Juan Atalaya

Continuum elastic modeling of graphene resonators

Starting from an atomistic approach, we have derived a hierarchy of successively more simplified continuum elasticity descriptions for modeling the mechanical properties of suspended graphene sheets. We find that already for deflections of the order of 0.5 A a theory that correctly accounts for nonlinearities is necessary and that for many purposes a set of coupled Duffing-type equations may be used to accurately describe the dynamics of graphene membranes. The descriptions are validated by applying them to square graphene-based resonators with clamped edges and studying numerically their mechanical responses. Both static and dynamic responses are treated, and we find good agreement with recent experimental findings.

Nanomechanical mass measurement using nonlinear response of a graphene membrane

We propose a scheme to measure the mass of a single particle using the nonlinear response of a 2D nanoresonator with degenerate eigenmodes. Using numerical and analytical calculations, we show that by driving a square graphene nanoresonator into the nonlinear regime, simultaneous determination of the mass and position of an added particle is possible. Moreover, this scheme only requires measurements in a narrow frequency band near the fundamental resonance.

Diffusion-Induced Bistability of Driven Nanomechanical Resonators

We study nanomechanical resonators with frequency fluctuations due to diffusion of absorbed particles. The diffusion depends on the vibration amplitude through inertial effect. We find that, if the diffusion coefficient D is sufficiently large, the resonator response to periodic driving displays bistability. The lifetime of the coexisting vibrational states exponentially increases with increasing D and displays a scaling dependence on the parameters close to bifurcation points.

Bacon-Shor code with continuous measurement of noncommuting operators

Author(s): Atalaya, Juan; Bahrami, Mohammad; Pryadko, Leonid P; Korotkov, Alexander N | Abstract: We analyze the operation of a four-qubit Bacon-Shor code with simultaneous continuous measurement of non-commuting gauge operators. The error syndrome in this case is monitored via time-averaged cross-correlators of the output signals. We find the logical error rate for several models of decoherence, and also find the termination rate for this quantum error detecting code. The code operation is comparable to that based on projective measurements when the collapse timescale due to continuous measurements is an order of magnitude less than the time period between the projective measurements. An advantage of the continuous-measurement implementation is the absence of time-dependence in the code operation, with passive continuous monitoring of the error syndrome.

General Elasticity Theory for Graphene Membranes Based on Molecular Dynamics

We have studied the mechanical properties of suspended graphene membranes using molecular dynamics (MD) and generalized continuum elasticity theory (GE) in order to develop and assess a continuum description for graphene. The MD simulations are based on a valence force field model which is used to determine the deformation and the elastic energy of the membrane (EMD) as a function of external forces. For the continuum description, we use the expression Econt = Estretching + Ebending for the elastic energy functional. The elastic parameters (tensile rigidity and Poisson ratio) entering Econt are determined by requiring that E cont = EMD for a set of deformations. Comparisons with the MD results show excellent agreement. We find that the elastic energy of a supported graphene sheets is typically dominated by the nonlinear stretching terms whereas a linear description is valid only for very small deflections. This implies that in some applications, i.e. NEMS, a linear description is of limited applicability.

Flux1/fαnoise in two-dimensional Heisenberg spin glasses: Effects of weak anisotropic interactions

We study the dynamics of a two-dimensional ensemble of randomly distributed classical Heisenberg spins with isotropic RKKY and weaker anisotropic dipole-dipole couplings. Such ensembles may give rise to the flux noise observed in SQUIDs with a

Elasticity Theory for Graphene Membranes

1/f^{\alpha}

Design and Optimization of Coreless Components Using Admittance Matrix and Efficiently Calculated Sensitivities

power spectrum (

Design of Inductors Using Efficiently-Calculated Sensitivities of the Admittance Matrix

\alpha \lesssim 1

Diffusion-induced dephasing in nanomechanical resonators

). We solve numerically the Landau-Lifshiftz-Gilbert equations of motion in the dissipationless limit. We find that Ising type fluctuators, which arise from spin clustering close to a spin-glass critical behavior with