%0 Journal Article %J Physical Review B %D 2015 %T A chemical potential for light %A M. Hafezi %A P. Adhikari %A J. M. Taylor %X 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. %B Physical Review B %V 92 %P 174305 %8 2014/05/22 %G eng %U http://arxiv.org/abs/1405.5821v2 %N 17 %R 10.1103/PhysRevB.92.174305