We find the supersymmetric structure involved in the Hamiltonian of an atom-cavity system when the atomic centre-of-mass motion is taken into account. By selecting suitable supersymmetric generators and using supersymmetric transformation the Hamiltonian is diagonalized and energy eigenvectors are obtained.
In the framework of algebraic dynamics, we investigate an atom-cavity system with atomic centre-of-mass motion included. Using nonlinear transformations, the Hamiltonian is linearized in terms of Lie algebraic generators so that the algebraic dynamical structure of the system appears quite clear and its solution is easy to handle by an algebraic dynamical method. In more detail, for the three-level system of Ξ configuration, we show that the momentum recoil of the atom can be eliminated under certain conditions.