Dynamics of entanglement and ‘attractor’ states in the Tavis–Cummings model

Abstract

We study the time evolution of Nq two-level atoms (or qubits) interacting with a single mode of a quantized radiation field. In the case of two qubits, we show that for a set of initial conditions the reduced density matrix of the atomic system approaches that of a pure state at , halfway between that start of the collapse and the first mini-revival peak, where tr is the time of the main revival. The pure state approached is the same for a set of initial conditions and is thus termed an ‘attractor state’. The set itself is termed the ‘basin of attraction’ and we concentrate on its features. Extending to more qubits, we find that attractors are a generic feature of the multiqubit Jaynes–Cummings model (JCM) and we therefore generalize the discovery by Gea–Banacloche for the one-qubit case. We give the ‘basin of attraction’ for Nq qubits and discuss the implications of the ‘attractor’ state in terms of the dynamics of Nq-body entanglement. We observe both the collapse and revival and the sudden birth/death of entanglement depending on the initial conditions.