Engineering bilinear mode coupling in circuit QED: Theory and experiment

Abstract

Photonic states of superconducting microwave cavities controlled by transmon\nancillas provide a platform for encoding and manipulating quantum information.\nA key challenge in scaling up the platform is the requirement to communicate on\ndemand the information between the cavities. It has been recently demonstrated\nthat a tunable bilinear interaction between two cavities can be realized by\ncoupling them to a bichromatically-driven transmon ancilla, which allows\nswapping and interfering the multi-photon states of the cavities [Gao et al.,\nPhys. Rev. X 8, 021073(2018)]. Here, we explore both theoretically and\nexperimentally the regime of relatively strong drives on the ancilla needed to\nachieve fast SWAP gates but which can also lead to undesired non-perturbative\neffects that lower the SWAP fidelity. We develop a theoretical formalism based\non linear response theory that allows one to calculate the rate of\nancilla-induced interaction, decay and frequency shift of the cavities in terms\nof a susceptibility matrix. We treat the drives non-perturbatively using\nFloquet theory, and find that the interference of the two drives can strongly\nalter the system dynamics even in the regime where the rotating wave\napproximation applies. We identify two major sources of infidelity due to\nancilla decoherence. i) Ancilla dissipation and dephasing leads to incoherent\nhopping among Floquet states which occurs even when the ancilla is at zero\ntemperature, resulting in a sudden change of the SWAP rate. ii) The cavities\ninherit finite decay from the relatively lossy ancilla through the inverse\nPurcell effect; the effect can be enhanced when the drive-induced AC Stark\nshift pushes certain ancilla transition frequencies to the vicinity of the\ncavity frequencies. The theoretical predictions agree quantitatively with the\nexperimental results, paving the way for using the theory to design future\nexperiments.\n