Stochastic dynamics of a Josephson junction threshold detector

We generalize the stochastic path integral formalism by considering Hamiltonian dynamics in the presence of general Markovian noise. Kramers' solution of the activation rate for escape over a barrier is generalized for non-Gaussian driving noise in both the overdamped and underdamped limit. We apply our general results to a Josephson junction detector measuring the electron counting statistics of a mesoscopic conductor. The activation rate dependence on the third current cumulant includes an additional term originating from the backaction of the measurement circuit.     

The Josephson junction as a macroscopic radiating atom

We investigate the electrodynamic properties of a Josephson junction emitting coherent radiation and establish that it can be regarded as a two-level atom within the framework of the microscopic theory of superconductivity.     

Application of nano-scale Josephson junction as phase sensitive detector for analysis of vortex states in mesoscopic superconductors

We study phase shifts in a Josephson junction induced by vortices in superconducting mesoscopic electrodes. The position of the vortices are controlled by suitable geometry of a nano-scale Nb–Pt_1−xNi_x–Nb junction of the overlap type made by Focused Ion Beam (FIB) sculpturing. The vortex is kept outside the junction, parallel to the junction plane. From the measured Fraunhofer characteristics the entrance and exit of vortices are detected. By changing the bias current through the junction at constant magnetic field the vortices can be manipulated and the system can be switched between two consecutive vortex states which are characterized by different critical currents of the junction. A mesoscopic superconductor thus acts as a non-volatile memory cell in which the junction is used both for reading and writing information (vortex). Furthermore, we observe that the critical current density of Nb–Pt_1−xNi_x–Nb junctions decreases non-monotonously with increasing Ni concentration. It exhibits a minimum at ∼40 at.% Ni, which is an indication of switching into the π state.     

Curved Josephson junction

The constant curvature one and quasi-one dimensional Josephson junction is considered. On the base of Maxwell equations, the sine–Gordon equation that describes an influence of curvature on the kink motion was obtained. It is showed that the method of geometrical reduction of the sine–Gordon model from three to lower dimensional manifold leads to an identical form of the sine–Gordon equation.     

Fluctuation power spectrum of a Josephson junction

The fluctuation power spectrum of the Josephson junction has been evaluated in the limit of large energy barriers [(U _n ^max−U _n ^min)γ]≫1 and small currents [x≪x _e]. The result is valid for finite capacitance of the junction. The effect of the fluctuating Josephson current on the voltageV(t) across the junction has also been taken into account.     

Detecting charge noise with a Josephson junction: a problem of thermal escape in presence of non-Gaussian fluctuations

Motivated by several experimental activities to detect charge noise produced by a mesoscopic conductor with a Josephson junction as on-chip detector, the switching rate out of its zero-voltage state is studied. This process is related to the problem of thermal escape in presence of non-Gaussian fluctuations. In the relevant case of weak higher than second order cumulants, an effective Fokker-Planck equation is derived, which is then used to obtain an explicit expression for the escape rate. Specific results for the rate asymmetry due to the third moment of current noise allow to analyze experimental data and to optimize detection circuits.     

Quantum coherence in a superfluid Josephson junction

We report a new kind of experiment in which we take an array of nanoscale apertures that form a superfluid (4)He Josephson junction and apply quantum phase gradients directly along the array. We observe collective coherent behaviors from aperture elements, leading to quantum interference. Connections to superconducting and Bose-Einstein condensate Josephson junctions as well as phase coherence among the superfluid aperture array are discussed.     

Josephson effect in a Coulomb-blockaded SINIS junction

The problem of a Josephson current through a Coulomb-blocked nanoscale superconductor-normal-superconductor structure with tunnel contacts is reconsidered. Two different contributions to the phase-biased supercurrent I(?) are identified, which are dominant in the limits of weak and strong Coulomb interaction. Full expression for the free energy valid at arbitrary Coulomb strength is found. The current derived from this free energy interpolates between known results for weak and strong Coulomb interaction as the phase bias changes from 0 to π. In the broad range of Coulomb strength, the current-phase relation is substantially nonsinusoidal and qualitatively different from the case of semiballistic SNS junctions. The Coulomb interaction leads to the appearance of a local minimum in the current at some intermediate value of the phase difference applied to the junction.     

