Annular Josephson tunnel junctions in an external magnetic field: The statics

Engineering double-well potentials with variable-width annular Josephson tunnel junctions

Long Josephson tunnel junctions are non-linear transmission lines that allow propagation of current vortices (fluxons) and electromagnetic waves and are used in various applications within superconductive electronics. Recently, the Josephson vortex has been proposed as a new superconducting qubit. We describe a simple method to create a double-well potential for an individual fluxon trapped in a long elliptic annular Josephson tunnel junction characterized by an intrinsic non-uniform width. The distance between the potential wells and the height of the inter-well potential barrier are controlled by the strength of an in-plane magnetic field. The manipulation of the vortex states can be achieved by applying a proper current ramp across the junction. The read-out of the state is accomplished by measuring the vortex depinning current in a small magnetic field. An accurate one-dimensional sine-Gordon model for this strongly non-linear system is presented, from which we calculate the position-dependent fluxon rest-mass, its Hamiltonian density and the corresponding trajectories in the phase space. We examine the dependence of the potential properties on the annulus eccentricity and its electrical parameters and address the requirements for observing quantum-mechanical effects, as discrete energy levels and tunneling, in this two-state system.

A quantum diffractor for thermal flux

Macroscopic phase coherence between weakly coupled superconductors leads to peculiar interference phenomena. Among these, magnetic flux-driven diffraction might be produced, in full analogy to light diffraction through a rectangular slit. This can be experimentally revealed by the electric current and, notably, also by the heat current transmitted through the circuit. The former was observed more than 50 years ago and represented the first experimental evidence of the phase-coherent nature of the Josephson effect, whereas the second one was still lacking. Here we demonstrate the existence of heat diffraction by measuring the modulation of the electronic temperature of a small metallic electrode nearby-contacted to a thermally biased short Josephson junction subjected to an in-plane magnetic field. The observed temperature dependence exhibits symmetry under magnetic flux reversal, and clear resemblance with a Fraunhofer-like modulation pattern. Our approach, joined to widespread methods for phase-biasing superconducting circuits, might represent an effective tool for controlling the thermal flux in nanoscale devices.

Deterministic Josephson vortex ratchet with a load

We investigate experimentally a deterministic underdamped Josephson vortex ratchet-a fluxon particle moving along a Josephson junction in an asymmetric periodic potential. By applying a sinusoidal driving current, one can compel the vortex to move in a certain direction, producing an average dc voltage across the junction. Being in such a rectification regime, we also load the ratchet, i.e., apply an additional dc bias current I(dc) (counterforce) which tilts the potential so that the fluxon climbs uphill due to the ratchet effect. The value of the bias current at which the fluxon stops climbing up defines the strength of the ratchet effect and is determined experimentally. This allows us to estimate the loading capability of the ratchet, the output power, and the efficiency. For the quasistatic regime we present a simple model which delivers straightforward analytic expressions for the above-mentioned figures of merit.

Do superconductors change as fast as possible when quenched?

If superconductors change as fast as possible as they pass through a phase transition, then the initial domain structure is constrained by causality. We shall see that Josephson junctions do indeed display such behaviour. However, we shall argue that causal bounds arise through the Gaussian nature of the order parameter, which can be thought of as a consequence of instabilities growing as fast as possible.

Flux cloning in Josephson transmission lines

We describe a novel effect related to the controlled birth of a single Josephson vortex. In this phenomenon, the vortex is created in a Josephson transmission line at a T-shaped junction. The "baby" vortex arises at the moment when a "mother" vortex propagating in the adjacent transmission line passes the T-shaped junction. In order to give birth to a new vortex, the mother vortex must have enough kinetic energy. Its motion can also be supported by an externally applied driving current. We determine the critical velocity and the critical driving current for the creation of the baby vortices and briefly discuss the potential applications of the found effect.

Josephson vortex in a ratchet potential: theory

We propose a type of Josephson vortex ratchet. In this system a Josephson vortex moves in a periodic asymmetric potential under the action of a deterministic or random force with zero time average. For some implementations the amplitude of the potential can be controlled during the experiment, thus allowing us to tune the performance of the system and build rocking as well as flashing ratchets. We discuss the differences between conventional and Josephson vortex ratchets and present a model describing the dynamics of the fluxon in such a system. We show numerical simulation results that predict rectification of a monochromatic, deterministic signal with zero time average. The investigation of this system may lead to the development of the fluxon rectifier-a device that produces a dc voltage from nonequilibrium fluctuations.

Whispering vortices

Experiments indicating the excitation of whispering-gallery-type electromagnetic modes by a vortex moving in an annular Josephson junction are reported. At relativistic velocities the Josephson vortex interacts with the modes of the superconducting stripline resonator giving rise to novel resonances on the current-voltage characteristic of the junction. The experimental data are in good agreement with analysis and numerical calculations based on the two-dimensional sine-Gordon model.