Volatility and arbitrage

The capitalization-weighted cumulative variation d i=1 0 µi(t)d(log µi)(t) in an equity market consisting of a fixed number d of assets with capitalization weights µi(·) ; is an observable and a nondecreasing function of time. If this observable of the market is not just nondecreasing but actually grows at a rate bounded away from zero, then strong arbitrage can be constructed relative to the market over sufficiently long time horizons. It has been an open issue for more than ten years, whether such strong outperformance of the market is possible also over arbitrary time horizons under the stated condition. We show that this is not possible in general, thus settling this long-open question. We also show that, under appropriate additional conditions, outperformance over any time horizon indeed becomes possible, and exhibit investment strategies that effect it

Two Brownian Particles with Rank-Based Characteristics and Skew-Elastic Collisions

We construct a two-dimensional diffusion process with rank-dependent local drift and dispersion coefficients, and with a full range of patterns of behavior upon collision that range from totally frictionless interaction, to elastic collision, to perfect reflection of one particle on the other. These interactions are governed by the left- and right-local times at the origin for the distance between the two particles. We realize this diffusion in terms of appropriate, apparently novel systems of stochastic differential equations involving local times, which we show are well posed. Questions of pathwise uniqueness and strength are also discussed for these systems. The analysis depends crucially on properties of a skew Brownian motion with two-valued drift of the bang-bang type, which we also study in some detail. These properties allow us to compute the transition probabilities of the original planar diffusion, and to study its behavior under time reversal.Comment: 33 pages, 4 figures; Remark 4.1 added, Theorem 4.2 improve

Deterministic quantum teleportation between distant atomic objects

Quantum teleportation is a key ingredient of quantum networks and a building block for quantum computation. Teleportation between distant material objects using light as the quantum information carrier has been a particularly exciting goal. Here we demonstrate a new element of the quantum teleportation landscape, the deterministic continuous variable (cv) teleportation between distant material objects. The objects are macroscopic atomic ensembles at room temperature. Entanglement required for teleportation is distributed by light propagating from one ensemble to the other. Quantum states encoded in a collective spin state of one ensemble are teleported onto another ensemble using this entanglement and homodyne measurements on light. By implementing process tomography, we demonstrate that the experimental fidelity of the quantum teleportation is higher than that achievable by any classical process. Furthermore, we demonstrate the benefits of deterministic teleportation by teleporting a dynamically changing sequence of spin states from one distant object onto another

Mesoscopic atomic entanglement for precision measurements beyond the standard quantum limit

Squeezing of quantum fluctuations by means of entanglement is a well recognized goal in the field of quantum information science and precision measurements. In particular, squeezing the fluctuations via entanglement between two-level atoms can improve the precision of sensing, clocks, metrology, and spectroscopy. Here, we demonstrate 3.4 dB of metrologically relevant squeezing and entanglement for ~ 10^5 cold cesium atoms via a quantum nondemolition (QND) measurement on the atom clock levels. We show that there is an optimal degree of decoherence induced by the quantum measurement which maximizes the generated entanglement. A two-color QND scheme used in this paper is shown to have a number of advantages for entanglement generation as compared to a single color QND measurement.Comment: 6 pages+suppl, PNAS forma

Spin squeezing of atomic ensembles via nuclear-electronic spin entanglement

Entangled many body systems have recently attracted significant attention in various contexts. Among them, spin squeezed atoms and ions have raised interest in the field of precision measurements, as they allow to overcome quantum noise of uncorrelated particles. Precise quantum state engineering is also required as a resource for quantum computation, and spin squeezing can be used to create multi-partite entangled states. Two-mode spin squeezed systems have been used for elementary quantum communication protocols. Until now spin squeezing has been always achieved via generation of entanglement between different atoms of the ensemble. In this Letter, we demonstrate for the first time ensemble spin squeezing generated by engineering the quantum state of each individual atom. More specifically, we entangle the nuclear and electronic spins of $10^{12}$ Cesium atoms at room temperature. We verify entanglement and ensemble spin squeezing by performing quantum tomography on the atomic state.Comment: 5 pages, 3 figure

