Realizing large, tunable dispersive shifts with parametric couplings – Part I

Parametric couplings are being deployed in a variety of applications, ranging from parametric gates or state preparation to quantum annealing, that require much stronger parametric coupling strengths, unlike their traditional applications such as quantum-limited amplification. The theoretical framework to capture the effect of such strong time-dependent couplings, however, remains rudimentary. In this talk, we will present a method that allows system diagonalization in the presence of such strong parametric interactions. Applying it to a single qubit parametrically coupled to a single bosonic mode, we show that even this simple system can support a rich structure in dispersive shifts that can be rendered large and tunable by choosing suitable parametric coupling drive amplitudes and frequencies. Further our analysis shows how significant corrections beyond the usual Jaynes-Cummings model can be crucial to describe new qualitative effects in dispersive regime, such as an exact cancellation of parametrically-induced shifts for optimal choice of pump frequencies. We will also introduce a circuit-QED realization of such a system based on a transmon coupled to a microwave cavity to investigate parametrically induced dispersive shifts, discussed further in the next talk.