Kerr nonlinearity and parametric amplification with an Al-InAs superconductor-semiconductor Josephson junction

Nearly quantum limited Josephson parametric amplifiers (JPAs) are essential components in superconducting quantum circuits. However, higher order nonlinearities of the Josephson cosine potential are known to cause gain compression, therefore limiting scalability. In an effort to reduce the fourth order, or Kerr nonlinearity, we realize a parametric amplifier with an Al-InAs superconductor-semiconductor hybrid Josephson junction (JJ). We extract the Kerr nonlinearity of the Al-InAs JJ from two different devices and show that it is three orders of magnitude lower compared to an Al-$\text{AlO}_\text{X}$ junction with identical Josephson inductance. We then demonstrate a four-wave-mixing (4WM) parametric amplifier made with an Al-InAs junction that achieves more than 20 dB of gain and -119 dBm of compression power, that outperforms single resonant JPAs based on Al junctions.