JOSEPHSON LADDERS
                         
                        
                            A. V. Ustinov
                        
      Physikalisches Institut III, Universitaet Erlangen-Nuernberg
                     91054 Erlangen, Germany


Josephson ladders are relatively simple planar structures that have properties 
of both 1D transmission lines and 2D arrays. By a ladder it is usually meant a 
1D array of identical superconducting cells, each containing 4 Josephson 
junctions. There is a rapidly growing interest in studying these structures. 
They turned to be of very few experimentally accessible nonlinear lattices 
where spatially-localized excitations such as discrete breathers can be 
observed directly in experiment. On the other hand, ladders mark the border 
between long 1D Josephson junctions, where the ballistic propagation of 
vortices is well known, and 2D arrays, where this matter still remains a 
dispute. By varying the ladder anisotropy parameter (the ratio of the critical 
current of junctions placed along the ladder to that of junctions placed 
across the ladder) one can trace the crossover in the vortex properties. 

I will review recent experiments with underdamped Josephson ladders performed 
by our group. Both the static properties mapped by Ic(H) patterns and the 
dynamics on I-V curves have been investigated for various values of the 
anisotropy parameter. Resonant steps similar to Fiske resonances and Eck peak 
are observed in ladders placed in a magnetic field [1]. Numerical simulations 
show that the ballistic vortex motion in ladders persists in a wide range of 
the anisotropy parameter.

Visualization of various dynamic states was performed with spatial resolution 
of about 1 micrometer using low temperature laser scanning technique. We were 
able to observe rotobreathers in Josephson ladders [2]. These localized 
excitations are phase whirling states of few Josephson junctions that persist 
under a spatially-uniform bias current.  We find a rich variety of stable 
dynamic states including pure symmetric, pure asymmetric, and mixed states. 
We also studied larger 2D arrays by the laser scanning and found novel dynamic 
states with broken symmetry of the voltage drop inside the arrays [3]. The 
latter states are manifested by fine branching in the current-voltage 
characteristics of the arrays. Numerical simulations show that such 
percolative patterns have an intrinsic origin and occur independently of 
positional disorder. We argue that the appearance of these dynamic states 
is due to the presence of various metastable superconducting states in 
ladders and 2D arrays.

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*) This review is based on recent joint works in collaboration with 
   D. Abraimov, P. Binder, P. Caputo, G. Filatrella, M. Fistul, S. Flach, 
   B. Malomed, M. Schuster, and Y. Zolotaryk.

[1] P. Caputo, M. V. Fistul, A. V. Ustinov, B. A. Malomed, and S. Flach.
    Phys. Rev. B 59, 14050 (1999).
[2] P. Binder, D. Abraimov, A. V. Ustinov, S. Flach, and Y. Zolotaryuk, 
    Phys. Rev. Lett. 84, 745 (2000).
[3] D. Abraimov, P. Caputo, G. Filatrella, M. V. Fistul, G. Yu. Logvenov, 
    and A. V. Ustinov, Phys. Rev. Lett. 83, 5354 (1999).