Conditions for the Quantum to Classical Transition: Trajectories vs. Phase Space Distributions

We contrast two sets of conditions that govern the transition in which classical dynamics emerges from the evolution of a quantum system. The first was derived by considering the trajectories seen by an observer (dubbed the ``strong'' transition) [Bhattacharya, et al., Phys. Rev. Lett. 85: 4852 (2000)], and the second by considering phase-space densities (the ``weak'' transition) [Greenbaum, et al., Chaos 15, 033302 (2005)]. On the face of it these conditions appear rather different. We show, however, that in the semiclassical regime, in which the action of the system is large compared to $\hbar$, and the measurement noise is small, they both offer an essentially equivalent local picture. Within this regime, the weak conditions dominate while in the opposite regime where the action is not much larger than Planck's constant, the strong conditions dominate.Comment: 8 pages, 2 eps figure

The Quantum Emergence of Chaos

The dynamical status of isolated quantum systems, partly due to the linearity of the Schrodinger equation is unclear: Conventional measures fail to detect chaos in such systems. However, when quantum systems are subjected to observation -- as all experimental systems must be -- their dynamics is no longer linear and, in the appropriate limit(s), the evolution of expectation values, conditioned on the observations, closely approaches the behavior of classical trajectories. Here we show, by analyzing a specific example, that microscopic continuously observed quantum systems, even far from any classical limit, can have a positive Lyapunov exponent, and thus be truly chaotic.Comment: 4 pages, 4 figure

Statics and dynamics of domain patterns in hexagonal-orthorhombic ferroelastics

We study the statics and the dynamics of domain patterns in proper hexagonal-orthorhombic ferroelastics; these patterns are of particular interest because they provide a rare physical realization of disclinations in crystals. Both our static and dynamical theories are based entirely on classical, nonlinear elasticity theory; we use the minimal theory consistent with stability, symmetry and ability to explain qualitatively the observed patterns. After scaling, the only parameters of the static theory are a temperature variable and a stiffness variable. For moderate to large stiffness, our static results show nested stars, unnested stars, fans and other nodes, triangular and trapezoidal regions of trapped hexagonal phase, etc observed in electron microscopy of Ta4N and Mg-Cd alloys, and also in lead orthovanadate (which is trigonal-monoclinic); we even find imperfections in some nodes, like those observed. For small stiffness, we find patterns like those observed in the mineral Mg-cordierite. Our dynamical studies of growth and relaxation show the formation of these static patterns, and also transitory structures such as 12-armed bursts, streamers and striations which are also seen experimentally. The major aspects of the growth-relaxation process are quite unlike those in systems with conventional order parameters, for it is inherently nonlocal; for example, the changes from one snapshot to the next are not predictable by inspection.Comment: 9 pages, 3 figures (1 b&w, 2 colour); animations may be viewed at http://huron.physics.utoronto.ca/~curnoe/sim.htm

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.Comment: 14 pages, 14 figures. v2: Revised version after referee comments. Accepted for publication by Physical Review

Standard Quantum Limits for broadband position measurement

I utilize the Caves-Milburn model for continuous position measurements to formulate a broadband version of the Standard Quantum Limit (SQL) for monitoring the position of a free mass, and illustrate the use of Kalman filtering to recover the SQL for estimating a weak classical force that acts on a quantum-mechanical test particle under continuous observation. These derivations are intended to clarify the interpretation of SQL's in the context of continuous quantum measurement.Comment: Replaced version: changed title, fixed algebra error at the very end, conclusions modified accordingly. Four pages, one eps figur

Cluster counting: The Hoshen-Kopelman algorithm vs. spanning tree approaches

Two basic approaches to the cluster counting task in the percolation and related models are discussed. The Hoshen-Kopelman multiple labeling technique for cluster statistics is redescribed. Modifications for random and aperiodic lattices are sketched as well as some parallelised versions of the algorithm are mentioned. The graph-theoretical basis for the spanning tree approaches is given by describing the "breadth-first search" and "depth-first search" procedures. Examples are given for extracting the elastic and geometric "backbone" of a percolation cluster. An implementation of the "pebble game" algorithm using a depth-first search method is also described.Comment: LaTeX, uses ijmpc1.sty(included), 18 pages, 3 figures, submitted to Intern. J. of Modern Physics

Optimal Unravellings for Feedback Control in Linear Quantum Systems

For quantum systems with linear dynamics in phase space much of classical feedback control theory applies. However, there are some questions that are sensible only for the quantum case, such as: given a fixed interaction between the system and the environment what is the optimal measurement on the environment for a particular control problem? We show that for a broad class of optimal (state-based) control problems (the stationary Linear-Quadratic-Gaussian class), this question is a semi-definite program. Moreover, the answer also applies to Markovian (current-based) feedback.Comment: 5 pages. Version published by Phys. Rev. Let

Holocene Environmental Change in the Frobisher Bay Area, Baffin Island, N.W.T.: Deglaciation, Emergence, and the Sequence of Vegetation and Climate

