Searching for pairing energies in phase space

We obtain a representation of pairing energies in phase space, for the Lipkin-Meshkov-Glick and boson Bardeen-Cooper-Schrieffer pairing mean-field-like Hamiltonians. This is done by means of a probability distribution of the quantum state in phase space. In fact, we prove a correspondence between the points at which this probability distribution vanishes and the pairing energies. In principle, the vanishing of this probability distribution is experimentally accessible and additionally gives a method to visualize pairing energies across the model control parameter space. This result opens new ways to experimentally approach quantum pairing systems.