Quantum Cross Nonlinearity for Photon-Number-Resolving Nondestructive Detection

We present an unconventional mechanism for quantum nonlinearity in a system comprising of a V-type quantum emitter (QE) and two Fabry-Perot cavities. The two transitions of the V-type QE are effectively coupled with two independent cavity modes. The system exhibits a strong quantum nonlinear control in the transmission even at the single-photon level, which we refer to as quantum cross nonlinearity. The underlying physics can be understood as quantum competition between the two transitions of the QE sharing a common ground state. By leveraging this quantum cross nonlinearity, we further show photon-number-resolving quantum nondestructive detection. Owing to the widespread nature of this V-type configuration, our approach can be readily extended to diverse cavity quantum electrodynamic systems beyond the realm of optics, encompassing, e.g., microwave photons and acoustic wave phonons. This versatility may facilitate numerous unique applications for quantum information processing.