Engineering a multi-level bath for transmons with three-wave mixing and parametric drives

A quantum system with a tunable bath temperature provides an additional degree of freedom for quantum simulators. Such a system can be realized by parametrically modulating the coupling between the system and the bath. Here, by coupling a transmon qubit to a lossy Superconducting Nonlinear Asymmetric Inductive eLement (SNAIL) mode, we experimentally create a tunable bath for the qubit mode. The effective temperature of this bath can be precisely controlled, ranging from negative to positive values. We show that the qubit can be thermalized to equilibrium with different population distributions under different parametric pumping conditions. We further extend our method to the third level of the transmon, demonstrating its potential utility beyond the two-level case. Our results provide a useful tool that can be readily integrated with quantum simulators that would benefit from a nontrivial photon population distribution.