Tuning non-reciprocity between two circuit QED modules II - nonlinear interactions

Non-reciprocity is an important property needed in quantum systems to further develop more complex and useful quantum architectures. The current research has primarily focused on non-reciprocal interactions between linear modes, which plays a peripheral role of classical signal routing for quantum devices. Here we aim to introduce non-reciprocity to nonlinear interactions that are central to quantum information processing. Using a pair of ferrite circulator modes as mediators, we render a hallmark interaction in circuit QED, the qubit-cavity dispersive interaction, (a^†aσ_z), non-reciprocal. By varying external magnetic fields we demonstrate tunable non-reciprocity, as measured from the difference in dispersive frequency shifts in the forward (cavity to qubit) and backward (qubit to cavity) directions. We further investigate photon shot-noise dephasing arising from this non-reciprocal dispersive interaction and compare it to theoretical predictions.