A non-reciprocal dispersive interaction in circuit QED: Part I, formulation and setup

Non-reciprocity is a valuable property for building interesting and complex quantum systems. Previous experimental studies have primarily focused on non-reciprocal excitation transfer between linear modes, which can be fully captured by a non-Hermitian effective Hamiltonian matrix. To go beyond these semi-classical descriptions, we implement a dispersive type of non-reciprocal interaction between a transmon qubit and a superconducting cavity. We achieve this by utilizing a custom designed ferrite circulator to mediate B-field tunable non-reciprocity between two cavities[1], with one of them housing the qubit. We were able to describe the input-output spectrum of this device with a 2 mode non-Hermitian linear model coupled to a qubit. By adjusting the coupling parameters we were able to put the system in a regime where the intermediary mode could be eliminated and the model could be adiabatically reduced to a master equation involving only the cavity and the qubit, utilizing a non-linear jump operator. This model can then be used to predict dispersive shifts and dephasing, showing notable asymmetry across magnetic fields due to the non-reciprocity.

[1] Y. Wang, S. van Geldern, T. Connolly, Y. Wang, A. Shilcusky, A. McDonald, A. A. Clerk and C. Wang, arXiv:2106.11283(2021).