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.     

Ground-state cooling of a suspended nanowire through inelastic macroscopic quantum tunneling in a current-biased Josephson junction

We demonstrate that a suspended nanowire forming a weak link between two superconductors can be cooled to its motional ground state by a supercurrent flow. The predicted cooling mechanism has its origins in magnetic field induced inelastic tunneling of the macroscopic superconducting phase associated with the junction. Furthermore, we show that the voltage drop over the junction is proportional to the average population of the vibrational modes in the stationary regime, a phenomenon which can be used to probe the level of cooling.     

Josephson effect between superconducting nanograins with discrete energy levels

We investigate the Josephson effect between two coupled superconductors, coupled by the tunneling of pairs of electrons, in the regime that their energy level spacing is comparable to the bulk superconducting gap, but neglecting any charging effects. In this regime, BCS theory is not valid, and the notion of a superconducting order parameter with a well-defined phase is inapplicable. Using the density matrix renormalization group, we calculate the ground state of the two coupled superconductors and extract the Josephson energy. The Josephson energy is found to display a reentrant behavior (decrease followed by increase) as a function of increasing level spacing. For weak Josephson coupling, a tight-binding approximation is introduced, which illustrates the physical mechanism underlying this reentrance in a transparent way. The DMRG method is also applied to two strongly coupled superconductors and allows a detailed examination of the limits of validity of the tight-binding model.Received: 8 September 2003, Published online: 28 May 2004PACS: 74.20.-z Theories and models of superconducting state - 74.78.-w Superconducting films and low-dimensional structures - 74.50. + r Tunneling phenomena; point contacts, weak links, Josephson effects     

Observation of a microwave induced resistive state in a long Josephson tunnel junction

We have observed a resistive state in a long Josephson tunnel junction in the presence of applied microwaves when the microwave power is greater than a certaib threshold value. At the threshold power, the dc cutoff voltage of the resistive state, V_co, and the microwave frequency, f, were found to satisfy the quantum relation 2eV_co = nhf.     

On the broadening of the vortex width in a long Josephson tunnel junction

A solution is obtained for a vortex in a long Josephson junction, satisfying boundary conditions on the junction edges. The vortex is shown to broaden remarkably with the decrease of the junctionwidth when the field distribution in free space is two dimensional.     

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.     

Josephson plasmons in a long S-I-S tunnel junction with quantum jumpers in a disordered I layer

The formula for the Josephson plasmon frequency in a disordered S-I-S junction is derived.     

Multiphoton transitions in direct-gap semiconductors

Multiphoton transitions in direct-gap semiconductors are studied considering a “non-perturbative” approach in which the final state is represented by a Volkov wavefunction. Analytical solutions are obtained for multiphoton transition rates. The relation between multiphoton absorption and tunneling is discussed.     

Nonequilibrium pure phase dynamics for the strong coupling Josephson tunnel junction

Starting from the microscopic BCS-interaction Hamiltonians inside and between the superconductors of a tunnel junction sandwich, the macroscopic part of the Schrödinger dynamics on the set of pure physical phase states is derived with the methods of algebraical statistical mechanics. The resulting nonlinear differential equations for the physical parameters, like the macroscopic phase difference, are solved numerically and compared with the Josephson relations. It is shown that the frequency of the tunnel current has sharp peaks, if it is considered as a function of applied voltage and phase difference. The calculated peak-parameters align to the characteristic fork of bifurcating systems in the voltage-phase parameterspace.     

Interaction between a BSCCO-type intrinsic Josephson junction and a microwave cavity

The electrical behavior of anisotropic BSCCO single crystals is modeled by mutually coupled long Josephson junctions. We show that although the fluxons in the different layers do not a priori prefer the in-phase motion desired for many potential applications it is possible to induce such behavior by coupling the system to a high-Q resonator with a resonance frequency corresponding to fluxon in-phase motion. The resulting model is a set of coupled non-linear partial differential equations. By direct numerical simulations we have demonstrated that the qualitative behavior of the combined stacked long Josephson junctions and cavity system can be understood on the basis of the general concepts of nonlinear oscillators interacting with a resonator. For some region of the parameter space it is possible to reach the desired synchronous state, making the system potentially suitable for applications. We also look at the different dynamical states defined by different fluxon dynamical states in combination with different cavity properties.     

Multiphoton transitions in a macroscopic quantum two-state system

We have observed multiphoton transitions between two macroscopic quantum-mechanical superposition states formed by two opposite circulating currents in a superconducting loop with three Josephson junctions. Resonant peaks and dips of up to three-photon transitions were observed in spectroscopic measurements when the system was irradiated with a strong rf-photon field. The widths of the multiphoton absorption dips are shown to scale with the Bessel functions in agreement with theoretical predictions derived from the Bloch equation or from a spin-boson model.     

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.     

Commensurability effects in a Josephson tunnel junction in the field of an array of magnetic particles

Commensurability effects have been theoretically studied in a hybrid system consisting of a Josephson junction located in a nonuniform field induced by an array of magnetic particles. A periodic phase-difference distribution in the junction that is caused by the formation of a regular lattice of Abrikosov vortices generated by the magnetic field of the particles in superconducting electrodes is calculated. The dependence of the critical current through the junction I _c on the applied magnetic field H is shown to differ strongly from the conventional Fraunhofer diffraction pattern because of the periodic modulation of the Josephson phase difference created by the vortices. More specifically, the I _c(H) pattern contains additional resonance peaks, whose positions and heights depend on the parameters and magnetic state of the particles in the array. These specific features of the I _c(H) dependence are observed when the period of the Josephson current modulation by the field of the magnetic particles and the characteristic scale of the change in the phase difference by the applied magnetic field are commensurable. The conditions that determine the positions of the commensurability peaks are obtained, and they are found to agree well with experimental results.     

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.     

Transitions between chaos and order in rf-driven Josephson junction

We investigate transitions between the chaotic and regular states through a perturbed chaotic solution of a rf-driven Josephson system. It is shown that the transition from order to chaos may occur when the system initially near the heteroclinic points. The chaotic solution tends to an unstable periodic one for the initial values sufficiently nearing the heteroclinic orbit but going beyond the heteroclinic points. Thus the Josephson chaos can be analytically and numerically controlled, by adjusting the initial conditions.