  We theoretically investigate a near-quantum-limited parametric amplifier
based on the nonlinear dynamics of quasiparticles flowing through a
superconducting-insulator-superconducting junction. Photon-assisted tunneling,
resulting from the combination of dc- and ac-voltage bias, gives rise to a
strong parametric interaction for the electromagnetic modes reflected by the
junction coupled to a transmission line. We show phase-sensitive and
phase-preserving amplification, together with single- and two-mode squeezing.
For an aluminum junction pumped at twice the center frequency,
$\omega_0/2\pi=6$~GHz, we predict narrow-band phase-sensitive amplification of
microwaves signals to more than 20 dB, and broadband phase-preserving
amplification of 20 dB over a 1.2 GHz 3-dB bandwidth. We also predict single-
and two-mode squeezing reaching more than -12 dB over 5.3 GHz 3-dB bandwidth.
Moreover, with a simple impedance matching circuit, we demonstrate 3 dB
bandwidth reaching 4.3 GHz for 20 dB of gain. A key feature of the device is
that its performance can be controlled in-situ with the applied dc- and
ac-voltage biases.
