The aim of this work is to show how supersymmetric (SUSY) quantum mechanics can be applied to
the Jaynes–Cummings (JC) Hamiltonian of quantum optics. These SUSY transformations connect
pairs of Jaynes–Cummings Hamiltonians characterized by different detuning parameters as well as
Jaynes–Cummings to anti-Jaynes–Cummings Hamiltonians. Therefore, JC Hamiltonians can be
classified in hierarchies or sequences which are connected through SUSY transformations. As a
byproduct, the symmetries of JC Hamiltonians are found as well as the special case of a sequence of
resonant-like interacting systems having the form of a simple shape invariant JC Hamiltonian
hierarchy.
