Collapse, Revival and Decoherence of Entanglement in Two Qubits Systems

We extend study of the Jaynes-Cummings model involving a pair of identical two-level atoms (or qubits) interacting with a single mode quantised field. We investigate the effects of replacing the radiation field mode with a ‘big spin’, comprising a collection of N qubits, or spin-1/2 particles. We demonstrate the similarities of this set-up to the qubits-field model in terms of the qubits state probability, occurrence of attractor states, generation of Schr¨odinger cat state, and in particular the collapse and revival of the entanglement between the two qubits in the qubit subsystem. We extend our analysis by taking into account a decoherence effect due to qubit imperfections. We study two cases of ‘error’ in the system for both the field mode and ‘big spin’ cases. In the first part, we consider the case of systems with non-resonance frequencies, and secondly we let the systems evolve with a difference in the dipole interaction strengths of the two qubits. We average over the errors in both of these parameters with distributions of varying width. We demonstrate the effects of such error modeling in both the field mode and the ‘big spin’ scenarios. We discover that increasing the width
of the ‘error’ distribution increases suppression of the coherent dynamics of the coupled system, including the collapse and revival of the entanglement between the qubits. We also find out that the decoherence effects are more significant in the system with difference in the coupling strength as opposed to the nonresonance case that has higher robustness against errors. At the end of the study, we investigate the qubit-big spin system with a modest value of N to identify the smallest size of the big spin that exhibits the important events in such interacting
model.