Experimental Implementation of Higher Order Nonlinear Processes by Cascading Lower Order Nonlinear Processes*

Nonlinear processes of order greater than four are gaining importance in quantum electrodynamics. In the case of superconducting circuits, the natural way to get higher order nonlinearities is through the higher order terms in the cosine potential of the Josephson junction. However, the magnitude of such nonlinearities reduces as we go to higher terms in the cosine expansion. Here, we explore another route to obtain higher order nonlinearities via cascading lower order nonlinear processes using a Raman transition. Specifically, we present experimental data demonstrating the cascading of a pair of two-photon conversion processes into a four-photon conversion process. Such a scheme will be useful in engineering four-photon driven-dissipative operations.