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Physical review. B, Condensed matter

Tunneling of vortices through a weak link in an insulating Josephson array

Apostol Vourdas, Timothy P. Spiller, Terrence D. Clark, D. A. Poulton

Published Feb 5, 2001• 3 citations
Publisher

Abstract

A Josephson array ring in the insulating phase with circulating vortices is considered. The persistent vortex current is calculated as a function of the charge at the center of the ring and the temperature, for the case of negligible dissipation. A weak link is introduced in the ring and the tunneling of vortices through it is described with the ``dual Josephson equations.'' The Hamiltonian that describes the interaction of these devices with electromagnetic fields is quantized. The use of such nonlinear devices as amplifiers and frequency converters of nonclassical microwaves is discussed.

DOI
10.1103/physrevb.63.104501

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A Josephson array ring in the insulating phase with circulating vortices is considered. The persistent vortex current is calculated as a function of the charge at the center of the ring and the temperature, for the case of negligible dissipation. A weak link is introduced in the ring and the tunneling of vortices through it is described with the ``dual Josephson equations.'' The Hamiltonian that describes the interaction of these devices with electromagnetic fields is quantized. The use of such nonlinear devices as amplifiers and frequency converters of nonclassical microwaves is discussed.
Mesoscopic Josephson devices, interacting with non-classical microwaves, are studied. The phase difference in Josephson's equations is a quantum mechanical operator, whose expectation value with respect to the density matrix describing the microwaves, determines the current. Dual phenomena with vortex condensates in Josephson array insulators are also considered. Dual Josephson junctions for vortices, made from two insulators separated by a weak link through which the vortices tunnel, are described by dual Josephson equations.
A ring made from a Josephson array in the insulating phase is considered. The ring contains a ‘dual Josephson junction’ (Josephson junction for vortices). External non-classical electromagnetic fields are coupled to the device and interact with the vortices that circulate the ring. The time evolution of this two-mode fully quantum mechanical system is studied. The effect of the quantum statistics of the photons on the quantum statistics of the vortices is discussed. The entanglement between the two systems is quantified.
The quantum dynamics of population-balanced fractional vortices and population-imbalanced vortices in an effective two-state bosonic system, made of two coupled discrete circuits with few sites, is addressed within the Bose-Hubbard model. We show that, for low on-site interaction, the tunneling of quantized vortices between the rings performs a coherent, oscillating dynamics connecting current states with chiral symmetry. The vortex-flux transfer dually follows the usual sinusoidal particle current of the Josephson effect, in good agreement with a mean-field approximation. Within such a regime, the switch of persistent currents in the rings resembles flux-qubit features and is feasible for experimental realization. On the contrary, strong interatomic interactions suppress the chiral current and lead the system into fragmented condensation.
Properties of weak links between two superconductors, or Josephson junctions, make them interesting for fundamental physics research. Since their discovery over four decades ago, they have provided a unique way to study the behavior of the superconducting quantum phase. More recently, ultra small, or mesoscopic, Josephson junctions with substantial single Cooper pair charging energy have gained interest due to their behavior as macroscopic quantum objects. In addition to the theoretical interest, Josephson junctions can be used as active elements in circuit applications. Particularly, in this Thesis we study two different devices. We develop the required theoretical treatments, derive device properties, and compare the results with experimental data. The first application is a Josephson voltage standard based on externally damped Superconductor - Insulator - Superconductor junctions. It consists of an array of large Josephson junctions connected in series and irradiated with a 70 GHz microwave signal. Phase locking the Josephson dynamics into the signal leads to the quantization of the voltage. This is utilized in metrology. We introduce a new circuit solution based on frequency dependent damping of the junctions. Optimization and some designs for practical arrays are presented. The purpose is to find such a design that the array is fast, has low power consumption and is as stable as possible. Arrays able to generate DC voltages of order 1 volt with metrological accuracy are demonstrated experimentally and their applicability in AC voltage calibrations is analyzed. The second application is the Bloch Oscillating Transistor (BOT). The BOT is based on controlling the Cooper pair current in an ultra small Josephson junction by means of quasiparticles tunneling through a normal junction. As part of the thesis work, the principle of operation is first demonstrated computationally. The model is then refined to yield quantitative predictions of the characteristics. Finally, an analytic theory for the device is developed and the properties as an amplifier are derived.
In quantum gases, weak links are typically realized with externally imposed optical potentials. We show that, in rotating binary condensates, quantized vortices in one component form hollow channels that act as self-induced weak links for the other, enabling superflow through otherwise impenetrable, phase-separated domains. This introduces a novel barrier mechanism: quantum pressure creates an effective barrier inside the vortex channel, set by the constriction width, which controls the superflow. Tuning the interspecies interaction strength drives a crossover from the hydrodynamic transport to Josephson tunneling regime. Long-range dipolar interactions further tune the weak-link properties, enabling both short links and two coupled junctions in series. Circuit models quantitatively capture the dc current-phase relations for both configurations. These results establish vortices as reconfigurable, interaction-controlled Josephson elements in superfluids.
Recent experiments on Josephson junction arrays (JJAs) in microwave cavities have opened up a new avenue for investigating the properties of these devices while minimizing the amount of external noise coming from the measurement apparatus itself. These experiments have already shown promise for probing many-body quantum effects in JJAs. In this work, we develop a general theoretical description of such experiments by deriving a quantum phase model for planar JJAs containing quantized vortices. The dynamical susceptibility of this model is calculated for some simple circuits, and signatures of the injection of additional vortices are identified. The effects of decoherence are considered via a Lindblad master equation.