Exact solutions to the time-dependent supersymmetric muliphoton Jaynes-Cummings model and the Chiao-Wu model

摘要

By using both the Lewis-Riesenfeld invariant theory and the invariant-relatedunitary transformation formulation, the present paper obtains the exactsolutions to the time-dependent supersymmetric two-level multiphotonJaynes-Cummings model and the Chiao-Wu model that describes the propagation ofa photon inside the optical fiber. On the basis of the fact that the two-levelmultiphoton Jaynes-Cummings model possesses the supersymmetric structure, aninvariant is constructed in terms of the supersymmetric generators by workingin the sub-Hilbert-space corresponding to a particular eigenvalue of theconserved supersymmetric generators (i.e., the time-independent invariant). Byconstructing the effective Hamiltonian that describes the interaction of thephoton with the medium of the optical fiber, it is further verified that theparticular solution to the Schr\"{o}dinger equation is the eigenfunction of thesecond-quantized momentum operator of photons field. This, therefore, meansthat the explicit expression (rather than the hidden form that involves thechronological product) for the time-evolution operator of wave function isobtained by means of the invariant theories.