Landauer formulation of photon transport in driven systems

Understanding the behavior of light in nonequilibrium scenarios underpins much of quantum optics and optical physics. While lasers provide a severe example of a nonequilibrium problem, recent interests in the near-equilibrium physics of so-called photon gases, such as in Bose condensation of light or in attempts to make photonic quantum simulators, suggest one re-examine 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 analog to the Landauer transport formula, and using nonequilbrium Green's functions, we can extend it to the case of an interacting region between two photonic leads 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 behavior such as two-mode squeezing can emerge.

Figure 1

(a) Our conceptually simplest system of two semi-infinite leads, with a time-dependent coupling between them and a photodetector connecting to the right lead. (b) A potential physical implementation with a Josephson parametric coupler, driven with a flux bias line, between two transmission lines.

Figure 2

(a) The generic mesoscopic scenario, with two semi-infinite leads coupled parametrically to an intermediate mesoscopic region $C$, provides a photonic equivalent to a voltage bias and a (nonlinear) impedance provided by the region $C$. (b) A schematic diagram of the parametric coupling mechanism, in which a low-energy photonic mode on the left side is up-converted via the pump photon with energy $\hslash {\omega }_p$ to a higher energy mode on the right. The case where $L$ and $R$ leads have a high (left) and low (right) frequency cutoff is shown to prevent anomalous squeezing terms.