We examine the dynamics of the Jaynes–Cummings model when it is restricted to the following initial conditions: atom in an arbitrary (pure or mixed) state and field in the vacuum state. It is shown that the model exhibits two dynamical symmetries that are characterized by the Lie algebras SU(2) × SU(2) and SU(3). A pair of interacting spins in a magnetic field also possesses the former symmetry, whereas the latter symmetry naturally describes a three-level atom driven by two laser fields; thus close correspondences with these systems are established. A pseudospin treatment of the model is devised and used to carry out a systematic investigation of its dynamics. On the basis of this treatment we (a) obtain the constants of motion of the problem, (b) establish bounds on the atomic and field inversions for arbitrary model conditions, (c) expose a striking symmetry between field and atomic (i.e., dipole) squeezing, and (d) discuss the occurrence of nonclassical correlations between the atom and the cavity field.
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