Efficient readout of micromechanical resonator arrays in ambient conditions

We present a method for efficient spectral readout of mechanical resonator arrays in dissipative environments. Magnetomotive drive and detection is used to drive double clamped resonators in the nonlinear regime. Resonators with almost identical resonance frequencies can be tracked individually by sweeping the drive power. Measurements are performed at room temperature and atmospheric pressure. These conditions enable application in high throughput resonant sensor arrays.Comment: 4 pages, 4 figure

Strongly coupled modes in a weakly driven micromechanical resonator

We demonstrate strong coupling between the flexural vibration modes of a clamped-clamped micromechanical resonator vibrating at low amplitudes. This coupling enables the direct measurement of the frequency response via amplitude- and phase modulation schemes using the fundamental mode as a mechanical detector. In the linear regime, a frequency shift of $\mathrm{0.8\,Hz}$ is observed for a mode with a line width of $\mathrm{5.8\,Hz}$ in vacuum. The measured response is well-described by the analytical model based on the Euler-Bernoulli beam including tension. Calculations predict an upper limit for the room-temperature Q-factor of $\mathrm{4.5\times10^5}$ for our top-down fabricated micromechanical beam resonators.Comment: 9 pages, 2 figure

Nanomechanical properties of few-layer graphene membranes

We have measured the mechanical properties of few-layer graphene and graphite flakes that are suspended over circular holes. The spatial profile of the flake's spring constant is measured with an atomic force microscope. The bending rigidity of and the tension in the membranes are extracted by fitting a continuum model to the data. For flakes down to eight graphene layers, both parameters show a strong thickness-dependence. We predict fundamental resonance frequencies of these nanodrums in the GHz range based on the measured bending rigidity and tension.Comment: 9 pages, 3 figures, This article has been accepted by Appl. Phys. Lett. After it is published, it will be found at http://apl.aip.org

Nonlinear Viscous Vortex Motion in Two-Dimensional Josephson-Junction Arrays

When a vortex in a two-dimensional Josephson junction array is driven by a constant external current it may move as a particle in a viscous medium. Here we study the nature of this viscous motion. We model the junctions in a square array as resistively and capacitively shunted Josephson junctions and carry out numerical calculations of the current-voltage characteristics. We find that the current-voltage characteristics in the damped regime are well described by a model with a {\bf nonlinear} viscous force of the form $F_D=\eta(\dot y)\dot y={{A}\over {1+B\dot y}}\dot y$, where $\dot y$ is the vortex velocity, $\eta(\dot y)$ is the velocity dependent viscosity and $A$ and $B$ are constants for a fixed value of the Stewart-McCumber parameter. This result is found to apply also for triangular lattices in the overdamped regime. Further qualitative understanding of the nature of the nonlinear friction on the vortex motion is obtained from a graphic analysis of the microscopic vortex dynamics in the array. The consequences of having this type of nonlinear friction law are discussed and compared to previous theoretical and experimental studies.Comment: 14 pages RevTex, 9 Postscript figure

Vortex reflection at boundaries of Josephson-junction arrays

We study the propagation properties of a single vortex in square Josephson-junction arrays (JJA) with free boundaries and subject to an applied dc current. We model the dynamics of the JJA by the resistively and capacitively shunted junction (RCSJ) equations. For zero Stewart-McCumber parameter $\beta_c$ we find that the vortex always escapes from the array when it gets to the boundary. For $\beta_c\geq 2.5$ and for low currents we find that the vortex escapes, while for larger currents the vortex is reflected as an antivortex at one edge and the antivortex as a vortex at the other, leading to a stationary oscillatory state and to a non-zero time-averaged voltage. The escape and the reflection of a vortex at the array edges are qualitatively explained in terms of a coarse-grained model of a vortex interacting logarithmically with its image. We also discuss the case when the free boundaries are at $45$ degrees with respect to the direction of the vortex motion. Finally, we discuss the effect of self-induced magnetic fields by taking into account the full-range inductance matrix of the array, and find qualitatively equivalent results.Comment: 14 pages RevTex, 9 Postscript figure

In-Chain Tunneling Through Charge-Density Wave Nanoconstrictions and Break-Junctions

We have fabricated longitudinal nanoconstrictions in the charge-density wave conductor (CDW) NbSe$_{3}$ using a focused ion beam and using a mechanically controlled break-junction technique. Conductance peaks are observed below the T$_{P1}$$=145$K and T$_{P2}$$=59$K CDW transitions, which correspond closely with previous values of the full CDW gaps $2\Delta_{1}$ and $2\Delta_{2}$ obtained from photo-emission. These results can be explained by assuming CDW-CDW tunneling in the presence of an energy gap corrugation $\epsilon_{2}$ comparable to $\Delta_{2}$, which eliminates expected peak at $\Delta_{1}+\Delta_{2}$. The nanometer length-scales our experiments imply indicate that an alternative explanation based on tunneling through back-to-back CDW-normal junctions is unlikely.Comment: 5 pages, 3 figures, submitted to physical review letter

Field-induced superconductor to insulator transition in Josephson-junction ladders

The superconductor to insulator transition is studied in a self-charging model for a ladder of Josephson-junctions in presence of an external magnetic field. Path integral Monte Carlo simulations of the equivalent (1+1)-dimensional classical model are used to study the phase diagram and critical behavior. In addition to a superconducting (vortex-free) phase, a vortex phase can also occur for increasing magnetic field and small charging energy. It is found that an intervening insulating phase separates the superconducting from the vortex phases. Surprisingly, a finite-size scaling analysis shows that the field-induced superconducting to insulator transition is in the KT universality class even tough the external field breaks time-reversal symmetry.Comment: 5 pages, 7 figures, to appear in Phys. Rev.

Discrete-time quadrature feedback cooling of a radio-frequency mechanical resonator

We have employed a feedback cooling scheme, which combines high-frequency mixing with digital signal processing. The frequency and damping rate of a 2 MHz micromechanical resonator embedded in a dc SQUID are adjusted with the feedback, and active cooling to a temperature of 14.3 mK is demonstrated. This technique can be applied to GHz resonators and allows for flexible control strategies.Comment: To appear in Appl. Phys. Let