High quality anti-relaxation coating material for alkali atom vapor cells

We present an experimental investigation of alkali atom vapor cells coated with a high quality anti-relaxation coating material based on alkenes. The prepared cells with single compound alkene based coating showed the longest spin relaxation times which have been measured up to now with room temperature vapor cells. Suggestions are made that chemical binding of a cesium atom and an alkene molecule by attack to the C=C bond plays a crucial role in such improvement of anti-relaxation coating quality

The Genetic Mechanisms Underlying the Concerted Expression of the yellow and tan Genes in Complex Patterns on the Abdomen and Wings of Drosophila guttifera

How complex morphological patterns form is an intriguing question in developmental biology. However, the mechanisms that generate complex patterns remain largely unknown. Here, we sought to identify the genetic mechanisms that regulate the tan (t) gene in a multi-spotted pigmentation pattern on the abdomen and wings of Drosophila guttifera. Previously, we showed that yellow (y) gene expression completely prefigures the abdominal and wing pigment patterns of this species. In the current study, we demonstrate that the t gene is co-expressed with the y gene in nearly identical patterns, both transcripts foreshadowing the adult abdominal and wing melanin spot patterns. We identified cis-regulatory modules (CRMs) of t, one of which drives reporter expression in six longitudinal rows of spots on the developing pupal abdomen, while the second CRM activates the reporter gene in a spotted wing pattern. Comparing the abdominal spot CRMs of y and t, we found a similar composition of putative transcription factor binding sites that are thought to regulate the complex expression patterns of both terminal pigmentation genes y and t. In contrast, the y and t wing spots appear to be regulated by distinct upstream factors. Our results suggest that the D. guttifera abdominal and wing melanin spot patterns have been established through the co-regulation of y and t, shedding light on how complex morphological traits may be regulated through the parallel coordination of downstream target genes

Two-dimensional array of microtraps with atomic shift register on a chip

Arrays of trapped atoms are the ideal starting point for developing registers comprising large numbers of physical qubits for storing and processing quantum information. One very promising approach involves neutral atom traps produced on microfabricated devices known as atom chips, as almost arbitrary trap configurations can be realised in a robust and compact package. Until now, however, atom chip experiments have focused on small systems incorporating single or only a few individual traps. Here we report experiments on a two-dimensional array of trapped ultracold atom clouds prepared using a simple magnetic-film atom chip. We are able to load atoms into hundreds of tightly confining and optically resolved array sites. We then cool the individual atom clouds in parallel to the critical temperature required for quantum degeneracy. Atoms are shuttled across the chip surface utilising the atom chip as an atomic shift register and local manipulation of atoms is implemented using a focused laser to rapidly empty individual traps.Comment: 6 pages, 4 figure

The Nylon Scintillator Containment Vessels for the Borexino Solar Neutrino Experiment

Borexino is a solar neutrino experiment designed to observe the 0.86 MeV Be-7 neutrinos emitted in the pp cycle of the sun. Neutrinos will be detected by their elastic scattering on electrons in 100 tons of liquid scintillator. The neutrino event rate in the scintillator is expected to be low (~0.35 events per day per ton), and the signals will be at energies below 1.5 MeV, where background from natural radioactivity is prominent. Scintillation light produced by the recoil electrons is observed by an array of 2240 photomultiplier tubes. Because of the intrinsic radioactive contaminants in these PMTs, the liquid scintillator is shielded from them by a thick barrier of buffer fluid. A spherical vessel made of thin nylon film contains the scintillator, separating it from the surrounding buffer. The buffer region itself is divided into two concentric shells by a second nylon vessel in order to prevent inward diffusion of radon atoms. The radioactive background requirements for Borexino are challenging to meet, especially for the scintillator and these nylon vessels. Besides meeting requirements for low radioactivity, the nylon vessels must also satisfy requirements for mechanical, optical, and chemical properties. The present paper describes the research and development, construction, and installation of the nylon vessels for the Borexino experiment