The late-glacial and Holocene paleoenvironmental sequence for the Frobisher Bay area is outlined using glacial, sea level, and palynological evidence. A rapid retreat of ice from the late Foxe glacial maximum in the lower part of the bay after 11,000 BP was followed by a series of stillstands or minor readvances between ca. 8500 and 7000 BP and possibly later, before the final disappearance of the inland ice centred near Amadjuak Lake. Lithostratigraphy of three buried organic sections which together represent deposition occurring over the period from 5500 to 400 BP indicates a change from a relatively warm, moist environment before 5500 BP to neoglacial conditions, with the coldest phases centred around 5000, 2700, 1200 BP and probably sometime after 400 radiocarbon years BP. As evidenced by peat growth and pollen data, milder, wetter conditions prevailed from 4500 to 3000 BP and again from ca. 2600 to 1800 BP. Peat growth and soil organic fractions point to lesser mild intervals ca. 900 BP and 400 BP, but these are not apparent in the pollen assemblage. The pollen record does not extend to the last four centuries; however, lichenometric studies of neoglacial moraines by DOWDESWELL (1984) show that the maximum late Holocene advance of glaciers in the area occurred within the last century. Modern pollen samples indicate that the present vegetation of the inner Frobisher Bay area is comparable to that of the milder intervals of the late Holocene.La présente étude porte sur l'évolution paléoenvironnementale fini-glaciaire et holocène de la région de la baie de Frobisher et se fonde sur les niveaux marins ainsi que sur des témoins polliniques et glaciaires. Le retrait rapide des glaciers dans la partie intérieure de la baie depuis 11 000 BP a été suivi d'épisodes de stabilité et de récurrences mineures entre 8500 et 7000 ans BP. et peut-être plus tard, avant la disparition définitive des glaces continentales dont le centre se trouvait près du lac Amadjuak. L'analyse a porté sur trois sections de sol enfoui qui représentent les dépôts accumulés entre 5500 et 400 ans BP. La lithostratigraphie révèle le passage d'un climat relativement humide et chaud, il y a plus de 5500 ans, à un climat néoglaciaire dont les périodes les plus froides se situent vers 5000, 2700 et 1200 ans BP et probablement après 400 ans BP. La tourbe et les données polliniques témoignent de conditions climatiques plus douces et plus humides pour les périodes allant de 4500 à 3000 ans BP et d'environ 2600 à 1800 ans BP. Mais, contrairement aux associations polliniques, la tourbe et certaines portions organiques de sol font penser qu'ont existé des intervalles plus frais environ de 900 à 400 ans BP. Les données pollinique ne donnent aucun renseignement sur les quatre derniers siècles. Cependant, les études Ii-chénométriques que DOWDESWELL (1984) a faites sur les moraines néoglaciaires révèlent que, dans la région pendant l'Holocène supérieur, l'avancée maximale des glaces s'est produite au siècle dernier. Des échantillons polliniques récents démontrent que la végétation actuelle de l'intérieur de la baie de Frobisher ressemble à celle qu'on trouvait pendant les intervalles tempérés de l'Holocène supérieur.Die spàtglaziale und holozàne Abfolge des Palâomilieus im Gebiete der Frobisher Bucht wird durch glaziale, Meeresspiegel- und palynologische Beweise umrissen. Ein rasches Zurùckweichen des Eises aus dem niederen Teil der Bucht hat sich nach 11 000 BP ereignet. gefolgt von mehreren Stillstânden oder kleinerem Wiedervorrùcken zwischen etwa 8500 und 7000 BP oder evtl. spater, bevor das Inlandeis schliesslich verschwunden ist. Drei verdeckte Bodenprofile sind analysiert worden, die zu-sammen die Ablagerung der Zeit von 5500 bis 400 BP darstellen. Die Lithostratigraphie hat eine relativ warme, feuchte Umgebung vor 5500 BP ergeben, die sich alsdann zu neoglazialen Zustânden geàndert hat, mit dem Mittel der kâltesten Phasen um etwa 5000, 2700, und wahrscheinlich auch irgandwann nach 400 Radiokohlenstoffjahren BP. Torfwuchs sowie auch palynologische Daten zeigen, dass milde, feuchte Zustânde von 4500 bis 3000 BP und dann nochmals von etwa 2600 bis 1800 BP vorgeherrscht haben. Der Torfwuchs und der organische Anteil des Bodens deuten auch auf kleinere milde Zeitspannen um etwa 900 und 400 BP, aber dièse sind nicht aus der Pollenvergesellschaftung ersichtlich. Fur die jùngsten vier Jahrhunderte fehlen Pollenunterlagen; aber durch Untersuchung der Flechten auf neoglazialen Morânen hat DOWDESWELL (1984) fur dieses Gebiet ein spatholozànes Gletschervorrùcken wahrend des letzten Jahrhunderts belegen konnen. Pollenmuster beweisen. dass sich im Gebiet der inneren Frobisher Bucht die heutige Pflanzendecke gut mit der Vegetation mlldererer Spâtholozànintervalle vergleichen làsst

A Model for the Production of Regular Fluorescent Light from Coherently Driven Atoms

It has been shown in recent years that incoherent pumping through multiple atomic levels provides a mechanism for the production of highly anti-bunched light, and that as the number of incoherent steps is increased the light becomes increasingly regular. We show that in a resonance fluorescence situation, a multi-level atom may be multiply coherently driven so that the fluorescent light is highly anti-bunched. We show that as the number of coherently driven levels is increased, the spontaneous emissions may be made increasingly more regular. We present a systematic method for designing the level structure and driving required to produce highly anti-bunched light in this manner for an arbitrary even number of levels.Comment: 6 pages multicol revtex, including figure