The present report deals with the condition under which an ensemble of atoms goes over into a regime of collective two-photon nutation, and with the behavior of Rabi frequency as function of external light. To simplify this problem, we consider a system of Λ-type atoms that enters into two-photon resonance with an external squeezed electromagnetic field relative to the forbidden transition ∣1> ∣2> , where ∣1> and ∣2> are ground and first exited states [1,2] The situation is examining, when the values of quantum fluctuations of electromagnetic field intensity have the same value as the mean value of electromagnetic field intensity. This is one of main difference between the our paper and [2]. The proposed mathematical model permits to take into account all the two-photon diagrams. These diagrams describe not only resonance two-photon transitions but two-photon scattering processes between ∣1> and ∣2> levels too. Using mathematical method which is proposed in [1,2] it is obtained the master equation for the atom subsystem. Two stationary solutions for the case when Rabi frequency is larger than the inverse value of the collective two-photon decay time and the case when external light is coherent are examined. It is showing that the absorption rate of an phase squeezed field is larger than the absorption rate of an amplitude squeezed light. We also obtained the behavior of inversion between the levels ∣1> and ∣2>, when the collective of atoms enters into two-photon resonance with external field.
Multiphoton interaction of single-mode squeezed-state light and a two-level atom is considered based on the K-photon Jaynes–Cummings model. Time evolution of quantum fluctuation and photon statistical properties of the initial squeezing light are discussed. It is found that through interaction with a two-level atom, larger squeezing levels cannot be achieved in one-photon or multiphoton processes. For photon antibunching behavior of the light field, it is shown that a smaller initial squeezing level and an appropriately larger coherent part of the initial average photon number of the radiation field favor the generation of this nonclassical behavior, especially in the lower-order interaction processes.
We investigate the dynamical evolution of nonclassical states of light undergoing a two-photon absorption process. We consider two distinct cases of initial states, a squeezed coherent state and an eigenstate of the two-photon annihilation operator (a superposition of macroscopically distinct coherent states). We analyze the fluctuations in the photon-number operator and in the quadrature components of the field. Whereas one-photon linear damping rapidly destroys quantum features such as squeezing, we demonstrate that substantial coherence is retained when such light interacts with a two-photon-absorbing reservoir. This surviving coherence is responsible for the preservation of squeezing in the steady state despite the effect of dissipation. We relate the origin of squeezing of initially unsqueezed light interacting with two-photon absorbers with the squeezing generated by simple superposition states of light.
When neglecting and considering the interaction between atoms,the quadrature squeezing and the photon-number squeezing of Bose-Einstein Condensate of V-type three level atoms interacting with two-mode squeezed light field are studied.The results show that the quadrature squeezing dependent on squeezing parameter and the photon-number squeezing is closely correlated to squeezing parameter and light field intensity.It is found that the two kinds of squeezing can be obtained at some conditions.and the interaction between atoms in BEC changes the period of fluctuation of light field and the amplitude of fluctuation of quadrature component.However,such atom-atom interaction does not affect the amplitude of fluctuation of photon-number squeezing.
The dependence of the multiphoton absorption probability for an atomic system on the statistical properties of the incident light is investigated. It is shown, by means of
nth-order time-dependent perturbation theory, that the multiphoton absorption probability depends on the
(n,n)th normally ordered correlation functions of the electromagnetic field. For stationary fields, the transition probability per unit time is constant and is directly related to the reduced cross-spectral correlation function of the electromagnetic field. This expression for the transition probability is then analyzed under various conditions of coherence. Explicit calculations are carried out for thermal light and for laser light, and the transition rates are compared when each has a Lorentzian spectrum. In particular, when the width of the final atomic level is much larger than the bandwidth of the field, the transition rate for thermal light is
n! times higher than with laser light of the same mean intensity. The other extreme case, i.e., when the width of the final atomic level is much smaller than the bandwidth of the field, is also considered in detail. An equation for the density operator of the field is derived; this equation governs the change in the statistical properties of the photon system in
n-photon absorption processes. On the basis of this equation, the time-dependent properties of the photon system are then studied and some physical consequences of these equations are discussed. Some numerical solutions relating to the time dependence of the factorial moments in two-photon absorption processes are presented.