Macroscopic quantum tunneling in globally coupled series arrays of Josephson junctions

We present a quantitative analysis of an escape rate for switching from the superconducting state to a resistive one in series arrays of globally coupled Josephson junctions. A global coupling is provided by an external shunting impedance. Such an impedance can strongly suppress both the crossover temperature from the thermal fluctuation to quantum regimes, and the macroscopic quantum tunneling (MQT) in short Josephson junction series arrays. However, in large series arrays we obtain an enhancement of the crossover temperature, and a giant increase of the MQT escape rate. The effect is explained by excitation of a spatial-temporal charge instanton distributed over a whole structure. The model gives a possible explanation of recently published experimental results on an enhancement of the MQT in single crystals of high-$T_c$ superconductors.

Figure 1

(Color online) Schematic of a dc biased layered high-$T_c$ superconductor and a series array of Josephson junctions. A strongly localized instanton (dashed line) and a charge instanton with long tails (solid line) are shown.

Figure 2

(Color online) Typical dependencies of the crossover temperature $T^{*}\left(N\right)$ on a number of junctions $N$. Both cases of inductive (upper curve) and capacitative (lower curve) impedance for particular sets of parameters are shown.

Figure 3

(Color online) The dependence of the MQT escape rate ${\Gamma }_{\mathit{MQT}}$ on the dc bias current $I$ for various values of $N=1,50,100$. Both cases of capacitative (a) and inductive (b) impedance for particular sets of parameters are shown.