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

TL;DR

This paper investigates the dynamics of entanglement and the emergence of attractor states in the Tavis-Cummings model, revealing that multi-qubit systems tend to evolve towards specific pure states, with implications for quantum entanglement behavior.

Contribution

It generalizes the concept of attractor states from one to multiple qubits in the Jaynes-Cummings model, providing the basin of attraction and analyzing entanglement dynamics.

Findings

Attractor states occur at specific times during evolution.

Attractors are a common feature in multi-qubit Jaynes-Cummings models.

Entanglement exhibits collapse, revival, and sudden death/birth phenomena.

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.