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Topological phase transitions and chiral inelastic transport induced by the squeezing of light

We show how the squeezing of light can lead to the formation of topological states. Such states are characterized by non-trivial Chern numbers, and exhibit protected edge modes which give rise to chiral elastic and inelastic photon transport. These topological bosonic states are not equivalent to their fermionic (topological superconductor) counterparts and cannot be mapped by a local transformation onto topological states found in particle-conserving models. They thus represent a new type of topological system. We study this physics in detail in the case of a Kagome lattice model, and discuss possible realizations using nonlinear photonic crystals or superconducting circuits.