Theory of Enhanced Interlayer Tunneling in Optically Driven High-$T_c$ Superconductors

Motivated by recent pump-probe experiments indicating enhanced coherent $c$-axis transport in underdoped YBCO, we study Josephson junctions periodically driven by optical pulses. We propose a mechanism for this observation by demonstrating that a parametrically driven Josephson junction shows an enhanced imaginary part of the low-frequency conductivity when the driving frequency is above the plasma frequency, implying an effectively enhanced Josephson coupling. We generalize this analysis to a bilayer system of Josephson junctions modeling YBCO. Again, the Josephson coupling is enhanced when the pump frequency is blue detuned to either of the two plasma frequencies of the material. We show that the emergent driven state is a genuine, nonequilibrium superconducting state, in which equilibrium relations between the Josephson coupling, current fluctuations, and the critical current no longer hold.

Figure 1

(a) Schematic depiction of YBCO. Superconducting ${\mathrm{CuO}}_2$ layers (grey) form series of bilayer Josephson junctions. THz pulses (wavy lines) excite apical oxigen atoms (circles) that induce oscillations of $j_1$ and $j_2$. (b) Comparison of the calculated imaginary part of the conductivity with experiments in Ref. [2] at 10 K. (The lower plasma frequency is $\sim 33{\mathrm{cm}}^{-1}$.) The optimal driven conditions near the higher plasma frequency are used for the calculations. (Theoretical curves are rescaled so that undriven curves from the experiment and theory coincide.)

Figure 2

The normalized effective Josephson coupling $J_{\mathrm{eff}}/J_0$. We note that a significant increase of the coupling is achieved when the driving frequency is just above the plasma frequency. Dynamically unstable regions are left blank.

Figure 3

(a) The relative change of the Josephson coupling $\delta J/J_0(\%)$ near ${\omega }_{\text{pump}}\simeq {\omega }_{\mathrm{Jp}1}$ at $A_1=0.6$ and $A_2=0.3$. (b) The relative change of the Josephson coupling $\delta J/J_0(\%)$ near ${\omega }_{\text{pump}}\simeq {\omega }_{\mathrm{Jp}2}$ at $A_1=1.0$ and $A_2=0.3$. (c) The temperature dependence of $J_0$ and $J_{\mathrm{eff}}$ [normalized by $J_0(0)$] at fixed driving frequencies, ${\omega }_{\text{pump}}=2.1$ and 26. (d) The current fluctuations at the weak junctions, $\overline{⟨{\sin }^2{\phi }_i{⟩}_{i\in \text{weak}}}$, near ${\omega }_{\text{pump}}\simeq {\omega }_{\mathrm{Jp}2}$. The dashed lines are at ${\omega }_{\mathrm{Jp}2},{\omega }_{\mathrm{Jp}2}\pm {\omega }_{\mathrm{Jp}1}$.

Figure 4

(a) Power spectrum of the weak junction current at $T=0.6$ around ${\omega }_{\mathrm{Jp}1}$; (b) dc current-voltage characteristics.