Reservoir engineering for nonreciprocal photon coupling in three-dimensional helical waveguides

A three-dimensional (3D) photonic waveguide array is proposed to simulate the concept of reservoir-engineering-induced nonreciprocal transmission. The reservoir is offered by coupling two optical modes simultaneously to an additional mode with loss, yielding a jump operator, which is a coherent superposition of annihilation operators of these two modes. The waveguides are helically curved, leading to a synthetic gauge field for the propagating photons and consequently an adjustable phase factor for the jump operator. The unidirectional coupling is derived analytically and verified numerically, and an intuitive interpretation is provided. Furthermore, the model is extended to a periodic lattice, where asymmetric hopping arises and unidirectional hopping appears for certain Bloch wave vectors. Our design is based on real-experiment parameters, which can be readily implemented by femtosecond laser direct writing of 3D waveguides in silica.