Engineering Purely Nonlinear Coupling with the Quarton

We propose using a quarton to facilitate purely nonlinear coupling between two linearly decoupled transmon qubits [1]. The quarton's zero φ² potential leads to a strong linear scaling of nonlinear coupling strength with Josephson energy; and the quarton's positive φ⁴ potential can cancel the negative self-Kerr of modes, causing atomic modes to behave more photonic. We show a >1 GHz nonlinear coupling, in the bare mode basis, between two linearized modes with zero self-Kerr; the resulting giant cross-Kerr between photons is promising for applications such as microwave photon detection and bosonic qubit control.

[1] Y. Ye, K. Peng, M. Naghiloo, G. Cunningham, K.P. O'Brien. arXiv: 2010.09959 (2020)