Non-Hermitian matter-wave mixing in Bose-Einstein condensates : Dissipation-induced amplification

We investigate the nonlinear scattering dynamics in interacting atomic Bose-Einstein condensates under non-Hermitian dissipative conditions. We show that, by carefully engineering a momentum-dependent atomic loss profile, one can achieve matter-wave amplification through four-wave mixing in a quasi-one-dimensional nearly-free-space setup - a process that is forbidden in the counterpart Hermitian systems due to energy mismatch. Additionally, we show that similar effects lead to rich nonlinear dynamics in higher dimensions. Finally, we propose a physical realization for selectively tailoring the momentum-dependent atomic dissipation. Our strategy is based on a two-step process: (i) exciting atoms to narrow Rydberg or metastable excited states, and (ii) introducing loss through recoil; all while leaving the bulk condensate intact due to protection by quantum interference.