Possible scheme for on-chip element for squeezed microwave generation

We propose a scheme to generate squeezed microwave radiation into a transmission line using a simple on-chip element. Instead of the more commonly used quadratic i(a(dagger 2)-a(2)) Hamiltonian, the element is based on parametric resonance drive, (a(dagger)+a)(2) cos 2 omega(0)t, which can approximately be realized using an ac magnetic flux on a superconducting quantum interference device (SQUID) loop. The dissipation arising from the coupling to the transmission line is also included in the dynamics, and it is, in fact, essential for the formation of the (periodically) steady squeezed SQUID state. The spectral properties of the radiation are calculated and they differ somewhat from the conventional squeezing. With a proper choice of parameters, the quadrature noise can be suppressed below its ground-state value, a direct evidence of reduction of the quantum fluctuations. We also present a measurement setup for direct verification of the phenomenon. The squeezing element provides a tool for quantum noise engineering and its simplicity allows a flexible integration into more complex quantum devices.