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 for the spanning of the coupling parameter from weakly interacting axion to tight interactions. As a result, we obtain an axion field that induces a change in the potential barrier, therefore determining a significant detectable effect for such a kind of elusive particle.

Anomalous transport effects on switching currents of graphene-based Josephson junctions.

We explore the effect of noise on the ballistic graphene-based small Josephson junctions in the framework of the resistively and capacitively shunted model. We use the non-sinusoidal current-phase relation specific for graphene layers partially covered by superconducting electrodes. The noise induced escapes from the metastable states, when the external bias current is ramped, given the switching current distribution, i.e. the probability distribution of the passages to finite voltage from the superconducting state as a function of the bias current, that is the information more promptly available in the experiments. We consider a noise source that is a mixture of two different types of processes: a Gaussian contribution to simulate an uncorrelated ordinary thermal bath, and non-Gaussian, α-stable (or Lévy) term, generally associated to non-equilibrium transport phenomena. We find that the analysis of the switching current distribution makes it possible to efficiently detect a non-Gaussian noise component in a Gaussian background.

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 use of standard signal processing tools can be prohibitive due to the extreme weakness of the source or to the huge amount of data. In this paper we show that the prescriptions for the experimental setup and some physical behaviors depend on the detection strategy. More specifically, by exploitation of the sample mean of escape times to perform detection, two resonant regions are identified. At low frequencies there is a stochastic resonance or activation phenomenon, while near the plasma frequency a geometric resonance appears. Furthermore, detection performance in the geometric resonance region is maximized at the prescribed value of the bias current. 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 is essentially limited by measurement electronics. The behavior of the likelihood ratio and sample mean detector for different values of incoming signal to noise ratio is discussed, and a relationship with the error probability is found. Detectors based on the likelihood ratio test 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, which 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 (where the all-sky gravitational and/or radio wave search for pulsars requires the analysis of nearly sinusoidal long-lived waveforms at very low signal-to-noise ratio) or to analyze weak signals in the subterahertz range (where the traditional electronics counterpart is difficult to implement).

Detection of noise-corrupted sinusoidal signals with Josephson junctions.

We investigate the possibility of exploiting the speed and low noise features of Josephson junctions for detecting sinusoidal signals masked by Gaussian noise. We show that the escape time from the static locked state of a Josephson junction is very sensitive to a small periodic signal embedded in the noise, and therefore the analysis of the escape times can be employed to reveal the presence of the sinusoidal component. We propose and characterize two detection strategies: in the first, the initial phase is supposedly unknown (incoherent strategy), while in the second, the signal phase remains unknown but is fixed (coherent strategy). Our proposals are both suboptimal, with the linear filter being the optimal detection strategy, but they present some remarkable features, such as resonant activation, that make detection through Josephson junctions appealing in some special cases.

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 equation, which includes the cubic-quintic nonlinearity and a conservative linear driving term, whose amplitude is a standing wave with wave number k and frequency omega, the motion of the SPs being possible at resonant velocities +/-omega/k, which provide for locking to the drive. The model may be realized in terms of 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.

Double parametric resonance for matter-wave solitons in a time-modulated trap.

We analyze the motion of solitons in a self-attractive Bose-Einstein condensate, loaded into a quasi-one-dimensional parabolic potential trap, which is subjected to time-periodic modulation with an amplitude epsilon and frequency Omega. First, we apply the variational approximation, which gives rise to decoupled equations of motion for the center-of-mass coordinate of the soliton, xi (t), and its width a (t). The equation for xi (t) is the ordinary Mathieu equation (ME) (it is an exact equation that does not depend on the adopted ansatz), the equation for a (t) being a nonlinear generalization of the ME. Both equations give rise to the same map of instability zones in the (epsilon,Omega) plane, generated by the parametric resonances (PRs), if the instability is defined as the onset of growth of the amplitude of the parametrically driven oscillations. In this sense, the double PR is predicted. Direct simulations of the underlying Gross-Pitaevskii equation give rise to a qualitatively similar but quantitatively different stability map for oscillations of the soliton's width a (t). In the direct simulations, we identify the soliton dynamics as unstable if the instability (again, realized as indefinite growth of the amplitude of oscillations) can be detected during a time comparable with, or smaller than, the lifetime of the condensate (therefore accessible to experimental detection). Two-soliton configurations are also investigated. It is concluded that multiple collisions between solitons are elastic, and they do not affect the instability borders.

Noise-induced dephasing of an ac-driven Josephson junction.

We consider the 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 the critical value of the effective phase-diffusion parameter on the drive's amplitude at the point of sharp transition from the phase-locked state to an unlocked one. However, 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 effect is found for a previously studied case of ac-driven Josephson junctions with intrinsic thermal noise. The predicted effects are relevant to applications to voltage standards, as they determine the stability of the Josephson phase-locked state.