Detection of Tiny Mechanical Motion by Means of the Ratchet Effect

We propose a position detection scheme for a nanoelectromechanical resonator based on the ratchet effect. This scheme has an advantage of being a dc measurement. We consider a three-junction SQUID where a part of the superconducting loop can perform mechanical motion. The response of the ratchet to a dc current is sensitive to the position of the resonator and the effect can be further enhanced by biasing the SQUID with an ac current. We discuss the feasibility of the proposed scheme in existing experimental setups.Comment: 8 pages, 9 figure

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

Metastability and the Casimir Effect in Micromechanical Systems

Electrostatic and Casimir interactions limit the range of positional stability of electrostatically-actuated or capacitively-coupled mechanical devices. We investigate this range experimentally for a generic system consisting of a doubly-clamped Au suspended beam, capacitively-coupled to an adjacent stationary electrode. The mechanical properties of the beam, both in the linear and nonlinear regimes, are monitored as the attractive forces are increased to the point of instability. There "pull-in" occurs, resulting in permanent adhesion between the electrodes. We investigate, experimentally and theoretically, the position-dependent lifetimes of the free state (existing prior to pull-in). We find that the data cannot be accounted for by simple theory; the discrepancy may be reflective of internal structural instabilities within the metal electrodes.Comment: RevTex, 4 pages, 4 figure

Singlet-triplet relaxation induced by confined phonons in nanowire-based quantum dots

The singlet-triplet relaxation in nanowire-based quantum dots induced by confined phonons is investigated theoretically. Due to the quasi-one-dimensional nature of the confined phonons, the singlet-triplet relaxation rates exhibit multi-peaks as function of magnetic field and the relaxation rate between the singlet and the spin up triplet state is found to be enhanced at the vicinity of the singlet-triplet anti-crossing. We compare the effect of the deformation-potential coupling and the piezoelectric coupling and find that the deformation-potential coupling dominates the relaxation rates in most cases.Comment: 7 pages, 5 figure

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

Superconducting Qubits Coupled to Nanoelectromechanical Resonators: An Architecture for Solid-State Quantum Information Processing

We describe the design for a scalable, solid-state quantum-information-processing architecture based on the integration of GHz-frequency nanomechanical resonators with Josephson tunnel junctions, which has the potential for demonstrating a variety of single- and multi-qubit operations critical to quantum computation. The computational qubits are eigenstates of large-area, current-biased Josephson junctions, manipulated and measured using strobed external circuitry. Two or more of these phase qubits are capacitively coupled to a high-quality-factor piezoelectric nanoelectromechanical disk resonator, which forms the backbone of our architecture, and which enables coherent coupling of the qubits. The integrated system is analogous to one or more few-level atoms (the Josephson junction qubits) in an electromagnetic cavity (the nanomechanical resonator). However, unlike existing approaches using atoms in electromagnetic cavities, here we can individually tune the level spacing of the ``atoms'' and control their ``electromagnetic'' interaction strength. We show theoretically that quantum states prepared in a Josephson junction can be passed to the nanomechanical resonator and stored there, and then can be passed back to the original junction or transferred to another with high fidelity. The resonator can also be used to produce maximally entangled Bell states between a pair of Josephson junctions. Many such junction-resonator complexes can assembled in a hub-and-spoke layout, resulting in a large-scale quantum circuit. Our proposed architecture combines desirable features of both solid-state and cavity quantum electrodynamics approaches, and could make quantum information processing possible in a scalable, solid-state environment.Comment: 20 pages, 14 separate low-resolution jpeg figure

Heat capacity of a thin membrane at very low temperature

We calculate the dependence of heat capacity of a free standing thin membrane on its thickness and temperature. A remarkable fact is that for a given temperature there exists a minimum in the dependence of the heat capacity on the thickness. The ratio of the heat capacity to its minimal value for a given temperature is a universal function of the ratio of the thickness to its value corresponding to the minimum. The minimal value of the heat capacitance for given temperature is proportional to the temperature squared. Our analysis can be used, in particular, for optimizing support membranes for microbolometers

On testing the violation of the Clausius inequality in nanoscale electric circuits

The Clausius inequality, one of the classical formulations of the second law, was recently found to be violated in the quantum regime. Here this result is formulated in the context of a mesoscopic or nanoscale linear RLC circuit interacting with a thermal bath. Previous experiments in this and related fields are analyzed and possibilities of experimental detection of the violation are pointed out. It is discussed that recent experiments reached the range of temperatures, where the effect should be visible, and that a part of the proposal was already confirmed.Comment: 5 pages revtex 4. No figure

Polysemy in the mental lexicon: relatedness and frequency affect representational overlap

Meaning relatedness affects storage of ambiguous words in the mental lexicon: unrelated meanings(homonymy) are stored separately whereas related senses (polysemy) are stored as one large representational entry. We hypothesised that word frequency could have similar effects on storage, with low-frequency words having high representational overlap and high-frequency words having low representational overlap. Participants performed lexical decision or semantic categorisation to high- and low-frequency nouns with few and many senses. Results showed a three-way interaction between frequency, task type, and polysemy. Low-frequency words showed a polysemy advantage with lexical decision but a polysemy disadvantage with semantic categorisation, whereas high-frequency words showed the opposite pattern. These results confirmed our hypothesis that relatedness and word frequency have similar effects on storage of ambiguous words