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Register a new userQuantum critical point and scaling in a layered array of ultrasmall Josephson junctions
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We have studied a quantum Hamiltonian that models an array of ultrasmall Josephson junctions with short range Josephson couplings, $E_J$, and charging energies, $E_C$, due to the small capacitance of the junctions. We derive a new effective quantum spherical model for the array Hamiltonian. As an application we start by approximating the capacitance matrix by its self-capacitive limit and in the presence of an external uniform background of charges, $q_x$. In this limit we obtain the zero-temperature superconductor-insulator phase diagram, $E_J^{rm crit}(E_C,q_x)$, that improves upon previous theoretical results that used a mean field theory approximation. Next we obtain a closed-form expression for the conductivity of a square array, and derive a universal scaling relation valid about the zero--temperature quantum critical point. In the latter regime the energy scale is determined by temperature and we establish universal scaling forms for the frequency dependence of the conductivity.
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We consider the problem of two capacitively coupled Josephson junction arrays made of ultrasmall junctions. Each one of the arrays can be in the semiclassical or quantum regimes, depending on their physical parameter values. The former case is dominated by a Cooper-pair superfluid while the quantum one is dominated by dynamic vortices leading to an insulating behavior. We first consider the limit when both arrays are in the semiclassical limit, and next the case when one array is quantum and the other semiclassical. We present WKB and Mean Field theory results for the critical temperature of each array when both are in the semiclassical limit. When one array is in the semiclassical regime and the other one in the quantum fluctuations dominated regimes, we derive a duality transformation between the charged and vortex dominated arrays that involve a gauge vector field, which is proportional to the site coupling capacitance between the arrays. The system considered here has been fabricated and we make some predictions as to possible experimentally measurable quantities that could be compared with theory.
This paper deal the effects of uncorrelated white noise, in a serie of Josephson Junctions coupled to a linear $RLC$ resonator. The junction are hysteretic, and hence can be considered birhythmic, that is capable to oscillate at different frequencies for the same set of parameters. Both Josephson Junctions with identical and disordered parameters are considered. With the uniform parameters, the array behaves similarly to single Josephson junctions, also in the presence of noise. The magnitude of the effective energy that characterizes the response to noise becomes smaller as the number of elements of the array increases, making the resonator less stable. Disorder in the parameters drastically changes the physics of the array. The disordered array of Josephson junctions misses the birhythmicity properties for large values of the variance of the disorder parameter. Nevertheless, the system remains birhythmic for low values of the disorder parameter. Finally, disorder makes it difficult to locate the separatrix, hinting to a more complex structure of the effective energy landscape.
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.
The magneto-electrostatic tailoring of the supercurrent in quantum point contact ballistic Josephson junctions is demonstrated. An etched InAs-based heterostructure is laterally contacted to superconducting niobium leads and the existence of two etched side gates permits, in combination with the application of a perpendicular magnetic field, to modify continuously the magnetic interference pattern by depleting the weak link. For wider junctions the supercurrent presents a Fraunhofer-like interference pattern with periodicity h/2e whereas by shrinking electrostatically the weak link, the periodicity evolves continuously to a monotonic decay. These devices represent novel tunable structures that might lead to the study of the elusive Majorana fermions.
Complex cryogenics is still a strong limitation to the spread of quantum voltage standards and cryogen-free operation is then particularly interesting for Josephson standards. The main difficulties in He-free refrigeration are related to chip thermalization. We tested different solutions and interface materials between the chip and the cooling surface, to improve thermal conduction. Some junctions were chosen as elements to dissipate electrical power, while some others were operated as on-chip temperature sensors. Indium foil between chip and Cu support was demonstrated to provide a good thermal interface suitable for programmable voltage standard operation. However, thermal conduction can be further increased by thermal contacting the chip at the top. Finally, general physical constraints in vacuum thermal contacts are analyzed in terms of known properties of thermal interfaces at cryogenics temperatures.
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