Quantum optical equilibrium states classified by Morse theory

The topology of the configuration space of any quantum optics (QO) model admitting a RWA frame constrains the number and types of level sets of observables such as absorption and fidelity at equilibrium. Adiabatic flow in the control parameters of the QO model then cause bifurcations between these level sets, analoguous to phase changes and phase boundaries in infinite dimensional systems. For one example we show that the transition to EIT in a three level RWA system is always a pitchfork bifurcation with critical exponent 1/2, even though there is no underlying mean field theory. We introduce the theory, apply it to EIT and EIA transitions and other 4 level, 3 field systems, indicating the utility of Morse theory as an economical and universal unifying framework for understanding constraints between QO equilíbrium states.