Manipulation of a two-photon state in aχ(2)-modulated nonlinear waveguide array

Abstract

We propose to engineer the quantum state in a high-dimensional Hilbert space by taking advantage of a ${\ensuremath{\chi}}^{(2)}$-modulated nonlinear waveguide array. By varying the pump condition and the waveguide array length, the momentum correlation between the signal and idler photons can be manipulated, exhibiting bunching, antibunching, and the evolution between these two states, which are characterized by the Schmidt number. We find the Schmidt number is dependent on a structure parameter, namely the ratio of the array length and the number of channels pumped. By designing the linear profile waveguide array, the degree of spatial entanglement shows a periodic relationship with the slope of linear profile, during which a high degree of position-bunching state is suggested. The two-photon self-focusing effect is disclosed when the ${\ensuremath{\chi}}^{(2)}$ modulation in the waveguide array contains a parabolic profile, which can be designed for efficient coupling between a waveguide array and fibers. These results shed light on a feasible way to achieve desirable quantum state on a single waveguide chip by a compact engineering of ${\ensuremath{\chi}}^{(2)}$ and also suggest a degree of freedom for quantum walk and other related applications.