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arXiv:cond-mat/9911437 · Journal of Low Temperature Physics

Annular Long Josephson Junctions in a Magnetic Field: Engineering and Probing the Fluxon Interaction Potential

Andreas J. Wallraff, Yu. I. Koval’, M. Levitchev, M. V. Fistul, Alexey Vladimirovich Ustinov

Published Mar 1, 2000• 53 citations
arXivHTMLPDF
DOI
10.1023/a:1004674908169

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IEEE Transactions on Applied Superconductivity•Jun 1, 2005•14 citations
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 technique of inserting magnetic fluxons into annular Josephson junctions is proposed and demonstrated experimentally. The method is based on local injection of current into one of the superconducting electrodes of the junction. The residual pinning of fluxons in the junction can be eliminated by choosing an appropriate injection current, which depends on the spacing between the injectors. The reported technique resolves the long-standing problem of a controlled preparation of fluxon states in annular Josephson junctions and can be used in various fluxon devices.
We have developed clock sources for rapid single flux quantum (RSFQ) digital circuits using high-quality long Josephson junction (LJJ) resonant oscillators of annular geometry. Being a topologically closed system and unperturbed by reflections from boundaries and collisions among the fluxons (flux quanta), the annular LJJ oscillator has demonstrated a high quality factor. The novel design of an annular junction clock that allows easier interface with RSFQ circuitry has been realized. Magnetic fluxons are inserted into an annular LJJ by local injection of current into the control line of the junction. This technique resolves the long-standing problem of achieving superior stability of the fluxon state for application as a clock source. The linewidth of the phase-locked clock source is measured as low as 24 Hz relative to a reference oscillator at 40 GHz. The cycle-to-cycle jitter was measured to be 9 fs at a frequency of 36 GHz, or 0.04% of the clock period which is in good agreement with theoretical estimation.