Ground-state cooling, Fock-state stabilization and photon-resolved thermalization dynamics in a hot 170 MHz resonator.

In order to observe coherent quantum effects, systems are usually cooled to their thermal ground states. Despite millikelvin temperatures being a dominant energy scale in a 170 MHz circuit QED mode, we show that quantum control of the mode can still be realized. This is achieved by coupling it to a cold mode at 5.9 GHz through the non-linearity of a Josephson junction shared between both modes. The resulting coupling leads to photon number splitting that allows reading out the state of the low frequency mode. Via four-wave mixing, we can sideband cool the low-frequency mode to its ground state, as well as stabilize one- and two-photon Fock states. In time-domain, we can then observe the photon-resolved thermalization dynamics of these stabilized states. Our platform could be used to resonantly interface quantum circuits with MHz frequency systems (e.g. mechanical elements) or enable further exploration of thermodynamical processes at the quantum scale.