Dynamics of an atomic Bose–Einstein condensate interacting with nonlinear quantized field under the influence of Stark effect

In this paper we propose a generalized f-deformed Dicke model for the dynamics of an atomic Bose–Einstein condensate (BEC) in the presence of collisional interactions and Stark effect. The BEC contains N two-level atoms and the nonlinear characteristics of quantized field originates from the f-deformation of the associated raising and lowering operators. After solving the time dependent Schrödinger equation corresponding to the model Hamiltonian, we investigate the dynamics of the system under various physical situations; in particular, two different initial states for the quantized field i.e., coherent and squeezed field. In this regard, at first, we obtain some analytical expressions correspond to the energy transfer and non-classical properties of the constituents of system and then proceed to analyze their dynamics, numerically. Our results show that the dynamical evolution of system can be governed by tuning the parameters describing the considered interactions. In particular, the energy levels can be controlled and shifted by changing the Stark effect. Collapse–revival phenomenon occurs in the patterns of atomic inversion, specially in the case of initial coherent state. However, with initial squeezed field typical revivals accompanied with short time collapses may be observed; moreover, the general behavior of atomic inversion shows irregular oscillatory manner. Short time squeezing takes place and can be exchanged between the field quadratures in the absence or presence of Stark effect. Also, the amount of entanglement depends on the nonlinearities which specify the interactions among the atoms in BEC and photons in the quantized field. Interestingly, the general pattern of Von Neumann entropy as a measure of entanglement is independent of the chosen initial states. However, the amplitude of entropy reduces in the case of squeezed state which means that the system possesses more separable states in this condition. In addition, the time evolution of Bloch sphere confirms irregular behavior of entanglement in the system.