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Journal of Physics A Mathematical and Theoretical

Exactly solving the general non-degenerate multimode multiphoton Jaynes–Cummings model with field nonlinearity

Heng-Mei Li, Hong-Yi Fan

Published Sep 7, 2009• 3 citations
Publisher

Abstract

For the general non-degenerate multimode multiphoton Jaynes–Cummings (JC) model, including any forms of intensity-dependent coupling, field-dependent detuning and field nonlinearity, we obtain its energy eigenvalues and eigenstates via the supersymmetric unitary transformation (SUT) method. In addition, its pseudo-invariant eigen-operator (PIEO) is also found, which directly leads to the energy-level gap.

DOI
10.1088/1751-8113/42/38/385304

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For the general non-degenerate multimode multiphoton Jaynes–Cummings (JC) model, including any forms of intensity-dependent coupling, field-dependent detuning and field nonlinearity, we obtain its energy eigenvalues and eigenstates via the supersymmetric unitary transformation (SUT) method. In addition, its pseudo-invariant eigen-operator (PIEO) is also found, which directly leads to the energy-level gap.
The unitary transformation method is utilized for the closed form solution of the nonlinear generalization of the Jaynes–Cummings (JC) model, which includes arbitrary multiphoton and intensity-dependent interactions between radiation and matter. Specifically, the unitary transformation leading to the diagonalization of the relevant Hamiltonian is established and energy levels and eigenstates are derived. It is also shown that the results for the JC model can be extended to the anti-Jaynes–Cummings (AJC) model through the map between the two models.