Flux Pumped Kerr-Free Parametric Amplifier

Abstract

We propose a flux-pumped superconducting parametric amplifier based on symmetrically threaded superconducting quantum interference devices (SQUIDs) that achieves a Kerr-free operating point under suitable drive conditions. Eliminating the Kerr nonlinearity is advantageous for quantum-limited amplification, as it mitigates unwanted distortions in squeezing and prevents degradation of both gain and quantum efficiency in the high-gain strong drive regime. By replacing the central junction in the symmetrically threaded SQUIDs (STS) configuration with a linear inductor, we find that the Kerr-nonlinearity can be eliminated and the effective Hamiltonian reduces to that of a degenerate parametric amplifier (DPA), up to higher-order corrections in the zero-point fluctuations of the superconducting phase operator. We show that the deviations from ideal DPA behavior introduced by these higher-order terms are significantly weaker than those associated with a Kerr nonlinearity. Consequently, the STS design can be driven strongly while maintaining near-quantum-limited performance at the Kerr-free point. Our analysis predicts phase-preserving gain and efficiency approaching the quantum limit, with robust operation demonstrated up to 25 dB of gain.

Figures (10)

• Figure 1: Circuit of a lossless lumped-element flux-pumped Kerr-free STS amplifier coupled to a transmission line propagating the signal input and output fields. The outer branches are composed of junctions ${J}_{1}$ and ${ J}_{2}$ whereas the middle branch consists of an inductor $L$. The double SQUID loop is shunted by a capacitor $C_{\rm S}$ and threaded by an external flux consisting of dc flux bias and ac flux modulation via pump line inductively coupled to the STS. The loop between $J_{1(2)}$ and $L$ is threaded by an external flux $\Phi_{\rm 1(2)e}$.
• Figure 2: (a) Deviation of JPAs from ideal DPA dynamics $(\Xi_{\rm JPA})$ plotted as a function of drive strength $\lambda$. For $K\neq 0$, we consider $|K|/\kappa=10^{-2}$ and $|\lambda|/\kappa\in[0,0.47]$ corresponds to $|\Lambda|/\kappa\in[0,2.36\times10^{-4}]$. (b) Deviation of JPAs plotted for $|K|=10^{-2}\kappa$, and $K=0$ as a function of $\Lambda$. Steady-state Wigner function plot for $|\lambda|=0.45\kappa$ (indicated by stars in (a)) in the (c) Kerr-free case, $K=0$, and (d) for $\Lambda = 0$. For (c), we consider $|\Lambda|/\kappa=2.25\times10^{-4}$, whereas for (d), we consider $|K|/\kappa=10^{-2}$. Note that, the $K=0$ case can only be realized with an STS circuit. We take $\Delta=0$ for all subfigures.
• Figure 3: Squeezing level for DPA, and JPAs plotted as a function of phase-preserving DPA gain. We consider, $\Delta=\gamma=0$, $\kappa/2\pi=300\space{\rm MHz}$, Josephson inductance $L_{J}=80\space{\rm pH}$, and capacitance $C_{\Sigma}=2\space{\rm pF}$.
• Figure 4: (a) Phase-preserving gain plotted against DPA gain and (b) Phase-preserving quantum efficiency plotted at $\omega=0$ against the given design's gain for DPA, Kerr-free STS amplifier, and single-SQUID JPAs with varying Kerr nonlinearities. Inset in (a) shows the phase-preserving gain calculated using Eq. (\ref{['eq:gain analytical']}) against signal detuning $\omega$ for DPA and STS amplifier. We take $\Delta=\gamma=0,\kappa/2\pi=300 \space {\rm MHz}$, and the sweep for the two-photon drive $0\leq\lambda<\kappa/2$. For STS, we consider capacitance $C_\Sigma=4\space {\rm pF}$, Josephson inductance $L_{\rm J}=80\space{\rm pH}$, and linear inductance $L=100\space{\rm pH}$.
• Figure 5: Circuit design of the flux-pumped JPA. The junctions ${\rm J}_{1}$ and ${\rm J}_{2}$ compose the DC SQUID, which is shunted by capacitance $C_{\rm S}$. The loop between ${\rm J}_{1}$ and ${\rm J}_{2}$ is threaded by an external flux $\Phi_{\rm e}$. $\hat{\Phi}_{\rm 1,2,S}$ are the branch flux operators.