Amplification of quantum signals by the non-Hermitian skin effect

The non-Hermitian skin effect (NHSE) is a phenomenon whereby certain non-Hermitian lattice Hamiltonians host an extensive number of eigenmodes condensed to the boundary, called skin modes. Although the NHSE has mostly been studied in the classical or single-particle regime, it can also manifest in interacting quantum systems with boson number nonconserving processes. We show that lattices of coupled nonlinear resonators can function as reciprocal quantum amplifiers. A one-dimensional chain exhibiting the NHSE can perform strong photon amplification aided by the skin modes, which scales exponentially with the chain length and outperforms alternative lattice configurations lacking the NHSE. Moreover, two-dimensional lattices can perform directional photon amplification between different lattice corners, due to the two-dimensional NHSE. These quantum amplifiers are based on experimentally feasible lattice configurations with uniform parametric driving schemes.