Quantum dynamics of a BEC interacting with a single-mode quantized field in the presence of interatom collisions

• N two-level atoms in a BEC interacting with a laser field in the presence of interatom interactions is considered.
• The atomic population inversion, degree of entanglement between the “atoms in BEC” and the “field” and the Mandel parameter are investigated.
• Collapse-revival phenomenon can be apparently observed in the atomic inversion and Mandel parameter.
• The considered parameters are sensitive to the number of atoms in BEC, intensity of field, interatom coupling and detuning.

In this paper, we consider a model in which N two-level atoms in a Bose–Einstein condensate (BEC) interact with a single-mode quantized laser field. Our goal is to investigate the quantum dynamics of atoms in the BEC in the presence of interatom interactions. To achieve the purpose, at first, using the collective angular momentum operators, we try to reduce the dynamical Hamiltonian of the system to a well-known Jaynes–Cummings like model (JCM). We also use the Dicke model to construct the state of atomic subsystem, by which the analytical solution of the system may be obtained. Then, we analyze the atomic population inversion, the degree of entanglement between the “atoms in BEC” and the “field” as well as the Mandel parameter. Numerical results show that, the atomic population inversion, atom-field entanglement and quantum statistics of photons are very sensitive to the evolved parameters in the model (and so can be well-adjusted), such as the number of atoms in BEC, the intensity of initial field, the interatom coupling constant and detuning. To investigate the entanglement properties, we pay attention to the entropy and linear entropy. It is shown that, oscillations in the two entropy criteria may be seen, with some maxima of entanglement at some moments of time. Finally, looking for the quantum statistics, we evaluate the Mandel parameter, by which we demonstrate the sub-Poissonian statistics and so the nonclassical characteristics of the field state of system. Collapse-revival phenomenon, which is a distinguishable nonclassical characteristic of the system, can be apparently observed in the atomic population inversion and the Mandel parameter.