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arXiv · 0906.4005

Dynamics of Entanglement and `Attractor' states in The Tavis-Cummings Model

C. E. A. Jarvis·D. A. Rodrigues·B. L. Györffy·T. P. Spiller·A. J. Short·J. F. Annett
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Abstract

We study the time evolution of $N_q$ two-level atoms (or qubits) interacting with a single mode of the quantised 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 $\sfrac{t_r}{4}$, halfway between that start of the collapse and the first mini revival peak, where $t_r$ 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 the features are at the center of our attention. Extending to more qubits, we find that attractors are a generic feature of the multi qubit Jaynes Cummings model (JCM) and we therefore generalise the discovery by Gea-Banacloche for the one qubit case. We give the `basin of attraction' for $N_q$ qubits and discuss the implications of the `attractor' state in terms of the dynamics of $N_q$-body entanglement. We observe both collapse and revival and sudden birth/death of entanglement depending on the initial conditions.

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C. E. A. Jarvis, D. A. Rodrigues, B. L. Györffy, T. P. Spiller, A. J. Short, J. F. Annett. 2009-06-22. Dynamics of Entanglement and `Attractor' states in The Tavis-Cummings Model. https://doi.org/10.1088/1367-2630%2F11%2F10%2F103047

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