Multivalued linear transformations of hyperspaces

The purpose of this paper is the study of multivalued linear transformations of hypervector spaces (or hyperspaces) in the sense of Tallini. In this regards first we introduce and study various multivalued linear transformations of hyperspaces and then constitute the categories of hyperspaces with respect the different linear transformations of hyperspaces as the morphisms in these categories. Also, we construct some algebraic hyperoperations on Hom K (V,W), the set of all multivalued linear transformations from a hyperspace V into hyperspaces W, and obtaine their basic properties. Finally, we construct the fundamental functor F from HV K , category of hyperspaces over field K into V K , the category of clasical vector space over K

Measurement and control of a mechanical oscillator at its thermal decoherence rate

In real-time quantum feedback protocols, the record of a continuous measurement is used to stabilize a desired quantum state. Recent years have seen highly successful applications in a variety of well-isolated micro-systems, including microwave photons and superconducting qubits. By contrast, the ability to stabilize the quantum state of a tangibly massive object, such as a nanomechanical oscillator, remains a difficult challenge: The main obstacle is environmental decoherence, which places stringent requirements on the timescale in which the state must be measured. Here we describe a position sensor that is capable of resolving the zero-point motion of a solid-state, nanomechanical oscillator in the timescale of its thermal decoherence, a critical requirement for preparing its ground state using feedback. The sensor is based on cavity optomechanical coupling, and realizes a measurement of the oscillator's displacement with an imprecision 40 dB below that at the standard quantum limit, while maintaining an imprecision-back-action product within a factor of 5 of the Heisenberg uncertainty limit. Using the measurement as an error signal and radiation pressure as an actuator, we demonstrate active feedback cooling (cold-damping) of the 4.3 MHz oscillator from a cryogenic bath temperature of 4.4 K to an effective value of 1.1$\pm$0.1 mK, corresponding to a mean phonon number of 5.3$\pm$0.6 (i.e., a ground state probability of 16%). Our results set a new benchmark for the performance of a linear position sensor, and signal the emergence of engineered mechanical oscillators as practical subjects for measurement-based quantum control.Comment: 24 pages, 10 figures; typos corrected in main text and figure

Role of structural defects on exchange bias in the epitaxial CoO/Co system

We have studied the influence of non-magnetic defects throughout the antiferromagnet Co_{1-y}O on the exchange bias (EB) in epitaxially grown Co_{1-y}O/Co bilayers. These defects are either substitutional or structural (twin boundaries and surface morphology) which both lead to an increase of the EB-field. We find a dominance of twin boundaries over surface morphology (roughness) in enhancing EB which is consistent with the domain state model for exchange bias. In contrast, the crystal orientation of the Co_{1-y}O layer does not show a significant effect on the EB in this system.Comment: 10 pages, 2 figure

Origin of training effect of exchange bias in Co/CoO due to irreversible thermoremanent magnetization of the magnetically diluted antiferromagnet

The irreversible thermoremanent magnetization of a sole, magnetically diluted epitaxial antiferromagnetic Co$_{1-y}$O(100) layer is determined by the mean of its thermoremanent magnetizations at positive and negative remanence. During hysteresis-loop field cycling, thermoremanent magnetization exhibits successive reductions, consistent with the training effect (TE) of the exchange bias measured for the corresponding Co$_{1-y}$O(100)/Co bilayer. The TE of exchange bias is shown to have its microscopic origin in the TE of the irreversible thermoremanent magnetization of the magnetically diluted AFM

Sensitive Voltammetric Determination of Acetaminophen at Poly(4-vinyl pyridine)/Graphene Composite Modified Electrode

This study demonstrates the use of a selective and sensitive voltammetric sensor for determination of acetaminophen (AC). This was performed by modifying a glassy carbon electrode with composite film of poly(4-vinylpyridine) and graphene sheet (P4VP/GR-GCE). The redox peak currents of AC increased significantly at P4VP/GR-GCE. The result was achieved by the synergistic effect of combined electron mediator property of P4VP along with remarkable physical properties of GR which improved the kinetics of the catalytic oxidation of AC. The P4VP/GR-GCE exhibited excellent sensitivity, good reproducibilityand long-termstability for measuring AC with detection limits of 3.2 nM in the linear range of 0.04-300 µM. The novel developed sensor was not interfered by physiologically common interference, viz. ascorbic acid (AA) and uric acid (UA). The P4VP/GR-GCE was also successfully applied for detection of AC in tablets and urine samples, so it is reasonable to expect its broad use as AC sensor

Appearance and Disappearance of Quantum Correlations in Measurement-Based Feedback Control of a Mechanical Oscillator

Quantum correlations between imprecision and backaction are a hallmark of continuous linear measurements. Here, we study how measurement-based feedback can be used to improve the visibility of quantum correlations due to the interaction of a laser field with a nanomechanical oscillator. Backaction imparted by the meter laser, due to radiation-pressure quantum fluctuations, gives rise to correlations between its phase and amplitude quadratures. These quantum correlations are observed in the experiment both as squeezing of the meter field fluctuations below the vacuum level in a homodyne measurement and as sideband asymmetry in a heterodyne measurement, demonstrating the common origin of both phenomena. We show that quantum feedback, i.e., feedback that suppresses measurement backaction, can be used to increase the visibility of the sideband asymmetry ratio. In contrast, by operating the feedback loop in the regime of noise squashing, where the in-loop photocurrent variance is reduced below the vacuum level, the visibility of the sideband asymmetry is reduced. This is due to backaction arising from vacuum noise in the homodyne detector. These experiments demonstrate the possibility, as well as the fundamental limits, of measurement-based feedback as a tool to manipulate quantum correlations.Research is funded by an ERC Advanced Grant (QuREM), a Marie Curie Initial Training Network Cavity Quantum Optomechanics, the Swiss National Science Foundation, and through support from the NCCR of Quantum Engineering (QSIT). D. J. W. acknowledges support from the European Commission through a Marie Curie Fellowship (IIF Project No. 331985)