Rabi-type oscillations in a classical Josephson junction

We study analytically and numerically the phase-modulation properties of a classical Josephson tunnel junction biased in the zero-voltage state and phase locked to an external ac field. We show that the phase-locked state is being modulated in the transients, or in response to perturbations, and the modulation frequency is calculated as a function of relevant system parameters, such as microwave field amplitude. Our analysis demonstrates that the modulation of a phase-locked state in an entirely classical Josephson junction produces oscillations analogous to quantum mechanical Rabi oscillations, expected to be observed under the same conditions.     

Temperature square dependence of the low frequency charge noise in the Josephson junction qubits

To verify the hypothesis about the common origin of the low-frequency 1/f noise and the quantum f noise recently measured in the Josephson charge qubits, we study the temperature dependence of the 1/f noise and decay of coherent oscillations. The T2 dependence of the 1/f noise is experimentally demonstrated, which supports the hypothesis. We also show that dephasing in the Josephson charge qubits off the electrostatic energy degeneracy point is consistently explained by the same low-frequency 1/f noise that is observed in the transport measurements.     

Novel spin dynamics in a Josephson junction

We address the dynamics of a single spin embedded in the tunneling barrier between two superconductors. As a consequence of pair correlations in the superconducting state, the spin displays a rich and unusual dynamics. To properly describe the time evolution of the spin we find the generalized Wess-Zumino-Witten-Novikov term in the effective action for the spin on the Keldysh contour. The superconducting correlations lead to an effective spin action which is nonlocal in time leading to unconventional precessions. Our predictions might be directly tested for macroscopic spin clusters.     

Fluxon interaction in a long Josephson junction

Fluxon interaction in a long Josephson junction with bias current and losses is investigated by means of a perturbational approach. A simple analytical theory of the congelation (bunching) of unipolar fluxons is presented. Asymptotic results are confirmed by numerical solutions. It is shown that a system of congealed fluxons reflects from an open end of the junction without being destroyed.     

Current noises in a topological Josephson junction

We study the transport properties of a superconductor-quantum spin Hall insulator-superconductor Josephson junction both in the absence and in the presence of a DC bias voltage. As the system is predicted to host Majorana fermions at its interfaces,the Andreev bond states are supposed to exhibit a distinct 4π periodicity in the superconducting phase difference, namely the fractional Josephson effect. Using the non-equilibrium Green's function method, we calculate the current and the related current noise based on a tight-binding Hamiltonian. Our direct results show that the fractional Josephson effect can not be seen in equilibrium junctions. While in non-equilibrium junctions, this effect can be confirmed by the multiple Andreev reflections induced peaks of the non-equilibrium noise, which appear at discrete frequencies ω = ne V with n being an integer number.     

Vibrating superconducting island in a Josephson junction

We consider a combined nanomechanical-supercondcuting device that allows the Cooper pair tunneling to interfere with the mechanical motion of the middle superconducting island. Coupling of mechanical oscillations of a superconducting island between two superconducting leads to the electronic tunneling generates a supercurrent that is modulated by the oscillatory motion of the island. This coupling produces alternating finite and vanishing supercurrent as function of the superconducting phases. Current peaks are sensitive to the superconducting phase shifts relative to each other. The proposed device may be used to study the nanoelectromechanical coupling in case of superconducting electronics.     

Steady oscillatory states of a finite Josephson junction

Under the assumption that solutions have traveling-wave form, time-periodic solutions are found for the Josephson phase equation for a finite-length tunnel junction with uniform current feed and linear loss term. Exact current-voltage characteristics are found and compared with simple approximations. The complete current-velocity and mean-width-velocity curves for isolated fluxons are found. Comparison with characteristics for a finite junction shows that end effects obtained from analysis of a circuit model of the junction shows that end effects introduce lower- and upper-current thresholds.     

Quantum transitions of a small Josephson junction array

We have experimentally studied a small Josephson junction array in the presence of microwave irradiation. The array has comparable energy scales for single-charge effects and the Josephson effect, resulting in a discrete set of macroscopic eigenenergy levels. Excitation of the array by low-power microwaves is possible at frequencies where the photon energy matches the level spacing. The microwave frequency and amplitude dependence show that the excitation mechanism involves resonant quantum coherent dynamics of the array.