Exploring tunneling in a tunable asymmetric double-well effective potential emerging from a driven Kerr parametric oscillator

Dissipative tunneling is ubiquitous in quantum mechanics, influencing processes like chemical reactions. One would expect tunneling to be modified in a double-well potential when there is a resonance between levels predominantly localized in one well or the other. In order to explore this effect, a fully controllable asymmetric double-well system was realized by a continuously driven Kerr parametric oscillator operating in the quantum regime. We investigate tunneling resonances by measuring the variations of well-switching rates with various parameters. Our experiments reveal two novel effects: (i) weak asymmetry can significantly reduce well-switching rates, even when the potential well is made shallower, and (ii) the widths of the tunneling resonances alternate between narrow and broad lines based on well depth and asymmetry. Both effects are predicted to also manifest themselves in chemical double wells in the quantum regime, as shown by numerical simulations. The reduction in well-switching rates due to weak asymmetry can extend the lifetimes of qubits encoded in Kerr parametric oscillators without the need for additional hardware. Additionally, our work paves the way for the analog simulation of proton tunneling in chemistry using Kerr parametric oscillators.