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Register a new userEffects of colored noise in short overdamped Josephson junction
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We investigate the transient dynamics of a short overdamped Josephson junction with a periodic driving signal in the presence of colored noise. We analyze noise induced henomena, specifically resonant activation and noise enhanced stability. We find that the positions both of the minimum of RA and maximum of NES depend on the value of the noise correlation time tau_c. Moreover, in the range where RA is observed, we find a non-monotonic behavior of the mean switching time as a function of the correlation time tau_c.
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The influence of fluctuations and periodical driving on temporal characteristics of short overdamped Josephson junction is analyzed. We obtain the standard deviation of the switching time in the presence of a dichotomous driving force for arbitrary noise intensity and in the frequency range of practical interest. For sinusoidal driving the resonant activation effect has been observed. The mean switching time and its standard deviation have a minimum as a function of driving frequency. As a consequence the optimization of the system for fast operation will simultaneously lead to minimization of timing errors.
We study the dynamic response to external currents of periodic arrays of Josephson junctions, in a resistively capacitively shunted junction (RCSJ) model, including full capacitance-matrix effects}. We define and study three different models of the capacitance matrix $C_{vec{r},vec{r}}$: Model A includes only mutual capacitances; Model B includes mutual and self capacitances, leading to exponential screening of the electrostatic fields; Model C includes a dense matrix $C_{vec{r},vec{r}}$ that is constructed approximately from superposition of an exact analytic solution for the capacitance between two disks of finite radius and thickness. In the latter case the electrostatic fields decay algebraically. For comparison, we have also evaluated the full capacitance matrix using the MIT fastcap algorithm, good for small lattices, as well as a corresponding continuum effective-medium analytic evaluation of a finite voltage disk inside a zero-potential plane. In all cases the effective $C_{vec{r},vec{r}}$ decays algebraically with distance, with different powers. We have then calculated current voltage characteristics for DC+AC currents for all models. We find that there are novel giant capacitive fractional steps in the I-Vs for Models B and C, strongly dependent on the amount of screening involved. We find that these fractional steps are quantized in units inversely proportional to the lattice sizes and depend on the properties of $C_{vec{r},vec{r}}$. We also show that the capacitive steps are not related to vortex oscillations but to localized screened phase-locking of a few rows in the lattice. The possible experimental relevance of these results is also discussed.
The boundary effects on the current-voltage characteristics in two-dimensional arrays of resistively shunted Josephson junctions are examined. In particular, we consider both the conventional boundary conditions (CBC) and the fluctuating twist boundary conditions (FTBC), and make comparison of the obtained results. It is observed that the CBC, which have been widely adopted in existing simulations, may give a problem in scaling, arising from rather large boundary effects; the FTBC in general turn out to be effective in reducing the finite-size effects, yielding results with good scaling behavior. To resolve the discrepancy between the two boundary conditions, we propose that the proper scaling in the CBC should be performed with the boundary data discarded: This is shown to give results which indeed scale well and are the same as those from the FTBC.
As the size of a Josephson junction is reduced, charging effects become important and the superconducting phase across the link turns into a periodic quantum variable. Isolated Josephson junction arrays are described in terms of such periodic quantum variables and thus exhibit pronounced quantum interference effects arising from paths with different winding numbers (Aharonov-Casher effects). These interference effects have strong implications for the excitation spectrum of the array which are relevant in applications of superconducting junction arrays for quantum computing. The interference effects are most pronounced in arrays composed of identical junctions and possessing geometric symmetries; they may be controlled by either external gate potentials or by adding/removing charge to/from the array. Here we consider a loop of N identical junctions encircling one half superconducting quantum of magnetic flux. In this system, the ground state is found to be non-degenerate if the total number of Cooper pairs on the array is divisible by N, and doubly degenerate otherwise (after the stray charges are compensated by the gate voltages).
We consider a short Josephson junction with a phase discontinuity $kappa$ created, e.g., by a pair of tiny current injectors, at some point $x_0$ along the length of the junction. We derive the effective current-phase relation (CPR) for the system as a whole, i.e., reduce it to an effective point-like junction. From the effective CPR we obtain the ground state of the system and predict the dependence of its critical current on $kappa$. We show that in a large range of $kappa$ values the effective junction behaves as a $varphi_0$ Josephson junction, i.e., has a unique ground state phase $varphi_0$ within each $2pi$ interval. For $kappaapproxpi$ and $x_0$ near the middle of the junction one obtains a $varphi_0pmvarphi$ junction, i.e., the Josephson junction with degenerate ground state phase $varphi_0pmvarphi$ within each $2pi$ interval. Further, in view of possible escape experiments especially in the quantum domain, we investigate the scaling of the energy barrier and eigenfrequency close to the critical currents and predict the behavior of the escape histogram width $sigma(kappa)$ in the regime of the macroscopic quantum tunneling.
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