Realization of quantum walks with negligible decoherence in waveguide lattices

Quantum random walks are the quantum counterpart of classical random walks, and were recently studied in the context of quantum computation. Physical implementations of quantum walks have only been made in very small scale systems severely limited by decoherence. Here we show that the propagation of photons in waveguide lattices, which have been studied extensively in recent years, are essentially an implementation of quantum walks. Since waveguide lattices are easily constructed at large scales and display negligible decoherence, they can serve as an ideal and versatile experimental playground for the study of quantum walks and quantum algorithms. We experimentally observe quantum walks in large systems ( approximately 100 sites) and confirm quantum walks effects which were studied theoretically, including ballistic propagation, disorder, and boundary related effects.     

Some problems associated with the control of distributed structures

Control of structures can be carried out conveniently by modal control, whereby the structure is controlled by controlling its modes. Modal control requires the estimation of the modal states for feedback, which can present a problem. One approach that does not require modal state estimation is direct feedback control, which implies collocated sensors and actuators. This paper examines some problems encountered in direct feedback control of distributed structures in conjunction with pole placement. A perturbation technique permits the computation of control gains for multi-input systems. The paper demonstrates that the difficulties experienced in using direct feedback in conjunction with pole placement are endemic to the approach.This research was sponsored by the Air Force Office of Scientific Research Grant No. AFOSR-83-0017, monitored by Dr. A. K. Amos, whose support is fully appreciated. This paper was presented at the Meeting on Optimal Control and Calculus of Variations, Oberwolfach, West Germany, June 15–21, 1986.     

Layer-by-layer assembly of ordinary and composite coordination multilayers

Coordination self-assembly of bishydroxamate-based metal-organic multilayers on gold employing a layer-by-layer (LbL) approach was investigated. It is shown that the solution chemistry of the participating metal ion has a marked influence on the composition and properties of the multilayers. Use of Ce4+ and particularly zirconium(IV) acetylacetonate (Zr(acac)4) solutions in the ion-binding step of multilayer construction leads to multilayers with a near-stoichiometric metal ion-to-ligand ratio, suggesting a structure close to that predicted by a simple coordination self-assembly scheme. On the other hand use of a ZrCl4 solution as the source of metal ions in the multilayer construction leads to a multilayer with greater thickness and a large excess of Zr(IV), evenly distributed between the organic layers. In the latter case, a ratio of ca. 1:2 between the excess Zr and oxygen, as well as long-term Zr4+ binding experiments showing deposition of ZrO2, suggest the formation of a zirconia-type nanophase between the bishydroxamate organic repeat units during multilayer self-assembly. Hence, while the multilayer prepared using Zr(acac)4 solution appears to represent a "true" coordination-based structure, the one prepared using ZrCl4 is best described as a composite organic-ceramic multilayer. Composite multilayers prepared in this way display different properties from those of the stoichiometric ones, such as improved dielectric behavior and higher stiffness. Even greater mechanical stability is obtained with multilayers constructed using alternate binding of ZrCl4 and Ce4+. The concept of LbL formation of coordination-based composite organic-ceramic structures may be useful in obtaining nanometer-scale structures with tunable properties.     

Effect of damping on observation spillover instability

The control of a distributed-parameter system can be effected by a transformation to a finite-dimensional discrete system in terms of modal coordinates. If only a limited number of modal coordinates is controlled, then a phenomenon that has come to be known as control and observation spillover occurs. Observation spillover has been demonstrated to cause instability in undamped systems. This paper shows that a minimal amount of damping can eliminate the instability, at least for the case considered.This work was supported by the Naval Research Laboratory, Space Systems Division, Advanced Systems Branch, under ONR Research Grant No. N00014-78-C-0194.     

Stochastic independent modal-space control of distributed-parameter systems

A method is presented for solving time-varying independent modal-space Kalman filter equations in terms of 2×2 transition matrices, rather than in terms of the more commonly used 4×4 transition matrix solution technique. The basic method consists of replacing the well-known product form solution for the differential matrix Riccati equation with an alternate solution form which consists of a steady-state plus transient term.     

Raman-induced localization in Kerr waveguide arrays

We show that during the spatiotemporal compression in a periodic Kerr waveguide array, stimulated Raman scattering can effectively balance the effects of self-phase modulation, diffraction, and group-velocity dispersion, eliminating collapse and breakup over a wide range of input powers and leading to stable propagation in a single site.     

Efficiency of monte carlo minimization procedures and their use in analysis of NMR data obtained from flexible peptides

The Monte Carlo minimization (MCM) method of Li and Scheraga is an efficient tool for generating low energy minimized structures of peptides, in particular the global energy minimum (GEM). In a recent article we proposed an enhancement to MCM, called the free energy Monte Carlo minimization (FMCM) procedure. With FMCM the conformational search is carried out with respect to the harmonic free energy, which approximates the free energy of the potential energy wells around the energy minimized structures (these wells are called localized microstates). In this work we apply both methods to the pentapeptide Leu-enkephalin described by the potential energy function ECEPP, and study their efficiency in identifying the GEM structure as well as the global harmonic free energy (GFM) structure. We also investigate the efficiency of these methods to generate localized microstates, which pertain to different energy and harmonic free energy intervals above the GEM and GFM, respectively. Such microstates constitute an important ingredient of our statistical mechanical methodology for analyzing nuclear magnetic resonance data of flexible peptides. Aspects of this methodology related to the stability properties of the localized microstates are examined. © 1997 by John Wiley & Sons, Inc.     

Microscopic origins of the anomalous melting behavior of sodium under high pressure

X-ray diffraction experiments have shown that sodium exhibits a dramatic pressure-induced drop in melting temperature, which extends from 1000 K at ~30 GPa to as low as room temperature at ~120 GPa. Despite significant theoretical effort to understand the anomalous melting, its origins are still debated. In this work, we reconstruct the sodium phase diagram by using an ab initio quality neural-network potential. Furthermore, we demonstrate that the reentrant behavior results from the screening of interionic interactions by conduction electrons, which at high pressure induces a softening in the short-range repulsion.