Broken symmetry and chirp: A view from quantum optics phase space

A quantum optical system with a broken discrete symmetry has a transient response that depends both on the timescale of the transient and the 'direction' of the transient. We explain how comparing the phase space volumes that the quantum coherences sweep out during these excursions relates to the associated chirp asymmetry, which is the dependence of the response on the direction of the transient. We detail this correspondence in both a physically motivated generalization of the two-level system subject to optical pulses and also in a three level system in electromagnetically induced transparency. Lessons learned from this study appear to be formally applicable to non-equilibrium dynamics in many non-linear systems that have broken discrete symmetries.