Response of discrete nonlinear systems with many degrees of freedom

We study the response of a large array of coupled nonlinear oscillators to parametric excitation, motivated by the growing interest in the nonlinear dynamics of microelectromechanical and nanoelectromechanical systems (MEMS and NEMS). Using a multiscale analysis, we derive an amplitude equation that captures the slow dynamics of the coupled oscillators just above the onset of parametric oscillations. The amplitude equation that we derive here from first principles exhibits a wavenumber dependent bifurcation similar in character to the behavior known to exist in fluids undergoing the Faraday wave instability. We confirm this behavior numerically and make suggestions for testing it experimentally with MEMS and NEMS resonators.Comment: Version 2 is an expanded version of the article, containing detailed steps of the derivation that were left out in version 1, but no additional result

Sexual behaviour in the face of risk : preliminary results from first AIDS-related surveys

Preliminary results are presented from nationally representative surveys of the adult populations of five African countries, conducted in 1989 and 1990. General awareness of AIDS was high, as was knowledge of sexual transmission. In four of the five surveys, large proportions, from 25 to 64 per cent, of both men and women perceived themselves to have a high or moderate risk of HIV infection. High proportions also reported that they had modified their behaviour typically by more care in selecting partners or greater faithfulness. Greater use of condoms was mentioned rarely. The results, particularly on behavioural change, should not be interpreted literally. But the fact that so many report modification of behaviour at least suggests a willingness to contemplate the need for change. The prognosis would have been much worse, had these surveys indicated widespread denial of risk and unwillingness to consider changes in behaviour

Qubit-induced phonon blockade as a signature of quantum behavior in nanomechanical resonators

The observation of quantized nanomechanical oscillations by detecting femtometer-scale displacements is a significant challenge for experimentalists. We propose that phonon blockade can serve as a signature of quantum behavior in nanomechanical resonators. In analogy to photon blockade and Coulomb blockade for electrons, the main idea for phonon blockade is that the second phonon cannot be excited when there is one phonon in the nonlinear oscillator. To realize phonon blockade, a superconducting quantum two-level system is coupled to the nanomechanical resonator and is used to induce the phonon self-interaction. Using Monte Carlo simulations, the dynamics of the induced nonlinear oscillator is studied via the Cahill-Glauber $s$-parametrized quasiprobability distributions. We show how the oscillation of the resonator can occur in the quantum regime and demonstrate how the phonon blockade can be observed with currently accessible experimental parameters

Perturbation of Tunneling Processes by Mechanical Degrees of Freedom in Mesoscopic Junctions

We investigate the perturbation in the tunneling current caused by non-adiabatic mechanical motion in a mesoscopic tunnel junction. A theory introduced by Caroli et al. \cite{bi1,bi2,bi3} is used to evaluate second order self-energy corrections for this non-equilibrium situation lacking translational invariance. Inelastic signatures of the mechanical degrees of freedom are found in the current-voltage $I(V)$ characteristics. These give rise to sharp features in the derivative spectrum, $d^2I/dV^2$.Comment: 22 pages LaTeX + 3 uuencoded PS picture

Influence of water adsorbed on gold on van der Waals/Casimir forces

In this paper we investigate the influence of ultra thin water layer (1-1.5 nm) on the van der Waals/Casimir force between gold surfaces. Adsorbed water is inevitably present on gold surfaces at ambient conditions as jump-up-to contact during adhesion experiments demonstrate. Calculations based on the Lifshitz theory give very good agreement with the experiment in absence of any water layer for surface separations d>10 nm. However, a layer of thickness h<1.5 nm is allowed by the error margin in force measurements. At shorter separations, d<10 nm, the water layer can have a strong influence as calculations show for flat surfaces. Nonetheless, in reality the influence of surface roughness must also be considered, and it can overshadow any water layer influence at separations comparable to the total sphere-plate rms roughness w_{shp}+w.Comment: 8 pages, 5 figure, to be published in Phys. Rev.

