy, they consistently explained only around 50% of the phytotoxicity induced by Thames Estuary extracts. Unaccounted for phytotoxicity in Thames surface waters is indicative of unidentified phytotoxins. The greatest phytotoxic response was measured at Charing Cross, Thames Estuary, and corresponded to a diuron equivalent concentration of 180 ng L-1. The study employs relative potencies (REP) of PSII impacting herbicides and demonstrates that chemical analysis alone is prone to omission of valuable information. Results of the study provide support for the incorporation of bioassays into routine monitoring programs where bioassay data may be used to predict and verify chemical contamination data, alert to unidentified compounds and provide the user with information regarding cumulative toxicity of complex mixtures. (c) 2005 Elsevier B.V. All rights reserved.

Quantum computation as geometry

Quantum computers hold great promise for solving interesting computational problems, but it remains a challenge to find efficient quantum circuits that can perform these complicated tasks. Here we show that finding optimal quantum circuits is essentially equivalent to finding the shortest path between two points in a certain curved geometry. By recasting the problem of finding quantum circuits as a geometric problem, we open up the possibility of using the mathematical techniques of Riemannian geometry to suggest new quantum algorithms or to prove limitations on the power of quantum computers.

Quantum entanglement in the two-impurity Kondo model

In order to quantify quantum entanglement in two-impurity Kondo systems, we calculate the concurrence, negativity, and von Neumann entropy. The entanglement of the two Kondo impurities is shown to be determined by two competing many-body effects, namely the Kondo effect and the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction, I. Due to the spin-rotational invariance of the ground state, the concurrence and negativity are uniquely determined by the spin-spin correlation between the impurities. It is found that there exists a critical minimum value of the antiferromagnetic correlation between the impurity spins which is necessary for entanglement of the two impurity spins. The critical value is discussed in relation with the unstable fixed point in the two-impurity Kondo problem. Specifically, at the fixed point there is no entanglement between the impurity spins. Entanglement will only be created [and quantum information processing (QIP) will only be possible] if the RKKY interaction exchange energy, I, is at least several times larger than the Kondo temperature, T-K. Quantitative criteria for QIP are given in terms of the impurity spin-spin correlation.

Quantum nondemolition measurements for quantum information

We discuss the characterization and properties of quantum nondemolition (QND) measurements on qubit systems. We introduce figures of merit which can be applied to systems of any Hilbert space dimension, thus providing universal criteria for characterizing QND measurements. The controlled-NOT gate and an optical implementation are examined as examples of QND devices for qubits. We also consider the QND measurement of weak values.

Relational time for systems of oscillators

Using an elementary example based on two simple harmonic oscillators, we show how a relational time may be defined that leads to an approximate Schrodinger dynamics for subsystems, with corrections leading to an intrinsic decoherence in the energy eigenstates of the subsystem.

Toy model for a relational formulation of quantum theory

In the absence of an external frame of reference-i.e., in background independent theories such as general relativity-physical degrees of freedom must describe relations between systems. Using a simple model, we investigate how such a relational quantum theory naturally arises by promoting reference systems to the status of dynamical entities. Our goal is twofold. First, we demonstrate using elementary quantum theory how any quantum mechanical experiment admits a purely relational description at a fundamental. Second, we describe how the original non-relational theory approximately emerges from the fully relational theory when reference systems become semi-classical. Our technique is motivated by a Bayesian approach to quantum mechanics, and relies on the noiseless subsystem method of quantum information science used to protect quantum states against undesired noise. The relational theory naturally predicts a fundamental decoherence mechanism, so an arrow of time emerges from a time-symmetric theory. Moreover, our model circumvents the problem of the collapse of the wave packet as the probability interpretation is only ever applied to diagonal density operators. Finally, the physical states of the relational theory can be described in terms of spin networks introduced by Penrose as a combinatorial description of geometry, and widely studied in the loop formulation of quantum gravity. Thus, our simple bottom-up approach (starting from the semiclassical limit to derive the fully relational quantum theory) may offer interesting insights on the low energy limit of quantum gravity.

Universal quantum computation with continuous-variable cluster states

We describe a generalization of the cluster-state model of quantum computation to continuous-variable systems, along with a proposal for an optical implementation using squeezed-light sources, linear optics, and homodyne detection. For universal quantum computation, a nonlinear element is required. This can be satisfied by adding to the toolbox any single-mode non-Gaussian measurement, while the initial cluster state itself remains Gaussian. Homodyne detection alone suffices to perform an arbitrary multimode Gaussian transformation via the cluster state. We also propose an experiment to demonstrate cluster-based error reduction when implementing Gaussian operations.

