Array of Josephson junctions

J. Niemeyer, J.H. Hinken, and R.L. Kautz, Microwave-Induced Constant-Voltage Steps at One Volt from a Series Array of Josephson Junctions, Appl. Phys. Lett. 45, 478 (1984). 

POSSIBLE IMPLEMENTATION OF TOPOLOGICALLY PROTECTED QUBITS BY A NOVEL CLASS OF JOSEPHSON JUNCTION ARRAYS... 

Figure 6. Left pane Location of the discrete degrees of freedom responsible for the dynamics of the Josephson junction array shown in Fig. 5. The spin degrees of freedom describing the state of the elementary rhombi are located on the bonds of the triangular lattice (shown in thick lines) while the constraints are defined on the sites of this lattice. The dashed line indicates the boundary condition imposed by a physical circuitry shown in Fig. 5 a. Contours 7 and 7 are used in the construction of topological order parameter and excitations. Right pane The lattice with K = 3 openings, the ground state of Josephson junction array on this lattice is 2fc = 8 fold degenerate.

Although quantum mechanics is required to explain the origin of the Josephson effect, we can nevertheless describe the dynamics of Josephson junctions in classical terms. Josephson junctions have been particularly useful for experimental studies of nonlinear dynamics, because the equation governing a single junction is the same as that for a pendulum In this section we will study the dynamics of a single junction in the overdamped limit. In later sections we will discuss underdamped junctions, as well as arrays of enormous numbers of junctions coupled together. 

N junctions, resistive load) Generalize Exercise 4.6.4 as follows. Instead of the two Josephson junctions in Figure 1, consider an array of N junctions in series. As before, assume the array is in parallel with a resistive load R, and that the junctions are identical, overdamped, and driven by a constant bias current 7. Show that the governing equations can be written in dimensionless form as... 

Introduced by Douqot and colleagues [113] in the context of Josephson junction arrays, this model (for t, n/2) admits a two-fold degenerate ground subspace that... 

Implementation of protected qubits by Josephson junction arrays... 

Figure 1 shows an array of two identical overdamped Josephson junctions. 

Figure 11. Array of pseudooortices along the barrier of a Josephson junction...

Dougot, B., Feigel man, M.V., Ioffe, L.B., and loselevich, A.S., Protected qubits and Chem-Simons theories in Josephson junction arrays, Phys. Rev. B, 71, 024505, 2005. Kitaev, A. Yu., Anyons in an exactly solved model and beyond. Annals of Physics, 321, 2, 2006. 

To conclude this section, systems of diffusively coupled nonlinear oscillators act as conceptual models that can explain the phenomenon of ERD. In general, the model discussed here not only applies to explaining ERD in the brain but can also explain similar occurrences of ERD in other systems such as Josephson junction arrays, Bose-Einstein condensates, system of coupled spin torque nano-oscillators, and the like. 

---