Entanglement and photon statistics of two dipole–dipole coupled superconducting qubits with Kerr-like nonlinearities.

• Solid state systems including superconducting qubits. • Time-dependent effect on the comportments of the quantum quantifiers in superconducting quantum technologies. • Superconducting qubits coupled to mode fields in a circuit quantum electrodynamics setup. • Detuning and dipole-dipole effect on the dynamical behavior of the quantum quantifiers. The engineering of Kerr and time-dependent coupling interactions is of great attention for treating quantum information in quantum systems and for investigating the collective behavior of large numbers of interacting particles in a cavity-qubit network. In this manuscript, we investigate the time evolution of the entanglement and some nonclassical properties of two superconducting qubits interacting with a single-mode field in the presence of a Kerr-like medium and dipole–dipole interaction without and with time-dependent coupling effect. We show that a slight alteration in the interaction, detuning, and Kerr parameters might cause a change in the entanglement of subsystem states during the evolution. By taking into account the influence of the different physical parameters, we show the statistical distributions produced in the photons of the single mode field through the calculation of the Mandel's parameter. Finally, we find that the time-dependent Mandel's parameter not only provide the statistical properties of the field, but also include the information of quantum entanglement for the subsystem states. [ABSTRACT FROM AUTHOR]