Analytical mode normalization and resonant state expansion for optical fibers - an efficient tool to model transverse disorder

We adapt the resonant state expansion to optical fibers such as capillary and photonic crystal fibers. As a key requirement of the resonant state expansion and any related perturbative approach, we derive the correct analytical normalization for all modes of these fiber structures, including leaky modes that radiate energy perpendicular to the direction of propagation and have fields that grow with distance from the fiber core. Based on the normalized fiber modes, an eigenvalue equation is derived that allows for calculating the influence of small and large perturbations such as structural disorder on the guiding properties. This is demonstrated for two test systems: a capillary fiber and an endlessly single mode fiber.Comment: 10 pages, 4 figure

Violation of the Leggett-Garg Inequality in Neutrino Oscillations

The Leggett-Garg inequality, an analogue of Bell's inequality involving correlations of measurements on a system at different times, stands as one of the hallmark tests of quantum mechanics against classical predictions. The phenomenon of neutrino oscillations should adhere to quantum-mechanical predictions and provide an observable violation of the Leggett-Garg inequality. We demonstrate how oscillation phenomena can be used to test for violations of the classical bound by performing measurements on an ensemble of neutrinos at distinct energies, as opposed to a single neutrino at distinct times. A study of the MINOS experiment's data shows a greater than $6{\sigma}$ violation over a distance of 735 km, representing the longest distance over which either the Leggett-Garg inequality or Bell's inequality has been tested.Comment: Updated to match published version. 6 pages, 2 figure

Qubit state detection using the quantum Duffing oscillator

We introduce a detection scheme for the state of a qubit, which is based on resonant few-photon transitions in a driven nonlinear resonator. The latter is parametrically coupled to the qubit and is used as its detector. Close to the fundamental resonator frequency, the nonlinear resonator shows sharp resonant few-photon transitions. Depending on the qubit state, these few-photon resonances are shifted to different driving frequencies. We show that this detection scheme offers the advantage of small back action, a large discrimination power with an enhanced read-out fidelity, and a sufficiently large measurement efficiency. A realization of this scheme in the form of a persistent current qubit inductively coupled to a driven SQUID detector in its nonlinear regime is discussed.Comment: 10 pages, 6 figures. To appear in Phys. Rev.

Theory of Nonlinear Dispersive Waves and Selection of the Ground State

A theory of time dependent nonlinear dispersive equations of the Schroedinger / Gross-Pitaevskii and Hartree type is developed. The short, intermediate and large time behavior is found, by deriving nonlinear Master equations (NLME), governing the evolution of the mode powers, and by a novel multi-time scale analysis of these equations. The scattering theory is developed and coherent resonance phenomena and associated lifetimes are derived. Applications include BEC large time dynamics and nonlinear optical systems. The theory reveals a nonlinear transition phenomenon, ``selection of the ground state'', and NLME predicts the decay of excited state, with half its energy transferred to the ground state and half to radiation modes. Our results predict the recent experimental observations of Mandelik et. al. in nonlinear optical waveguides

The twist-2 Compton operator and its hidden Wandzura-Wilczek and Callan-Gross relations

Power corrections for virtual Compton scattering at leading twist are etermined at operator level. From the complete off-cone representation of the twist-2 Compton operator integral representations for the trace, antisymmetric and symmetric part of that operator are derived. The operator valued invariant functions are written in terms of iterated operators and may lead to interrelations. For matrix elements they go over into relations for generalized parton distributions. -- Reducing to the s-channel relevant part one gets operator pre-forms of the Wandzura-Wilczek and the (target mass corrected) Callan-Gross relations whose structure is exactly the same as known from the case of deep inelastic scattering; taking non-forward matrix elements one reproduces earlier results [B. Geyer, D. Robaschik and J. Eilers, Nucl. Phys. B 704 (2005) 279] for the absorptive part of the virtual Compton amplitude. -- All these relations, obtained without any approximation or using equations of motion, are determined solely by the twist-2 structure of the underlying operator and, therefore, are purely of geometric origin.Comment: 13 pages, Latex 2e, Introduction shortend, Section Prerequisites added, more obvious formulations used, some formulas rewritten as well as added, conclusions extended, references added. Final version as appearing in PR

Semiclassical theory of energy diffusive escape in a Duffing oscillator

Motivated by recent experimental progress to read out quantum bits implemented in superconducting circuits via the phenomenon of dynamical bifurcation, transitions between steady orbits in a driven anharmonic oscillator, the Duffing oscillator, are analyzed. In the regime of weak dissipation a consistent master equation in the semiclassical limit is derived to capture the intimate relation between finite tunneling and reflection and bath induced quantum fluctuations. From the corresponding steady state distributions analytical expressions for the switching probabilities are obtained. It is shown that a reduction of the transition rate due to finite reflection at the phase-space barrier is overcompensated by an increase due to environmental quantum fluctuations that are specific for diffusion processes over dynamical barriers. Moreover, it is revealed that close to the bifurcation threshold the escape dynamics enters an overdamped domain such that the quantum mechanical energy scale associated with friction even exceeds the thermal energy scale

Anomalous escape governed by thermal 1/f noise

We present an analytic study for subdiffusive escape of overdamped particles out of a cusp-shaped parabolic potential well which are driven by thermal, fractional Gaussian noise with a $1/\omega^{1-\alpha}$ power spectrum. This long-standing challenge becomes mathematically tractable by use of a generalized Langevin dynamics via its corresponding non-Markovian, time-convolutionless master equation: We find that the escape is governed asymptotically by a power law whose exponent depends exponentially on the ratio of barrier height and temperature. This result is in distinct contrast to a description with a corresponding subdiffusive fractional Fokker-Planck approach; thus providing experimentalists an amenable testbed to differentiate between the two escape scenarios

Limitation of entanglement due to spatial qubit separation

We consider spatially separated qubits coupled to a thermal bosonic field that causes pure dephasing. Our focus is on the entanglement of two Bell states which for vanishing separation are known as robust and fragile entangled states. The reduced two-qubit dynamics is solved exactly and explicitly. Our results allow us to gain information about the robustness of two-qubit decoherence-free subspaces with respect to physical parameters such as temperature, qubit-bath coupling strength and spatial separation of the qubits. Moreover, we clarify the relation between single-qubit coherence and two-qubit entanglement and identify parameter regimes in which the terms robust and fragile are no longer appropriate.Comment: 7 pages, 3 figures; revised version, accepted for publication in Europhys. Let

Spintronics of a Nanoelectromechanical Shuttle

We consider effects of the spin degree of freedom on the nanomechanics of a single-electron transistor (SET) containing a nanometer-sized metallic cluster suspended between two magnetic leads. It is shown that in such a nanoelectromechanical SET(NEM-SET) the onset of an electromechanical instability leading to cluster vibrations and "shuttle" transport of electrons between the leads can be controlled by an external magnetic field. Different stable regimes of this spintronic NEM-SET operation are analyzed. Two different scenarios for the onset of shuttle vibrations are found.Comment: 4 pages, 3 figure

Measurable Consequences of the Local Breakdown of the Concept of Temperature

Local temperature defined by a local canonical state of the respective subsystem, does not always exist in quantum many body systems. Here, we give some examples of how this breakdown of the temperature concept on small length scales might be observed in experiments: Measurements of magnetic properties of an anti-ferromagnetic spin-1 chain. We show that those magnetic properties are in fact strictly local. As a consequence their measurement reveals whether the local (reduced) state can be thermal. If it is, a temperature may be associated to the measurement results, while this would lead to inconsistencies otherwise.Comment: some comments added, results remain unchange