We study the interaction between the single-mode electromagnetic field and the pair of indistinguishable two-level atoms via the intensity-dependent coupling. This problem is equivalent to the equidistant three-level atom with equal dipole moment matrix transition elements between the adjacent levels. The exact analytical solution for the tom-field state- vector is obtained assuming that at the initial moment the field is in the Holstein-Primakoff SU (1,1) coherent state. The quantum-statistical and squeezing properties of the field are investigated. The obtained results are compared with those for the single two-level atom. It is observed that the exact periodicity of the field squeezing that takes place in the case of the single two-level atom is violated in the case of the pair of cold atoms. In other words, the exact periodicity of the physical quantities can be destroyed only if the radiation field interacts with a system of more than one two-level atom.
Abstract We show that, under certain circumstances, an optical field in a two-mode squeezed vacuum (TMSV) state can propagate through a lossy atomic medium without degradation or evolution. Moreover, the losses give rise to that state when a different state is initially injected into the medium. Such a situation emerges in a Λ-type atomic system, in which both optical transitions are driven by strong laser fields that are two-photon resonant with the respective signal modes. Then the interactions of the two signal modes with the ground-state atomic coherence interfere destructively, thereby ensuring the preservation of the TMSV with a particular squeezing parameter. This mechanism permits unified interpretation of recent experimental results and predicts new phenomena.
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 N-photon interaction of two two-level atoms with a single-mode quantized radiation field is studied. The general expression for the state vector of the atom–field system is presented with the probability amplitudes in analytic form. For the initial condition in which the atoms are both at their upper levels and the field is in a squeezed state, we study the time evolution of the atomic population inversions and that of the statistics of the field. We find that the ratio of the two coupling constants, the initial squeezing of the field, and N have significant effects on the features of the atoms and of the field.
The interaction between a squeezed vacuum and a two-level atom coupled to a cavity mode is studied via its influence on the intracavity photon number, the simplest measurable quantity. When the system is driven by a coherent field a remarkable sensitivity to the relative phase between the driving field and the squeezed vacuum appears. The effect is very sensible to the excess of two-photon correlation between a squeezed vacuum and a maximally correlated classical field. The possibility of an experimental demonstration of the effect is established by means of numerical calculations corresponding to a slight modification of an experiment previously reported in the literature.
We investigate in detail the role of a reservoir concerning the squeezing effect in a driven coupled-oscillator system. In our model, a harmonic oscillator (single cavity mode) is coupled to a two-state oscillator (two-level atom) driven by a classical field. The oscillators are coupled to their respective reservoirs, by which the oscillators are damped. The degree of squeezing in the short-time limit is found to be independent of the damping rate of the harmonic oscillator in a perturbative regime. More remarkably, the harmonic oscillator, which is in a coherent state in the absence of its reservoir, gets squeezed in the steady state when it is coupled to the reservoir. The reservoir assumes two competing roles of assisting and suppressing the squeezing effect induced by the nonlinear interaction of the coupled oscillators. As a result, the squeezing effect is increased to some extent with the damping rate of the harmonic oscillator. In addition, the ``matching condition'' for the optimal squeezing is obtained such that the pumping field intensity should be inversely proportional to the damping rate.