Modified Josephson Equation for Mesoscopic Parallel LC Circuit Including a Josephson Junction

By introducing the entangled state representation, parallel LC circuit including a 3osephson junction equation associated with the modification of the motion equation. the Cooper-pair number-phase quantization of the mesoscopic is realized. In the Heisenberg picture, the modified Josephson Faraday equation about the inductance is deduced from the     

Quantum fluctuations in a distributed Josephson junction and the spectral properties of Josephson oscillators

Within the framework of a tunneling Hamiltonian, we obtain an equation for the reduced density matrix to describe quasiclassical dynamics and fluctuation effects in distributed Josephson junctions for voltages comparable with the superconducting gap. For quasiclassical dynamics, we derive the Langevin equation describing in a self-consistent way the resistive state and fluctuations due to both the tunneling current and the electromagnetic field. Current-voltage characteristics of a Josephson oscillator are calculated in the high magnetic field approximation. The intensity and shape of the spectral line of radiation due to vortices moving in a distributed Josephson junction are found.     

Cooper-Pair Number-Phase Quantization for a Mesoscopic LC Circuit Including a Josephson Junction

By introducing the entangled state representation and Feynman assumption that ＇electron pairs are bosons, ..., a bound pair acts as a Bose particle ＇, we construct an operator Hamiltonian for a mesoscopic inductance-capacitance （LC） circuit including a Josephson junction, then we use the Heisenberg equation of motion to derive the current equation and the voltage equation across the inductance as well as across the Josephson junction. The result manifestly shows how the junction voltage is affected by the capacitance coupling. In this way the Cooper-pair number-phase quantization for this system is completed.     

Time dilation of a bound half-fluxon pair in a long Josephson junction with a ferromagnetic insulator

The fluxon dynamics in a long Josephson junction with a ferromagnetic insulating layer is investigated. It is found that the Josephson phase obeys a double sine-Gordon equation involving a bound pi fluxon solution, and the internal oscillations of the bound pair acting as a clock exhibit Lorentz reductions in their frequencies regarded as a relativistic effect in the time domain, i.e., time dilation. This is the complement to the Lorentz contraction of fluxons with no clock. A possible observation scheme is also discussed.     

Coherent interaction of an electromagnetic field with a medium of two-level particles and with a superconducting current in a Josephson structure

The propagation of electromagnetic pulses in Josephson structures is investigated theoretically. An analogy with interaction of light pulses with a twolevel medium is traced. Under certain conditions the propagation of electromagnetic radiation in a two-level medium and in a Josephson structure is described by the same wave equation.Lebedev Physics Institute, Academy of Sciences of the USSR, Moscwow. Translated from Preprint No. 233 of the Lebedev Physics Institute, Academy of Sciences of the USSR, Moscow, 1938.     

Calculation of the vortex pinning energy in a long periodically modulated Josephson contact

An analytical method for evaluating the Josephson and magnetic energies of a vortex, as well as the vortex pinning energy and its components, in a long periodically modulated Josephson contact is suggested. The method allows one to take into account the variation of the vortex shape with the position of the vortex. The results obtained with this method are much closer to those of exact computer analysis compared with results of the conventional techniques. The discrepancy between the exact shape of the vortex and a function obtained by solving a differential equation approximating the exact difference equation is studied.     

直流和交流Josephson效应的研究

基于Feynman模型得到的Josephson方程,在求解过程中采取了ρ1=ρ2的假设,但这个假设在数学处理上并不严格。为了得到严格的结果,未进行上述假设,通过解微分方程得到了严格的Josephson方程,结果显示在一定条件下才能得到通常所说的Josephson方程。     

Vortices in a Josephson junction sandwiched between two superconducting waveguides

For a Josephson junction magnetically coupled to the superconducting waveguides enclosing it, solutions to the equation for the difference of the Cooper pair phases over the Josephson junction are found and the corresponding magnetic field values are calculated. Two gaps imposing an upper limit for the vortex velocity are found for free vortices (moving without dissipation). Existence conditions are found for fast vortices in the two high-velocity allowed regions. The dependence of the transport current on vortex velocity is established in cases where the current flows through the Josephson junction only or through the entire structure. A reverse current phenomenon is discovered in which vortices inside allowed velocity regions move opposite to the usual direction.     

Cooper-pair number-phase quantization analysis in double-Josephson-junction mesoscopic circuit coupled by a capacitor

This paper examines the quantization of mesoscopic circuit including Josephson junctions. Following Feynman＇s assumption, via the Hamilton dynamic approach and by virtue of the entangled state representation, it constructs Hamiltonian operator for the double-Josephson-junction mesoscopic circuit coupled by a capacitor. Then it uses the Heisenberg equation of motion to derive the induction voltage across each Josephson junction. The result manifestly shows how the voltage is affected by the capacitance coupling.     

Nonlocal Josephson electrodynamics of electromagnetic excitations in a superconducting magnetic (three-dimensional) thin film

The integro-differential equation for the dynamics of the phase difference with temporal and spatial nonlocality for a Josephson junction in a superconducting three-dimensional magnetic thin film is derived. The equation is valid for any type of magnetic ordering. The magnetic subsystem is shown to significantly renormalize the spectrum of small-amplitude electromagnetic excitations, which, as a result, are damped.     

