Excitation of coherent correlated states in the Jaynes-Cummings model by external deterministic forces: II

In terms of excitation creation and annihilation operators of the Jaynes-Cummings model, acting in the representation of dressed states, the Hamiltonian is written which describes the character of the spectrum of excitations of two modes, representing a quantum analog of the classical behavior of two interacting one-dimensional anharmonic oscillators, namely, the field and atomic oscillators. The anharmonicity is caused by the nonlinearity of the oscillator interaction and manifests itself in the dependence of the frequencies of both modes on the number of excitations, i.e., on the energy. It is shown that an external deterministic force, acting on the system during a certain time t ₀, transfers it from a vacuum state to a coherent state or from one of the coherent states to another coherent state. The probability of the transition from the vacuum state to the coherent state with a given number of excitations represents the Poissonian distribution for the number of excitations formed in the (atom + field) system by the end of action of the external force. It was found to be proportional to the excitation time t ₀.