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.     

The underdamped Josephson junction subjected to colored noises

The properties of the underdamped Josephson junction subjected to colored noises were investigated with large and small phase difference (φ). For the case of the large φ, we found numerically that: (i) the probability distribution function of φ exhibits monostability → bistability → monostability transitions as the autocorrelation rate (λ) of a colored noise increases; (ii) in the bistability region the multiplicative noise drives the phase difference to turn over periodically; (iii) the slope K of the linear response of the junction potential difference (〈V 〉) can be somewhat reduced by means of tuning an optimal λ; (iv) the amplitude of φ in response to external sinusoidal signals changes with λ. For the case of small φ, after deriving the analytical expressions of the potential difference amplitude (〈V 〉_max) and the K in the presence of a dichotomous noise, we found nonmonotonic behavior of 〈V 〉_max and the slope K as a function of λ.     

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.     

Quantum fluctuations in Josephson junction comparators

We have developed a method for calculation of quantum fluctuation effects, in particular, of the uncertainty zone developing at the potential curvature sign inversion, for a damped harmonic oscillator with arbitrary time dependence of frequency and for arbitrary temperature, within the Caldeira-Leggett model. The method has been applied to the calculation of the gray zone width Delta Ix of Josephson-junction balanced comparators. The calculated temperature dependence of Delta Ix in the range 1.5 to 4.2 K is in virtually perfect agreement with experimental data for Nb-trilayer comparators with critical current densities of 1.0 and 5.5 kA/cm2, without any fitting parameters.     

Quantum phase expectation values of a mesoscopic Josephson junction from quantum current measurements

A simple way to acquire information on the mean values of the phase operators sinϕ and cosϕ of an ultrasmall Josephson junction prepared in an arbitrary pure or not state is reported. Our proposal exploits the recently predicted occurrence of current spikes in the I-V characteristic of a mesojunction irradiated by a quantum single-mode low-intensity coherent electromagnetic field. A necessary condition for the validity of our treatment is presented and discussed. Received 11 April 2001     

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.     

Rectification by an imprinted phase in a Josephson junction

A Josephson phase shift can be induced in a Josephson junction by a strategically nearby pinned Abrikosov vortex (AV). For an asymmetric distribution of an imprinted phase along the junction (controlled by the position of the AV) such a simple system is capable of rectification of ac current in a broad and tunable frequency range. The resulting rectified voltage is a consequence of the directed motion of a Josephson antivortex which forms a pair with the AV when at local equilibrium. The proposed realization of the ratchet potential by an imprinted phase is more efficient than the asymmetric geometry of the junction itself, is easily realizable experimentally, and provides rectification even in the absence of an applied magnetic field.     

Quantum phase transition in one-dimensional arrays of resistively shunted small Josephson junctions

We have observed a superconductor-insulator transition in one-dimensional (1D) arrays of small Josephson junctions by changing both the resistance R(S) of normal metal resistors shunting each junction and the ratio of the Josephson coupling energy E(J) to the charging energy E(C). The phase boundary lies at R(S) approximately R(Q) (R(Q) identical with h/4e(2)=6.45 kOmega) when E(J)/E(C) is smaller than about unity. We discuss the obtained phase diagram in terms of theoretical models of the dissipation-driven quantum phase transition, with particular attention to differences from 2D arrays.     

Two-point phase correlations of a one-dimensional bosonic Josephson junction

We realize a one-dimensional Josephson junction using quantum degenerate Bose gases in a tunable double well potential on an atom chip. Matter wave interferometry gives direct access to the relative phase field, which reflects the interplay of thermally driven fluctuations and phase locking due to tunneling. The thermal equilibrium state is characterized by probing the full statistical distribution function of the two-point phase correlation. Comparison to a stochastic model allows us to measure the coupling strength and temperature and hence a full characterization of the system.     

