Quantum Terahertz Electrodynamics and Macroscopic Quantum Tunneling in Layered Superconductors

We derive a quantum field theory of Josephson plasma waves (JPWs) in layered superconductors, which describes two types of interacting JPW bosonic quanta (one heavy and one lighter). We propose a mechanism of enhancement of macroscopic quantum tunneling (MQT) in stacks of intrinsic Josephson junctions. Because of the long-range interaction between junctions in layered superconductors, the calculated MQT escape rate $\Gamma$ has a nonlinear dependence on the number of junctions in the stack. We show that the crossover temperature between quantum and thermal escape increases when increasing the number of junctions. This allows us to quantitatively describe striking recent experiments in ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$ stacks.

Figure 1

(a) The MQT escape rate $\Gamma$ versus dimensionless external current $j$. Red and blue points are the experimental data, from Ref. 5, for two different samples. Red and blue dashed lines are the curves ${\Gamma }_0(j)$ for these samples taken from 5. Red and blue solid lines are the functions $\Gamma (j)$ calculated from our Eq. (7), while the green dashed-dotted line was obtained numerically from the nontruncated potential (5), using data from Table 1 of [5], for their samples US1 and US4. We use $s=15\AA$, $\gamma =300$ for blue and $\gamma =150$ for red solid curves. The inset of (a) shows the dependence of the escape rate $\Gamma$ versus the number of contacts $N$ in the stack of Josephson junctions (JJs), using parameters for sample US4 of 5 at $j=0.97$ (red solid line). The blue dashed line shows $N{\Gamma }_0$. (b) Our analytically obtained ratio ${\Gamma }_T/\Gamma$ of thermal to quantum escape rates for the single-junction sample SJ1 (blue dashed) and the stack US4 (blue solid). Top inset in (b) shows the geometry studied, with a nucleating fluxon (red shadow). Bottom inset of (b) schematically shows a trial function (solid green line) and its periodic extension (red dashed line).