  We demonstrate a coupled cavity realization of a Bose Hubbard dimer to
achieve quantum limited amplification and to generate frequency entangled
microwave fields with squeezing parameters well below -12 dB. In contrast to
previous implementations of parametric amplifiers our dimer can be operated
both as a degenerate and as a nondegenerate amplifier. The large measured
gain-bandwidth product of more than 250 MHz for nondegenerate operation and the
saturation at input photon numbers as high as 2000 per us are both expected to
be improvable even further, while maintaining wide frequency tunability of
about 2 GHz. Featuring flexible control over all relevant system parameters,
the presented Bose-Hubbard dimer based on lumped element circuits has
significant potential as an elementary cell in nonlinear cavity arrays for
quantum simulation.
