Predicted third-order sweet spots for phi-junction Josephson parametric amplifiers

Abstract

Hybrid superconductor-semiconductor nanowire Josephson junctions exhibit skewed and phi-shifted current phase relations when an in-plane magnetic field is applied along the weak link's spin-orbit effective field direction. These junctions can have an asymmetric Josephson potential with odd-order nonlinearities. A dominant third-order nonlinearity can be achieved by tuning the magnetic field to a sweet spot. Sweet spots persist when higher order Josephson harmonics are included. This makes it possible to have a single Josephson junction dipole element with three-wave mixing capability, which is favorable for pump-efficient amplification. Electrostatic gate tunability of the semiconductor weak link can make it operable within an extended range of working frequencies, and the inclusion of micromagnets can facilitate near-zero magnetic field operation.

Figures (13)

• Figure 1: (a) Amplitudes $I_n$ from numerical simulations as a function of field $B$. (b) Numerical data (symbols) and fits (solid lines) for $I_n = \alpha_{n} (1- \beta_{n} B^2)$, where $\alpha_{n}$ and $\beta_{n}$ are fitting parameters. (c) Skewed $\phi_0$-junction potential as function of field $B$ and phase $\phi$ for values $a = 8.83$ and $c=9.60$ at an optimal point. (d) Line-cuts of potential $U(\phi)$ from panel (c).
• Figure 2: Non-linear coefficients $c_n$ as function of $B$ for a set of optimized values $a = 8.83$ and $c=9.60$. Sweet spots with$|c_4| \propto 0$ and a significant $|c_3|$ are at $B \approx \pm 0.26,\pm 0.39$ shown by red and black dashed lines.
• Figure 3: (a) Nonlinear coefficient $c_3$ as function of $c$ and $B$ at $a=1$. Black dashed lines at $c_4=0$, black dotted lines at $c_3=0$. (b) Nonlinear coefficient $c_4$ as a function of $c$ and $B$ at $a=1$. Black dashed lines at $c_4=0$.
• Figure 4: (a) Schematic of a parametric amplifier circuit with nanowire (NW) Josephson junction coupled to a resonator. A micromagnet (MM) is placed close to the junction and NW electron density is tuned with a gate voltage $V_g$. (b) Detailed schematic of the NW and MM with thin superconducting shell (S), a break in the shell defines the JJ. An external magnetic field $B_\text{ext}$ can be used in conjunction with the micromagnet to fine-tune the effective field near the sweet spot.
• Figure 5: Nonlinear terms $g_3$ and $g_4$ as a function of field $B$. Black and red dashed lines show sweet points where $|g_3|>0$ and $g_4=0$. Here $\omega_0= 20$ GHz, $L_J \approx 3.2$ nH and $L \approx 0.4$ nH.