TY - JOUR T1 - A chemical potential for light JF - Physical Review B Y1 - 2015 A1 - M. Hafezi A1 - P. Adhikari A1 - J. M. Taylor AB - Photons are not conserved in interactions with other matter. Consequently, when understanding the equation of state and thermodynamics of photons, while we have a concept of temperature for energy conservation, there is no equivalent chemical potential for particle number conservation. However, the notion of a chemical potential is crucial in understanding a wide variety of single- and many-body effects, from transport in conductors and semi-conductors to phase transitions in electronic and atomic systems. Here we show how a direct modification of the system-bath coupling via parametric oscillation creates an effective chemical potential for photons even in the thermodynamic limit. Specific implementations, using circuit-QED or optomechanics, are feasible using current technologies, and we show a detailed example demonstrating the emergence of Mott Insulator-superfluid transition in a lattice of nonlinear oscillators. Our approach paves the way for quantum simulation, quantum sources and even electron-like circuits with light. VL - 92 U4 - 174305 UR - http://arxiv.org/abs/1405.5821v2 CP - 17 U5 - 10.1103/PhysRevB.92.174305 ER -