  We analyze the quantum dynamics of two electromagnetic oscillators coupled in
series to a voltage biased Josephson junction. When the applied voltage leads
to a Josephson frequency across the junction which matches the sum of the two
mode frequencies, tunneling Cooper pairs excite photons in both modes
simultaneously leading to far-from-equilibrium states. These states display
highly non-classical features including strong anti-bunching, violation of
Cauchy-Schwartz inequalities, and number squeezing. The regimes of low and high
photon occupancies allow for analytical results which are supported by a full
numerical treatment. The impact of asymmetries between the two modes is
explored, revealing a pronounced enhancement of number squeezing when the modes
are damped at different rates.
