Breathing Modes of Long Josephson Junctions with Phase-Shifts

We consider a spatially inhomogeneous sine-Gordon equation with a time-periodic drive, modeling a microwave driven long Josephson junction with phase-shifts. Under appropriate conditions, Josephson junctions with phase-shifts can have a spatially nonuniform ground state. In recent reports [K. Buckenmaier et al., Phys. Rev. Lett., 98 (2007), 117006], [J. Pfeiffer et al., http://arxiv.org/abs/0903.1046 (2009)], it is experimentally shown that a microwave drive can be used to measure the eigenfrequency of a junction's ground state. Such a microwave spectroscopy is based on the observation that when the frequency of the applied microwave is in the vicinity of the natural frequency of the ground state, the junction can switch to a resistive state, characterized by a nonzero junction voltage. It was conjectured that the process is analogous to the resonant phenomenon in a simple pendulum motion driven by a time-periodic external force. In the case of long junctions with phase-shifts, it would be a resonance bet...

[1]  H. Hilgenkamp.  Pi-phase shift Josephson structures , 2008 .

[2]  L. Bulaevskii,et al.  Superconducting system with weak coupling to the current in the ground state , 1977 .

[3]  C. Pegrum.  Can a Fraction of a Quantum Be Better Than a Whole One? , 2006, Science.

[4]  P. Kevrekidis,et al.  Dynamics of lattice kinks , 2000, nlin/0003006.

[5]  G Torrioli,et al.  Microwave-induced thermal escape in Josephson junctions. , 2004, Physical review letters.

[6]  Imaging spontaneous currents in superconducting arrays of π-junctions , 2007, 0708.0230.

[7]  O. Mielke,et al.  Flip-Flopping Fractional Flux Quanta , 2006, Science.

[8]  G. Kälbermann.  The sine-Gordon wobble , 2004 .

[9]  H. Segur.  Wobbling kinks in φ4 and sine‐Gordon theory , 1983 .

[10]  I. V. Barashenkov,et al.  Resonantly driven wobbling kinks. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  D. Bambusi,et al.  On dispersion of small energy solutions of the nonlinear Klein Gordon equation with a potential , 2009, 0908.4548.

[12]  Oscillatory eigenmodes and stability of one and two arbitrary fractional vortices in long Josephson 0-κ-junctions , 2004, cond-mat/0410340.

[13]  1 Ju l 2 00 9 Wobbling kinks in φ 4 theory , 2008 .

[14]  Horst Rogalla,et al.  Ordering and manipulation of the magnetic moments in large-scale superconducting π-loop arrays , 2003, Nature.

[15]  L. Bulaevskii,et al.  On possibility of the spontaneous magnetic flux in a Josephson junction containing magnetic impurities , 1978 .

[16]  Gianne Derks,et al.  Stability Analysis of π-Kinks in a 0-π Josephson Junction , 2007, SIAM J. Appl. Dyn. Syst..

[18]  M. Siegel,et al.  Long Josephson junction embedded into a planar resonator at microwave frequencies: Numerical simulation of fluxon dynamics , 2002 .

[19]  W. Schleich,et al.  Quantum tunneling of semifluxons in a 0-π-0 long Josephson junction , 2005, cond-mat/0504507.

[20]  L. A. Ferreira,et al.  Wobbles and other kink-breather solutions of the sine-Gordon model. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  ac-induced thermal vortex escape in magnetic-field-embedded long annular Josephson junctions , 2004, cond-mat/0404721.