Dynamics of a tunable superfluid junction

We study the population dynamics of a Bose-Einstein condensate in a double-well potential throughout the crossover from Josephson dynamics to hydrodynamics. At barriers higher than the chemical potential, we observe slow oscillations well described by a Josephson model. In the limit of low barriers, the fundamental frequency agrees with a simple hydrodynamic model, but we also observe a second, higher frequency. A full numerical simulation of the Gross-Pitaevskii equation giving the frequencies and amplitudes of the observed modes between these two limits is compared to the data and is used to understand the origin of the higher mode. Implications for trapped matter-wave interferometers are discussed.     

Multifluxon dynamics in driven Josephson junctions

The dynamics of fluxons in a long Josephson junction driven by time-varying nonuniform bias currents are described by a generalization of the sine-Gordon equation. This equation has solitary wave solutions which correspond to current vortices or quantized packets of magnetic flux in the junction. As with the sine-Gordon equation, multifluxon solutions may be demonstrated for the long Josephson junction. Our numerical calculations show that several fluxons may be launched or annihilated at the end of a junction. We also show multiple steady state conditions which correspond to one or more flux quanta trapped in the junction.     

External electric field control in the charge qubits including three Josephson junctions

Based on the standard canonical quantization principle, this paper gives the quantization scheme for the charge qubits mesoscopic circuit including three Josephson junctions coupled capacitively. By virtue of the Heisenberg equation, the time evolution of the phase difference operators across the polar plates and the number operators of the Cooper-pairs on the island are investigated and the modification of the Josephson equation is discussed. The time evolution of the phase difference operators is analysed when the Josephson junctions are irradiated by the external electrical field, which is referred to as also the obtainable controlling parameter.     

Interior crises and symmetries in a driven Josephson junction

The dynamics of a harmonically driven and nonlinearly damped pendulum is related to a current-fed Josephson junction. Through an extensive numerical simulation we show that the symmetry properties of the equation of motion are closely related with the development of chaotic solutions. Two different interior crises are discussed, both of them involve two broken-symmetric chaotic attractors.     

Sound wave interaction with Josephson junction and transformation of the contact coherent binding energy into ultrasonic waves

The problem of ultrasonic wave propagation in narrow Josephson junctions at nonzero temperature has been investigated. Using the derived solution of the nonstationary Fokker-Planck equation, the total current flowing through the narrow Josephson junction is calculated, and the coefficient of the ultrasonic wave passage through the Josephson junction is determined. The singularity of this coefficient is studied in the ultrasound amplification mode associated with the transformation of coherent binding energy of the contact into ultrasonic waves, and the possibility of experimental measurement of the lifetime of the Josephson junction in the metastable state under the conditions of maximum ultrasound amplification by the contact is discussed.     

Josephson结的阵发混沌与低频噪声

本文运用数值计算的方法研究了射频电流驱动下包含干涉项电流的Josephson结的分岔、混沌和阵发混沌。讨论了Josephson结的低频噪声,以及它与通向混沌途径的关系。 关键词：     

Josephson Dynamics of a Bose-Einstein Condensate Trapped in a Double-Well Potential

The Josephson equations for a Bose Einstein Condensate gas trapped in a double-well potential are derived with the two-mode approximation by the Gross Pitaevskii equation. The dynamical characteristics of the equations are obtained by the numerical phase diagrams. The nonlinear self-trapping effect appeared in the phase diagrams are emphatically discussed, and the condition EcN 〉 4E3 is presented.     

Fluxons interactions in a Josephson junction with a phase-shift

We consider a long Josephson junction with a discontinuity point characterized by a gauge phase-shift. The system is described by a modified sine-Gordon equation. We study, in particular, the interactions between a fluxon and a fractional fluxon. A perturbation theory is developed in the small phase-shift limit to understand the characteristics of the interaction. Finally, numerical computations of the threshold bias current and the threshold velocity for a fluxon running over a fractional fluxon are presented.     

Analytical solution of fluxons in a non-homogeneous Josephson junction

In order to study the fluxon behavior in a Josephson junction, a dielectric with variable thickness was inserted between two superconductors, which can be position-dependent. An analytical solution of the sine-Gordon equation is obtained. Subsequently, the relation between the kinetic and potential energy of a fluxon is obtained along with the analytic relationships between the velocity of the fluxon and the dielectric thickness. Finally, an exact topological soliton solution is obtained for the sine-Gordon equation with and without strong perturbations through the use of the ansatz method.     

On Bosonic Magnetic Flux Operator and Bosonic Faraday Operator Formula

In the literature about mesoscopic Josephson devices the magnetic flux is considered as an operator, the fundamental commutative relation between the magnetic flux operator and the Cooper-pair charge operator is usually preengaged. In this paper we show that such a relation can be deduced from the basic Bose operators＇ commutative relation through the entangled state representation. The Faraday formula in bosonic form is then equivalent to the second Josephson equation. The current operator equation for LC mesoscopic circuit is also derived.