Understanding the behavior of light in non-equilibrium scenarios underpins much of quantum optics and optical physics. While lasers provide a severe example of a non-equilibrium problem, recent interests in the near-equilibrium physics of photon {\textquoteleft}gases\&$\#$39;, such as in Bose condensation of light or in attempts to make photonic quantum simulators, suggest one reexamine some near-equilibrium cases. Here we consider how a sinusoidal parametric coupling between two semi-infinite photonic transmission lines leads to the creation and flow of photons between the two lines. Our approach provides a photonic analogue to the Landauer transport formula, and using non-equilbrium Green\&$\#$39;s functions, we can extend it to the case of an interacting region between two photonic {\textquoteleft}leads\&$\#$39; where the sinusoid frequency plays the role of a voltage bias. Crucially, we identify both the mathematical framework and the physical regime in which photonic transport is directly analogous to electronic transport, and regimes in which other new behavior such as two-mode squeezing can emerge.

}, doi = {10.1103/PhysRevB.94.155437}, url = {https://doi.org/10.1103/PhysRevB.94.155437}, author = {Chiao-Hsuan Wang and Jacob M. Taylor} }