Probing quantum nonlinearity of cavity-QED systems with quantum light

Giant optical circular birefringence (GCB) induced by a single quantum-dot-confined spin in an optical microcavity finds wide applications in quantum and optical technologies, such as quantum gates, quantum transistors, quantum repeaters, quantum routers, etc. If the system is probed with a classical light, such as the laser light where the photons are uncorrelated with each other, then the single-photon GCB is detected. In this work we develop a general approach to investigate the many-body dynamics of n photons bound to one quantum emitter and apply this method to calculate the n-photon GCB probed with quantum light in Fock states. With suppressed atomic saturation, quantum light loads photons into dressed states more efficiently than classical light such that the whole Jaynes-Cummings energy ladder and the quantum nonlinearity related to the multiphoton transitions can be observed. The n-photon GCB lying at the cavity mode resonance allows the spin-cavity quantum gates and quantum transistors to extend from single-photon to n-photon operations and generate entangled photonic Fock states, i.e., the NOON states which are useful for quantum metrology and lithography.