Force-detected nuclear magnetic resonance: Recent advances and future challenges

We review recent efforts to detect small numbers of nuclear spins using magnetic resonance force microscopy. Magnetic resonance force microscopy (MRFM) is a scanning probe technique that relies on the mechanical measurement of the weak magnetic force between a microscopic magnet and the magnetic moments in a sample. Spurred by the recent progress in fabricating ultrasensitive force detectors, MRFM has rapidly improved its capability over the last decade. Today it boasts a spin sensitivity that surpasses conventional, inductive nuclear magnetic resonance detectors by about eight orders of magnitude. In this review we touch on the origins of this technique and focus on its recent application to nanoscale nuclear spin ensembles, in particular on the imaging of nanoscale objects with a three-dimensional (3D) spatial resolution better than 10 nm. We consider the experimental advances driving this work and highlight the underlying physical principles and limitations of the method. Finally, we discuss the challenges that must be met in order to advance the technique towards single nuclear spin sensitivity -- and perhaps -- to 3D microscopy of molecules with atomic resolution.Comment: 15 pages & 11 figure

Surface dissipation in nanoelectromechanical systems: Unified description with the standard tunneling model and effects of metallic electrodes

By modifying and extending recent ideas [C. Seoanez et al., Europhys. Lett. 78, 60002 (2007)], a theoretical framework to describe dissipation processes in the surfaces of vibrating micro- and nanoelectromechanical devices, thought to be the main source of friction at low temperatures, is presented. Quality factors as well as frequency shifts of flexural and torsional modes in doubly clamped beams and cantilevers are given, showing the scaling with dimensions, temperature, and other relevant parameters of these systems. Full agreement with experimental observations is not obtained, leading to a discussion of limitations and possible modifications of the scheme to reach a quantitative fitting to experiments. For nanoelectromechanical systems covered with metallic electrodes, the friction due to electrostatic interaction between the flowing electrons and static charges in the device and substrate is also studied.Comment: 17 pages, 7 figure

Giant slip lengths of a simple fluid at vibrating solid interfaces

It has been shown recently [PRL 102, 254503 (2009)] that in the plane-plane configuration a mechanical resonator vibrating close to a rigid wall in a simple fluid can be overdamped to a frozen regime. Here, by solving analytically the Navier Stokes equations with partial slip boundary conditions at the solid fluid interface, we develop a theoretical approach justifying and extending these earlier findings. We show in particular that in the perfect slip regime the above mentioned results are, in the plane-plane configuration, very general and robust with respect to lever geometry considerations. We compare the results with those obtained previously for the sphere moving perpendicularly and close to a plane in a simple fluid and discuss in more details the differences concerning the dependence of the friction forces with the gap distance separating the moving object (i.e., plane or sphere) from the fixed plane. Finally, we show that the submicron fluidic effect reported in the reference above, and discussed further in the present work, can have dramatic implications in the design of nano-electromechanical systems (NEMS).Comment: submitted to PRE (see also PRL 102, 254503 (2009)

Generation of Squeezed States of Nanomechanical Resonators by Reservoir Engineering

An experimental demonstration of a non-classical state of a nanomechanical resonator is still an outstanding task. In this paper we show how the resonator can be cooled and driven into a squeezed state by a bichromatic microwave coupling to a charge qubit. The stationary oscillator state exhibits a reduced noise in one of the quadrature components by a factor of 0.5 - 0.2. These values are obtained for a 100 MHz resonator with a Q-value of 10$^4$ to 10$^5$ and for support temperatures of T $\approx$ 25 mK. We show that the coupling to the charge qubit can also be used to detect the squeezed state via measurements of the excited state population. Furthermore, by extending this measurement procedure a complete quantum state tomography of the resonator state can be performed. This provides a universal tool to detect a large variety of different states and to prove the quantum nature of a nanomechanical oscillator.Comment: 13 pages,9 figure