We study interaction between a pair of indistinguishable two-level atoms and the single-mode cavity field. It is supposed that the pair of two-level atoms is laser cooled and trapped into the ground vibrational state, in which vibrational quantum number
⟨nv⟩=0 . Two Jaynes–Cummings models are investigated. One is the Jaynes–Cummings model with intensity-dependent coupling and the another is the two-photon Jaynes–Cummings model of a pair of indistinguishable two-level atoms. It should be noted that in the present model, at initial moment
t=0 , in intensity-dependent Jaynes–Cummings model the cavity field is prepared in Holstein–Primakoff SU(1,1) CS, while in two-photon Jaynes–Cummings model it is prepared in the squeezed vacuum state. Moreover, at initial moment
t=0 , pair of atoms is supposed to be in the first excited state
∣e1⟩ in both models. By using exact analytical solutions for state-vectors of the coupled atom-field systems amplitude-squared squeezing of the quantized cavity field is examined as a function of the
∣ξ∣ parameter. In this situation, in both models higher-order squeezing has the tendency towards oscillations, but exact periodicity of these oscillations is violated by the analogy with the second-order squeezing.
The k-photon Jaynes-Cummings model is studied with respect to the properties of the radiation mode. In particular, the generation of coherence and squeezing in the one- and two-photon model is examined for the case that the field is initially in the vacuum state and the atom is prepared in a coherent superposition of states. Coherence is found in the one-photon model, and squeezing appears in both the one- and the two-photon model, the maximum noise reduction being 25% and 45%, respectively. In the one-photon model coherent squeezed radiation is generated, whereas the two-photon model yields a squeezed vacuum. For an initial atomic preparation close to the ground state, this squeezed vacuum may be interpreted as the result of two-photon interaction between the quantized cavity field and a classical atomic current.
A complete description of the electric field in the Jaynes-Cummings model is presented using the exact operator solutions for the field variables. Two-time field correlation functions are calculated which display the destruction and subsequent partial revival of field coherence. It is shown that squeezing of the field can be enhanced for small n\ifmmode\bar\else\textasciimacron\fi{} when the atom is initially in a coherent superposition state. Amplitude-squared squeezing of both field quadratures occurs for all values of n\ifmmode\bar\else\textasciimacron\fi{} with these initial conditions. The squeezing is not related to collapse and revival phenomena.