In this talk, we construct the so-called Fourier-Jacobi cycles on unitary Shimura varieties. The height pairing of these cycles can be regarded as the arithmetic analogue of classical Fourier-Jacobi periods for the pair of unitary groups of equal rank. 

We will propose a conjectural formula relating such height pairing and derivative of certain Rankin-Selberg L-function of symplectic type. We will also explain an approach toward this conjecture using arithmetic relative trace formula.