Effects of fire on the structure and composition of open eucalypt forests

Fires are integral to the healthy functioning of most ecosystems and are often poorly understood in policy and management, however, the relationship between floristic composition and habitat structure is intrinsically linked, particularly after fire. The aim of this study was to test whether the variability of habitat structure or floristic composition and abundance in forests at a regional scale can be explained in terms of fire frequency using historical data and experimental prescribed burns. We tested this hypothesis in open eucalypt forests of Fraser Island off the east coast of Australia. Fraser Island dunes show progressive stages in plant succession as access to nutrients decreases across the Island. We found that fire frequency was not a good predictor of floristic composition or abundance across dune systems; rather, its affects were dune specific. In contrast, habitat structure was strongly influenced by fire frequency, independent of dune system. A dense understorey occurred in frequently burnt areas, whereas infrequently burnt areas had a more even distribution of plant heights. Plant communities returned to pre-burn levels of composition and abundances within 6 months of a fire and frequently burnt areas were dominated by early successional species of plant. These ecosystems were characterized by low diversity and frequently burnt areas on the east coast were dominated by Pteridium. Greater midstorey canopy cover in low frequency areas reduces light penetration and allows other species to compete more effectively with Pteridium. Our results strongly indicate that frequent fires on the Island have resulted in a decrease in relative diversity through dominance of several species. Prescribed fire represents a powerful management tool to shape habitat structure and complexity of Fraser Island forests.

Spontaneous combustion and simulation of mine fires and their effects on mine ventilation systems

The structure of a comprehensive research project into mine fires study applying the Ventgraph mine fire simulation software, preplanning of escape scenarios and general interaction with rescue responses is outlined. The project has Australian Coal Association Research Program (ACARP) funding and also relies on substantial mining company site support. This practical input from mine operators is essential and allows the approach to be introduced in the most creditable way. The effort is built around the introduction of fire simulation computer software to the Australian mining industry and the consequent modelling of fire scenarios in selected different mine layouts. Application of the simulation software package to the changing mine layouts requires experience to achieve realistic outcomes. Most Australian mines of size currently use a ventilation network simulation program. Under the project a small subroutine has been written to transfer the input data from the existing mine ventilation network simulation program to ‘Ventgraph’. This has been tested successfully. To understand fire simulation behaviour on the mine ventilation system, it is necessary to understood the possible effects of mine fires on various mine ventilation systems correctly first. Case studies demonstrating the possible effects of fires on some typical Australian coal mine ventilation circuits have been examined. The situation in which there is some gas make at the face and effects with fire have also been developed to emphasise how unstable and dangerous situations may arise. The primary objective of the part of the study described in this paper is to use mine fire simulation software to gain better understanding of how spontaneous combustion initiated fires can interact with the complex ventilation behaviour underground during a substantial fire. It focuses on the simulation of spontaneous combustion sourced heatings that develop into open fires. Further, it examines ventilation behaviour effects of spontaneous combustion initiated pillar fires and examines the difficulties these can be present if a ventilation reversal occurs. It also briefly examines simulation of use of the inertisation to assist in mine recovery. Mine fires are recognised across the world as a major hazard issue. New approaches allowing improvement in understanding their consequences have been developed as an aid in handling this complex area.

Finitely coordinated models for low-temperature phases of amorphous systems

We introduce models of heterogeneous systems with finite connectivity defined on random graphs to capture finite-coordination effects on the low-temperature behaviour of finite-dimensional systems. Our models use a description in terms of small deviations of particle coordinates from a set of reference positions, particularly appropriate for the description of low-temperature phenomena. A Born-von Karman-type expansion with random coefficients is used to model effects of frozen heterogeneities. The key quantity appearing in the theoretical description is a full distribution of effective single-site potentials which needs to be determined self-consistently. If microscopic interactions are harmonic, the effective single-site potentials turn out to be harmonic as well, and the distribution of these single-site potentials is equivalent to a distribution of localization lengths used earlier in the description of chemical gels. For structural glasses characterized by frustration and anharmonicities in the microscopic interactions, the distribution of single-site potentials involves anharmonicities of all orders, and both single-well and double-well potentials are observed, the latter with a broad spectrum of barrier heights. The appearance of glassy phases at low temperatures is marked by the appearance of asymmetries in the distribution of single-site potentials, as previously observed for fully connected systems. Double-well potentials with a broad spectrum of barrier heights and asymmetries would give rise to the well-known universal glassy low-temperature anomalies when quantum effects are taken into account. © 2007 IOP Publishing Ltd.