Quantum-limited amplification and entanglement in coupled nonlinear resonators.

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 the nondegenerate operation and the saturation at input photon numbers as high as 2000 per μs 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 simulations.