Bath-engineering qubit systems with 3-wave mixing

Three-wave parametric couplings have traditionally been used to create parametric gain between two low-Q modes by driving at the sum of their frequencies, and photon conversion by driving at their difference. In this talk we extend this idea to qubits by coupling a low-Q mode containing a SNAIL (Superconducting Nonlinear Asymmetric Inductive eLement) to a high-Q transmon. Driving the SNAIL at the sum of the SNAIL and transmon 0 to 1 photon transition frequencies creates a pair of photons. The SNAIL is designed to promptly lose its photon, and this, together with the transmon anharmonicity, creates a parametrically controlled heating rate from the ground to first excited state. Driving the SNAIL and qubit 0 to 1 transition difference frequency creates cooling via a similar process. Heating and cooling between higher qubit states are also accessible via distinct drive frequencies. By combining these drives we can create quite unusual transmon steady states, with full control over both the transmon temperature and relaxation time scale, which we demonstrate experimentally. We will also discuss plans to use this parametrically driven bath to control more complicated multi-mode systems of qubits and linear modes.