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Observation of Discrete Breathers in Josephson Arrays


Under the exotic name of discrete breathers or intrinsic localized modes we refer to the dynamical phenomenon of energy localization by nonlinearity and discreteness in perfect – disorder free – lattices. Our group at ICMA has been pioneering in the theoretical study of such modes. We have also carried out the theoretical prediction and experimental detection of discrete breathers in Josephson arrays, a type of superconducting solid-state devices. This work is one of the first and, to our opinion, one of the clearest observations of discrete breathers in any real system.

Before the discovering of discrete breathers, the phenomenon of energy localization in physical lattices was associated with the existence of defects or disorder in the lattice. It was thought that any initially localized state would radiate energy and delocalize emitting plane waves or phonons, the linear vibrational modes of the lattice. However, an intense theoretical and computational work starting in the late 1980s showed the existence of long-living localized modes in discrete and non-linear lattices without disorder. Such modes correspond to – usually periodic – localized vibrations or rotations in the lattices. Intrinsic localized modes exist both for the case of Hamiltonian lattices (energy is conserved) or dissipative and biased ones (where external bias balances the losses due to the intrinsic dissipation). It is also important to say that, contrary to other nonlinear excitations, discrete breathers exist in one-, two- or three-dimensional systems. [1]

Figure 1 shows a numerical simulation of a localized vibrational mode in a Frenkel-Kontorova chain. This system is formed by a chain of nonlinear pendula joined by harmonic springs and subjected to dissipation and a periodic external force; see the small amplitude oscillation of particles in the ends. As it can be seen, the breather solution corresponds to a highly localized vibration of the chain. The particles in the core of the breather describe large amplitude oscillations meanwhile other particles librate with small amplitude under the effect of the external force. From the point of view of the theory of dynamical systems, the solution is an attracting limit cycle, and it is structurally stable and robust under thermal fluctuations.

Figure1 shows an example of a mode with localized oscillation or oscillobreather. However, for the case of arrays made of interacting rotors it is possible to have also localized rotations or rotobreathers.

Figure 1: One discrete breather (oscillobreather)

After some years of intense theoretical and numerical work; recently, most of the efforts in this field have been focused on the experimental detection of discrete breathers in real physical systems. In fact, up to the date they have been observed in solid state mixed-valence transition metal complexes, quasi-1D antiferromagnetic chains, superconducting arrays made of Josephson-junctions, micromechanical oscillators, optical waveguide systems and 2D photonic structures. [1]


Our team of the department of Theory and Simulation of Complex Systems at ICMA has played a key role in the achievement of the experimental observation of discrete breathers in Josephson arrays.

In the work of 1996 [2] it was proposed a particular Josephson-junction configuration, the ladder as an ideal experimental system to study the phenomenon of intrinsic localization. There, and in following works, the theoretical basis was established and the existence of discrete breathers in such arrays predicted. Based on such theoretical studies, the experimental effort to excite and detect localized solutions was carried out independently by the group of Terry Orlando at MIT [3] – in close collaboration with the author, Visiting Scholar at MIT at the time –, and the group of Alexey Ustinov in Erlangen [4] – also linked to our group through a common European project –. The experiments were successfully carried out in both laboratories. A nice brief presentation of both works can be found in [5] and a longer, still popularized one in [6]. For more authorized reviews, see [P2, 7].

Figure 2: The Josephson ladder (Josephson junctions are sketched in red at the bottom right panel)

Figure 2 shows one of the superconducting Josephson ladders fabricated to observe rotobreather states. The junctions are made by Niobium superconducting islands connected by thin Aluminium Oxide insulating barriers. The ladder consists on two rows with 9 Niobium islands each one, connected through a total of 25 Josephson-junctions: 9 vertical and 16 horizontal (8 in the top row and 8 in the bottom one).

Each junction in the ladder can be modelled by a nonlinear rotor characterized by a phase, an angular variable. The localized state we are looking for is a rotobreathers: a few of the junctions are in a resistive state (which corresponds to a rotation of the phase) and the others in a superconducting one (these phases do not rotate). Figure 3 illustrates some of the many different breather states that were observed in Josephson ladders. There, crosses have been used to denote resistive (rotating) junctions and shorts for superconducting ones. Some of them are up-down symmetric, others not; some correspond to one-site solutions, others to m-site ones. Figure 4 shows one of the current-voltage curves measured in the ladder that allowed detecting the discrete breather solutions.

Figure 3: Zoo of breather excitations

 

Figure 4: The experimental detection


Figure 5: Rotobreather in a 2D Josephson array

After observation in the ladder, the new challenge of the field is the experimental detection of a discrete breather in a two-dimensional array. Recently, we have numerically found the existence of such states, see figure 5 for a simulation, and established the experimental conditions for the excitation and detection of discrete breathers in a two-dimensional array [P1]. Recent experiments, not yet published, performed by Ustinov's group valid this scenario.

Principal publication

  1. J. J. Mazo, Phys. Rev. Lett. 89, 234101 (2002).
  2. J.J. Mazo, T.P. Orlando, Chaos 13, 733 (2003)

Acknowledgements

Financial support by DGES PB98-1592, EU HPRN-CT-1999-00163 and MCyT BFM2002-00113 .
References
  1. For a general introduction and references, see D.K. Campbell et al, Physics Today 57(1), 43, 2004.
  2. L.M. Floría, J.L. Marín, P.J. Martínez, F. Falo and S. Aubry, Europhys. Lett. 36, 539 (1996).
  3. E. Trías, J.J. Mazo and T.P. Orlando. Phys. Rev. Lett. 84, 741 (2000).
  4. P. Binder et al., Phys. Rev. Lett. 84, 745 (2000).
  5. L.M. Floría, Physics World 13(4), 23 (2000).
  6. L.M. Floría, J.L. Marín, J.J. Mazo. Investigación y Ciencia , Junio 2002.
  7. J.J. Mazo in “Energy localization and transfer”. Advances Series in Nonlinear Dynamics, vol 22. Pp.. 193-246, World Scientific (2004).

 

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©2017 Instituto de Ciencia de Materiales de Aragón | Tfno: 976 761 231 - Fax: 976 762 453
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