Noise Estimate of Pendular Fabry-Perot through Reflectivity Change

A key issue in developing pendular Fabry-Perot interferometers as very accurate displacement measurement devices, is the noise level. The Fabry-Perot pendulums are the most promising device to detect gravitational waves, and therefore the background and the internal noise should be accurately measured and reduced. In fact terminal masses generates additional internal noise mainly due to thermal fluctuations and vibrations. We propose to exploit the reflectivity change, that occurs in some special points, to monitor the pendulums free oscillations and possibly estimate the noise level. We find that in spite of long transients, it is an effective method for noise estimate. We also prove that to only retain the sequence of escapes, rather than the whole time dependent dynamics, entails the main characteristics of the phenomenon. Escape times could also be relevant for future gravitational wave detector developments.Comment: PREPRINT Metrology for Aerospace (MetroAeroSpace), 2014 IEEE Publication Year: 2014, Page(s): 468 - 47

Noise-induced dephasing of an ac-driven Josephson junction

We consider phase-locked dynamics of a Josephson junction driven by finite-spectral-linewidth ac current. By means of a transformation, the effect of frequency fluctuations is reduced to an effective additive noise, the corresponding (large) dephasing time being determined, in the logarithmic approximation, by the Kramers' expression for the lifetime. For sufficiently small values of the drive's amplitude, direct numerical simulations show agreement of the dependence of the dephasing activation energy on the ac-drive's spectral linewidth and amplitude with analytical predictions. Solving the corresponding Fokker-Planck equation analytically, we find a universal dependence of a critical value of the effective phase-diffusion parameter on the drive's amplitude at a point of a sharp transition from the phase-locked state to an unlocked one. For large values of the drive amplitude, saturation and subsequent decrease of the activation energy are revealed by simulations, which cannot be accounted for by the perturbative analysis. The same new effect is found for a previously studied case of ac-driven Josephson junctions with intrinsic thermal noise. The work was performed in the framework of a cooperation agreement between Consiglio Nazionale di Ricerca (Italy) and the Israeli Ministry of Science and Technology.Comment: latex text file and six eps figure files. Physical Review E, in pres

Characterization of escape times of Josephson Junctions for signal detection

The measurement of the escape time of a Josephson junction might be used to detect the presence of a sinusoidal signal embedded in noise when standard signal processing tools can be prohibitive. We show that the prescriptions for the experimental set-up and some physical behaviors depend on the detection strategy. More specifically, by exploiting the sample mean of escape times to perform detection, two resonant regions are identified. At low frequencies there is a stochastic resonance/activation phenomenon, while near the plasma frequency a geometric resonance appears. The naive sample mean detector is outperformed, in terms of error probability, by the optimal likelihood ratio test. The latter exhibits only geometric resonance, showing monotonically increasing performance as the bias current approaches the junction critical current. In this regime the escape times are vanishingly small and therefore performance are essentially limited by measurement electronics. The behavior of the likelihood ratio and sample mean detector for different values of incoming signal to noise ratio are discussed, and a relationship with the error probability is found. The likelihood ratio test based detectors could be employed also to estimate unknown parameters in the applied input signal. As a prototypical example we study the phase estimation problem of a sinusoidal current, that is accomplished by using the filter bank approach. Finally we show that for a physically feasible detector the performances are found to be very close to the Cramer- Rao theoretical bound. Applications might be found for example in some astronomical detection problems or to analyze weak signals in the sub-terahertz range.Comment: 22 pages, 14 figure

Inverse ac Josephson Effect for a Fluxon in a Long Modulated Junction

We analyze motion of a fluxon in a weakly damped ac-driven long Josephson junction with a periodically modulated maximum Josephson current density. We demonstrate both analytically and numerically that a pure {\it ac} bias current can drive the fluxon at a {\it resonant} mean velocity determined by the driving frequency and the spatial period of the modulation, provided that the drive amplitude exceeds a certain threshold value. In the range of strongly ``relativistic'' mean velocities, the agreement between results of a numerical solution of the effective (ODE) fluxon equation of motion and analytical results obtained by means of the harmonic-balance analysis is fairly good; morever, a preliminary PDE result tends to confirm the validity of the collective-coordinate (PDE-ODE) reduction. At nonrelativistic mean velocities, the basin of attraction, in position-velocity space, for phase-locked solutions becomes progressively smaller as the mean velocity is decreased.Comment: 15 pages, 26 kbytes, of text in plain LaTeX. A uuencoded, Z-compressed tar archive, 21 kbytes, containing 3 PostScript, [email protected], [email protected], [email protected]

The ac-Driven Motion of Dislocations in a Weakly Damped Frenkel-Kontorova Lattice

By means of numerical simulations, we demonstrate that ac field can support stably moving collective nonlinear excitations in the form of dislocations (topological solitons, or kinks) in the Frenkel-Kontorova (FK) lattice with weak friction, which was qualitatively predicted by Bonilla and Malomed [Phys. Rev. B{\bf 43}, 11539 (1991)]. Direct generation of the moving dislocations turns out to be virtually impossible; however, they can be generated initially in the lattice subject to an auxiliary spatial modulation of the on-site potential strength. Gradually relaxing the modulation, we are able to get the stable moving dislocations in the uniform FK lattice with the periodic boundary conditions, provided that the driving frequency is close to the gap frequency of the linear excitations in the uniform lattice. The excitations have a large and noninteger index of commensurability with the lattice (suggesting that its actual value is irrational). The simulations reveal two different types of the moving dislocations: broad ones, that extend, roughly, to half the full length of the periodic lattice (in that sense, they cannot be called solitons), and localized soliton-like dislocations, that can be found in an excited state, demonstrating strong persistent internal vibrations. The minimum (threshold) amplitude of the driving force necessary to support the traveling excitation is found as a function of the friction coefficient. Its extrapolation suggests that the threshold does not vanish at the zero friction, which may be explained by radiation losses. The moving dislocation can be observed experimentally in an array of coupled small Josephson junctions in the form of an {\it inverse Josephson effect}, i.e., a dc-voltage response to the uniformly applied ac bias current.Comment: Plain Latex, 13 pages + 9 PostScript figures. to appear on Journal of Physics: condensed matte

Axion field influence on Josephson junction quasipotential

The direct effect of an axion field on Josephson junctions is analyzed through the consequences on the effective potential barrier that prevents the junction from switching from the superconducting to the finite-voltage state. We describe a method to reliably compute the quasipotential with stochastic simulations, which allows to span the coupling parameter from weakly interacting axion to tight interactions. As a result, we obtain that the axion field induces a change in the potential barrier, therefore determining a significant detectable effect for such a kind of elusive particle.Comment: 12 pages, 3 figure

Moving and colliding pulses in the subcritical Ginzburg-Landau model with a standing-wave drive

We show the existence of steadily moving solitary pulses (SPs) in the complex Ginzburg-Landau (CGL) equation, which includes the cubic-quintic (CQ) nonlinearity and a conservative linear driving term, whose amplitude is a standing wave with wavenumber $k$ and frequency $\omega$, the motion of the SPs being possible at velocities $\pm \omega /k$, which provide locking to the drive. A realization of the model may be provided by traveling-wave convection in a narrow channel with a standing wave excited in its bottom (or on the surface). An analytical approximation is developed, based on an effective equation of motion for the SP coordinate. Direct simulations demonstrate that the effective equation accurately predicts characteristics of the driven motion of pulses, such as a threshold value of the drive's amplitude. Collisions between two solitons traveling in opposite directions are studied by means of direct simulations, which reveal that they restore their original shapes and velocity after the collision.Comment: 7 pages, 5 eps figure