Jason F. Ralph

The emergence of chaos in an open quantum system

Abstract We take a simple open quantum system and demonstrate that it can exhibit behaviour, similar to that found in its chaotic classical analogue, when it is treated as an individual system, rather than using a statistical ensemble.

Molecular-Dynamics Simulations of Dynamic Phenomena in Complex Plasmas

Complex plasmas consist of micrometer-sized spheres immersed into an ordinary ion-electron plasma. They exist in solid, liquid, and gaseous states, sustain particle-mediated waves, and exhibit a range of nonlinear and dynamic effects. Here, we present a numerical study of nonlinear-wave steepening (tsunami effect), interaction of solitons, and shock-wave propagation in monolayer complex plasmas. The simulated results are found to be in a good agreement with the experiments. It was also found that the simulation using a tenth-order confinement potential produced more homogeneous lattices with fewer defects than that with the conventional parabolic potential.

Automatic Induction of Projection Pursuit Indices

Projection techniques are frequently used as the principal means for the implementation of feature extraction and dimensionality reduction for machine learning applications. A well established and broad class of such projection techniques is the projection pursuit (PP). Its core design parameter is a projection index, which is the driving force in obtaining the transformation function via optimization, and represents in an explicit or implicit way the users perception of the useful information contained within the datasets. This paper seeks to address the problem related to the design of PP index functions for the linear feature extraction case. We achieve this using an evolutionary search framework, capable of building new indices to fit the properties of the available datasets. The high expressive power of this framework is sustained by a rich set of function primitives. The performance of several PP indices previously proposed by human experts is compared with these automatically generated indices for the task of classification, and results show a decrease in the classification errors.

Generalized Regression Neural Networks With Multiple-Bandwidth Sharing and Hybrid Optimization

This paper proposes a novel algorithm for function approximation that extends the standard generalized regression neural network. Instead of a single bandwidth for all the kernels, we employ a multiple-bandwidth configuration. However, unlike previous works that use clustering of the training data for the reduction of the number of bandwidths, we propose a distinct scheme that manages a dramatic bandwidth reduction while preserving the required model complexity. In this scheme, the algorithm partitions the training patterns to groups, where all patterns within each group share the same bandwidth. Grouping relies on the analysis of the local nearest neighbor distance information around the patterns and the principal component analysis with fuzzy clustering. Furthermore, we use a hybrid optimization procedure combining a very efficient variant of the particle swarm optimizer and a quasi-Newton method for global optimization and locally optimal fine-tuning of the network bandwidths. Training is based on the minimization of a flexible adaptation of the leave-one-out validation error that enhances the network generalization. We test the proposed algorithm with real and synthetic datasets, and results show that it exhibits competitive regression performance compared to other techniques.

Quantum Statistics and Entanglement of Two Electromagnetic Field Modes Coupled via a Mesoscopic SQUID Ring

In this paper we investigate the behaviour of a fully quantum mechanical system consisting of a mesoscopic SQUID ring coupled to one or two electromagnetic field modes. We show that we can use a static magnetic flux threading the SQUID ring to control the transfer of energy, the entanglement and the statistical properties of the fields coupled to the ring. We also demonstrate that at, and around, certain values of static flux the effective coupling between the components of the system is large. The position of these regions in static flux is dependent on the energy level structure of the ring and the relative field mode frequencies, In these regions we find that the entanglement of states in the coupled system, and the energy transfer between its components, is strong.

The Response of a Superconducting Weak-Link Ring to External Adiabatic Noise (*).

SummaryWe discuss the response of a superconducting weak-link ring to externally applied adiabatic noise and show that this can be used as a probe of the low-lying energy eigenstates of the ring. We compare the observable consequences of this with new experimental results.

Fully quantum mechanical model of a SQUID ring coupled to an electromagnetic field

A quantum system comprising of a monochromatic electromagnetic field coupled to a superconducting quantum interference device (SQUID) ring with sinusoidal nonlinearity is studied. A magnetostatic flux Fx is also threading the SQUID ring, and is used to control the coupling between the two systems. It is shown that for special values of Fx the system is strongly coupled. The time evolution of the system is studied. It is shown that exchange of energy takes place between the two modes and that the system becomes entangled. A second quasiclassical model that treats the electromagnetic field classically is also studied. A comparison between the fully quantum-mechanical model with the electromagnetic field initially in a coherent state and the quasiclassical model is made.

Local versus global strategies in multiparameter estimation

We consider the problem of estimating multiple phases using a multi-mode interferometer. In this setting we show that while global strategies that estimate all the phases simultaneously can lead to high precision gains, the same enhancements can be obtained with local strategies where each phase is estimated individually. A key resource for the enhancement is shown to be a large particle-number variance in the probe state, and for states where the total particle number is not fixed, this can be obtained for mode-separable states and the phases can be read out with local measurements. This has important practical implications because local strategies are generally preferred to global ones for their robustness to local estimation failure, flexibility in the distribution of resources, and comparatively easier state preparation. We obtain our results by analyzing two different schemes: the first uses a set of interferometers, which can be used as a model for a network of quantum sensors, and the second looks at measuring a number of phases relative to a reference, which is concerned primarily with quantum imaging.

Ideal Gas Behavior of a Strongly Coupled Complex (Dusty) Plasma

In a laboratory, a two-dimensional complex (dusty) plasma consists of a low-density ionized gas containing a confined suspension of Yukawa-coupled plastic microspheres. For an initial crystal-like form, we report ideal gas behavior in this strongly coupled system during shock-wave experiments. This evidence supports the use of the ideal gas law as the equation of state for soft crystals such as those formed by dusty plasmas.

Rapid-state purification protocols for a Cooper pair box

We propose techniques for implementing two different rapid state purification schemes, within the constraints present in a superconducting charge qubit system. Both schemes use a continuous measurement of charge (z) measurements, and seek to minimize the time required to purify the conditional state. Our methods are designed to make the purification process relatively insensitive to rotations about the x-axis, due to the Josephson tunnelling Hamiltonian. The first proposed method, based on the scheme of Jacobs [Phys. Rev. A 67, 030301(R) (2003)] uses the measurement results to control bias (z) pulses so as to rotate the Bloch vector onto the x-axis of the Bloch sphere. The second proposed method, based on the scheme of Wiseman and Ralph [New J. Phys. 8, 90 (2006)] uses a simple feedback protocol which tightly rotates the Bloch vector about an axis almost parallel with the measurement axis. We compare the performance of these and other techniques by a number of different measures.