Proposed Parametric Cooling of Bilayer Cuprate Superconductors by Terahertz Excitation

We propose and analyze a scheme for parametrically cooling bilayer cuprates based on the selective driving of a $c$-axis vibrational mode. The scheme exploits the vibration as a transducer making the Josephson plasma frequencies time dependent. We show how modulation at the difference frequency between the intrabilayer and interbilayer plasmon substantially suppresses interbilayer phase fluctuations, responsible for switching $c$-axis transport from a superconducting to a resistive state. Our calculations indicate that this may provide a viable mechanism for stabilizing nonequilibrium superconductivity even above $T_c$, provided a finite pair density survives between the bilayers out of equilibrium.

Figure 1

(a) A schematic of a bilayer cuprate such as YBCO composed of Josephson junctions, each with a phase difference ${\varphi }_j$ and alternating interbilayer (low) ${\varpi }_l$ and intrabilayer (high) ${\varpi }_h$ plasma frequencies. (b) Parametric cooling scheme where the coupling between the low and high frequency normal modes ${\omega }_l$ and ${\omega }_h$ is modulated. Tuning the modulation to ${\omega }_d=\frac{1}{2}({\omega }_h-{\omega }_l)\mathrm{THz}$ cools the low frequency mode by up-converting fluctuations to the high frequency one.

Figure 2

Parametric cooling in a two-junction unit cell with (undriven) normal modes ${\omega }_l=2\pi \times 1\mathrm{THz}$, ${\omega }_h=2\pi \times 10\mathrm{THz}$, ${\gamma }_l=0.19\mathrm{THz}$, ${\gamma }_h=3.63\mathrm{THz}$, $\alpha =1$, ${\eta }_l=0$, and ${\eta }_h=0.1$. (a) Phase and conjugate momentum quadratures of the interbilayer and intrabilayer modes. Before $t=0$ (indicated), $T_{\text{initial}}/T_0=0.1$; then parametric driving is applied, after which fluctuations on both quadratures of the interbilayer (intrabilayer) mode are cooled to $0.6T_{\text{initial}}$ (heated to $1.2T_{\text{initial}}$). Analytic predictions of the steady state (dotted line) and asymptotic cooling rate (dashed line) are also shown. (b) Cooling or heating sidebands of the interbilayer mode as the driving frequency ${\omega }_d$ is varied.

Figure 3

(a) Reduction of ${\phi }_{l,i}$ fluctuations for a 100-junction stack over time, at $T/T_c\approx 0.7$. A selection of 10 modes have been displayed across the interbilayer band as shown in the inset. (b) In the steady-state for relative fluctuations for each mode in the interbilayer band is plotted for a selection of ${\omega }_d$. (c) A contour plot of the $⟨{\sin }^2{\phi }_{l,i}⟩/⟨{\sin }^2{\phi }_{l,i}{⟩}_0$ averaged across the interbilayer band sweeping over the damping ${\gamma }_l$ and capacitive coupling $\alpha$. Here we have taken ${\gamma }_h=0.1\min ({\omega }_{h,i})$, $\mathrm{m}\mathrm{i}\mathrm{n}({\omega }_{h,i})/min({\omega }_{l,i}=10$. For each value of $\alpha$, we drive at a frequency targeting the bottom of the $l$ band.

Figure 4

(a) Q-Q plot of switching current distributions for driving strengths ${\eta }_h=0\to 0.1$, at $T/T_c\approx 0.7$. Thermal curves are relative to this temperature. The dashed line indicates the initial thermal distribution. (b) Numerically computed CDF of switching current at $\alpha =1$ with a sweep time $\mathrm{\Delta }t=1\mathrm{ns}$. Solid lines are the driven stack with different driving strengths as in (a), while the dotted lines correspond to thermal benchmarks.