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.
We use the recently-established asymptotic solution (AS) for large fields to study squeezing in the Jaynes-Cummings model. Arbitrary initial atomic states (including atomic coherence) are considered. We find that most features of squeezing can be understood from the properties of the asymptotic field states, and from the observation, which we establish numerically, that for large fields the interference between the two branches of the wavefunction does not contribute significantly to the squeezing (not even near the revival times, when the two field states being superposed have very nearly the same phase). We obtain a limit on the time over which the field may show any squeezing and find that it scales as the 3/4 power of the number of photons. We also obtain a bound on the maximum achievable squeezing for a given number of photons, which is an improvement over earlier estimates. Finally, we discuss some of the shortcomings of the AS, and in particular the existence of a small ghost peak in the field Q function for initial conditions where the AS predicts a single peak, which is enough to destroy the squeezing for certain times.