Resonant generation of $p$-wave Cooper pair in non-Hermitian Kitaev chain at exceptional point

We investigate a non-Hermitian extension of Kitaev chain by considering imaginary $p$-wave pairing amplitudes. The exact solution shows that the phase diagram consists two phases with real and complex Bogoliubov-de-gens spectra, associated with $mathcal{PT}$-symmetry breaking, which is separated by a hyperbolic exceptional line. The exceptional points (EPs) correspond to a specific Cooper pair state $( 1+c_{k}^{dagger }c_{-k}^{dagger }) leftvert 0rightrangle $ with movable $k$ when the parameters vary along the exceptional line. The non-Hermiticity around EP supports resonant generation of such a pair state from the vacuum state $% leftvert 0rightrangle $ of fermions via the critical dynamic process. In addition, we propose a scheme to generate a superconducting state through a dynamic method.