Noise processes in nanomechanical resonators

Nanomechanical resonators can be fabricated to achieve high natural resonance frequencies, approaching 1 GHz, with quality factors in excess of 10^(4). These resonators are candidates for use as highly selective rf filters and as precision on-chip clocks. Some fundamental and some nonfundamental noise processes will present limits to the performance of such resonators. These include thermomechanical noise, Nyquist-Johnson noise, and adsorption-desorption noise; other important noise sources include those due to thermal fluctuations and defect motion-induced noise. In this article, we develop a self-contained formalism for treating these noise sources, and use it to estimate the impact that these noise processes will have on the noise of a model nanoscale resonator, consisting of a doubly clamped beam of single-crystal Si with a natural resonance frequency of 1 GHz

Fabrication of high frequency nanometer scale mechanical resonators from bulk Si crystals

We report on a method to fabricate nanometer scale mechanical structures from bulk, single-crystal Si substrates. A technique developed previously required more complex fabrication methods and an undercut step using wet chemical processing. Our method does not require low pressure chemical vapor deposition of intermediate masking layers, and the final step in the processing uses a dry etch technique, avoiding the difficulties encountered from surface tension effects when wet processing mechanically delicate or large aspect ratio structures. Using this technique, we demonstrate fabrication of a mechanical resonator with a fundamental resonance frequency of 70.72 MHz and a quality factor of 2 x 10^(4)

Quantum pumping in deformable quantum dots

The charge current pumped adiabatically through a deformable quantum dot is studied within the Green's function approach. Differently from the non-deformable case, the current shows an undefined parity with respect to the pumping phase \phi. The unconventional current-phase relation, analyzed in the weak pumping regime, is due to a dynamical phase shift \phi_D caused by the elastic deformations of the central region (classical phonons). The role of the quality factor Q of the oscillator, the effects induced by a mechanical resonance and the implications for current experiments on molecular systems are also discussed

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

Mechanically probing coherent tunnelling in a double quantum dot

We study theoretically the interaction between the charge dynamics of a few-electron double quantum dot and a capacitively-coupled AFM cantilever, a setup realized in several recent experiments. We demonstrate that the dot-induced frequency shift and damping of the cantilever can be used as a sensitive probe of coherent inter-dot tunnelling, and that these effects can be used to quantitatively extract both the magnitude of the coherent interdot tunneling and (in some cases) the value of the double-dot T_1 time. We also show how the adiabatic modulation of the double-dot eigenstates by the cantilever motion leads to new effects compared to the single-dot case.Comment: 6 pages, 2 figure

Asymmetric Franck-Condon factors in suspended carbon nanotube quantum dots

Electronic states and vibrons in carbon nanotube quantum dots have in general different location and size. As a consequence, the conventional Anderson-Holstein model, coupling vibrons to the dot total charge only, may no longer be appropriated in general. Here we explicitly address the role of the spatial fluctuations of the electronic density, yielding space-dependent Franck-Condon factors. We discuss the consequent marked effects on transport which are compatible with recent measurements. This picture can be relevant for tunneling experiments in generic nano-electromechanical systems.Comment: 4+ pages, 3 figures (2 color, 1 BW

Dissipation in a rotating frame: master equation, effective temperature and Lamb-shift

Motivated by recent realizations of microwave-driven nonlinear resonators in superconducting circuits, the impact of environmental degrees of freedom is analyzed as seen from a rotating frame. A system plus reservoir model is applied to consistently derive in the weak coupling limit the master equation for the reduced density in the moving frame and near the first bifurcation threshold. It turns out that additional interactions between momenta of system and bath appear which have been omitted in previous studies. Explicit expressions for the effective temperature and the Lamb-shift are given which for ohmic baths are in agreement with experimental findings, while for structured environments population inversion is predicted that may qualitatively explain recent observations.Comment: 7 pages, 5 figure