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

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

2003-05-10

arxiv.org/abs/quant-ph/0305057v2

Shen J Q, Zhu H Y 2003 Ann. Phys.(Leipzig) Vol.12 p.131-145

Physics

Quantum Physics

14 pages, Latex. This is a revised version of the published paper: Shen J Q, Zhu H Y 2003 Ann. Phys.(Leipzig) Vol.12 p.131-145

Scientific paper

10.1002/andp.200310001

By using both the Lewis-Riesenfeld invariant theory and the invariant-related unitary transformation formulation, the present paper obtains the exact solutions to the time-dependent supersymmetric two-level multiphoton Jaynes-Cummings model and the Chiao-Wu model that describes the propagation of a photon inside the optical fiber. On the basis of the fact that the two-level multiphoton Jaynes-Cummings model possesses the supersymmetric structure, an invariant is constructed in terms of the supersymmetric generators by working in the sub-Hilbert-space corresponding to a particular eigenvalue of the conserved supersymmetric generators (i.e., the time-independent invariant). By constructing the effective Hamiltonian that describes the interaction of the photon with the medium of the optical fiber, it is further verified that the particular solution to the Schr\"{o}dinger equation is the eigenfunction of the second-quantized momentum operator of photons field. This, therefore, means that the explicit expression (rather than the hidden form that involves the chronological product) for the time-evolution operator of wave function is obtained by means of the invariant theories.

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