Non-disturbing quantum measurements

We consider pairs of quantum observables (POVMs) and analyze the relation between the notions of non-disturbance, joint measurability and commutativity. We specify conditions under which these properties coincide or differ---depending for instance on the interplay between the number of outcomes and the Hilbert space dimension or on algebraic properties of the effect operators. We also show that (non-)disturbance is in general not a symmetric relation and that it can be decided and quantified by means of a semidefinite program.Comment: Minor corrections in v

Weighted complex projective 2-designs from bases: optimal state determination by orthogonal measurements

We introduce the problem of constructing weighted complex projective 2-designs from the union of a family of orthonormal bases. If the weight remains constant across elements of the same basis, then such designs can be interpreted as generalizations of complete sets of mutually unbiased bases, being equivalent whenever the design is composed of d+1 bases in dimension d. We show that, for the purpose of quantum state determination, these designs specify an optimal collection of orthogonal measurements. Using highly nonlinear functions on abelian groups, we construct explicit examples from d+2 orthonormal bases whenever d+1 is a prime power, covering dimensions d=6, 10, and 12, for example, where no complete sets of mutually unbiased bases have thus far been found.Comment: 28 pages, to appear in J. Math. Phy

Quantum kinetic theory of shift current electron pumping in semiconductors

We develop a theory of laser beam generation of shift currents in non-centrosymmetric semiconductors. The currents originate when the excited electrons transfer between different bands or scatter inside these bands, and asymmetrically shift their centers of mass in elementary cells. Quantum kinetic equations for hot-carrier distributions and expressions for the induced currents are derived by nonequilibrium Green functions. In applications, we simplify the approach to the Boltzmann limit and use it to model laser-excited GaAs in the presence of LO phonon scattering. The shift currents are calculated in a steady-state regime.Comment: 23 pages, 5 figures (Latex

On the coexistence of position and momentum observables

We investigate the problem of coexistence of position and momentum observables. We characterize those pairs of position and momentum observables which have a joint observable

Position Reconstruction in Drift Chambers operated with Xe, CO2 (15%)

We present measurements of position and angular resolution of drift chambers operated with a Xe,CO$_2$(15%) mixture. The results are compared to Monte Carlo simulations and important systematic effects, in particular the dispersive nature of the absorption of transition radiation and non-linearities, are discussed. The measurements were carried out with prototype drift chambers of the ALICE Transition Radiation Detector, but our findings can be generalized to other drift chambers with similar geometry, where the electron drift is perpendicular to the wire planes.Comment: 30 pages, 18 figure

Creation of a monopole in a spinor condensate

We propose a method to create a monopole structure in a spin-1 spinor condensate by applying the basic methods used to create vortices and solitons experimentally in single-component condensates. We show, however, that by using a two-component structure for a monopole, we can simplify our proposed experimental approach and apply it also to ferromagnetic spinor condensates. We also discuss the observation and dynamics of such a monopole structure, and note that the dynamics of the two-component monopole differs from the dynamics of the three-component monopole.Comment: The focus of the paper is shifted towards creation and observation of monopole

Frictional quantum decoherence

The dynamics associated with a measurement-based master equation for quantum Brownian motion are investigated. A scheme for obtaining time evolution from general initial conditions is derived. This is applied to analyze dissipation and decoherence in the evolution of both a Gaussian and a Schr\"{o}dinger cat initial state. Dependence on the diffusive terms present in the master equation is discussed with reference to both the coordinate and momentum representations.Comment: 18 pages, 7 figure

An accurate determination of the Avogadro constant by counting the atoms in a 28Si crystal

The Avogadro constant links the atomic and the macroscopic properties of matter. Since the molar Planck constant is well known via the measurement of the Rydberg constant, it is also closely related to the Planck constant. In addition, its accurate determination is of paramount importance for a definition of the kilogram in terms of a fundamental constant. We describe a new approach for its determination by "counting" the atoms in 1 kg single-crystal spheres, which are highly enriched with the 28Si isotope. It enabled isotope dilution mass spectroscopy to determine the molar mass of the silicon crystal with unprecedented accuracy. The value obtained, 6.02214084(18) x 10^23 mol^-1, is the most accurate input datum for a new definition of the kilogram.Comment: 4 pages, 5 figures, 3 table