Quasiparticle dynamics and phase locking in a S-I-S multilayer Josephson junction

New dynamical equations describing the Josephson effect and nonequilibrium quasiparticle distribution in a multilayer Josephson tunnel structure at T∼T _c are obtained, starting from the microscopic theory. It is shown that quasiparticle dynamics has a strong influence on the Josephson effect. Novel regimes with giant charge-imbalance oscillations are found. A new type of hysteresis on the current-voltage characteristic is predicted. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 10, 755–759 (25 May 1997) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Frequency divider by underdamped Josephson transmission line

A parallel array of coupled short Josephson junctions under boundary ac driving is theoretically investigated. The driving response is monitored via numerical simulations on the associated Frenkel-Kontorova model as an oscillating output current at the other boundary junction. The theoretical analysis is conducted assuming the phase locking of boundary driving with exact stationary solution of sine-Gordon equation that can be represented by a kink (fluxon) motion back and forth in the restricted geometry of the array. As a consequence the results suggest the conception of a device which could switch to the conducting regime not according to intensity range but rather to given (quantized) frequency range. Moreover our findings indicate also a frequency converting scenario by choosing appropriately the system length and injected fluxon number.     

Discontinuous current-phase relations in small one-dimensional Josephson junction arrays

We study the Josephson effect in small one-dimensional (1D) Josephson junction arrays. For weak Josephson tunneling, topologically different regions in the charge-stability diagram generate distinct current-phase (I-phi) relationships. We present results for a three-junction system in the vicinity of charge-degeneracy lines and triple points. We explain the generalization to larger arrays, show that discontinuities of the I-phi relation at phase pi persist and that, at maximum degeneracy, the problem can be mapped to a tight-binding model providing analytical results for arbitrary system size.     

Enhancement of Josephson phase diffusion by microwaves

We report an experimental and theoretical study of the phase diffusion in small Josephson junctions under microwave irradiation. A peculiar enhancement of the phase diffusion by microwaves is observed. The enhancement manifests itself by a pronounced current peak in the current-voltage characteristics. The voltage position V(top) of the peak increases with the power P of microwave radiation as V(top) proportional to sqrt[P], while its current amplitude weakly decreases with P. As the microwave frequency increases, the peak feature evolves into Shapiro steps with a finite slope. Our theoretical analysis, taking into account the enhancement of incoherent superconducting current by multiphoton absorption, is in good agreement with experimental data.     

Reentrant behavior of the phase stiffness in Josephson junction arrays

The phase diagram of a 2D Josephson junction array with large substrate resistance, described by a quantum XY model, is studied by means of Fourier path-integral Monte Carlo. A genuine Berezinskii-Kosterlitz-Thouless transition is found up to a threshold value g( small star, filled ) of the quantum coupling, beyond which no phase coherence is established. Slightly below g( small star, filled ) the phase stiffness shows a reentrant behavior with temperature, in connection with a low-temperature disappearance of the superconducting phase, driven by strong nonlinear quantum fluctuations.     

Quantum electrodynamic fluctuations of the macroscopic Josephson phase

We study the equilibrium dynamics of the relative phase in a superconducting Josephson link taking into account the quantum fluctuations of the electromagnetic vacuum. The photons act as a superohmic heat bath on the relative Cooper pair number and thus, indirectly, on the macroscopic phase difference φ. This leads to an enhancement of the mean square 〈φ²〉 that adds to the spread due to the Coulomb interaction carried by the longitudinal electromagnetic field. We also include the interaction with the electronic degrees of freedom due to quasiparticle tunneling, which couple to the phase and only indirectly to the particle number. The simultaneous inclusion of both the radiation field fluctuations and quasiparticle tunneling leads to a novel type of particle-bath Hamiltonian in which the quantum particle couples through its position and momentum to two independent bosonic heat baths. We study the interplay between the two mechanisms in the present context and find interference contributions to the quantum fluctuations of the phase. We explore the observability of the QED effects discussed here.