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

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.

37 pages, 14 figures

References in corpus (8)

• Finite-Time Disentanglement via Spontaneous Emission
• Sudden Death of Entanglement
• Dark periods and revivals of entanglement in a two qubit system
• Sudden Death of Entanglement of Two Jaynes-Cummings Atoms
• A Study on the Sudden Death of Entanglement
• Photon exchange and correlations transfer in atom-atom entanglement dynamics
• Quantum corrections to the semiclassical collective dynamics in the Tavis-Cummings model
• Entanglement of superconducting charge qubits by homodyne measurement

Cited by in corpus (14)

• Collapse and Revival and Cat States with an N Spin System
• Atomic Bell measurement via two-photon interactions
• Impurity in a bosonic Josephson junction: swallowtail loops, chaos, self-trapping and the poor man's Dicke model
• Unambiguous atomic Bell measurement assisted by multiphoton states
• Some entanglement features of three-atoms Tavis-Cummings model: Cooperative case
• Overcoming decoherence in the collapse and revival of spin Schrödinger cats
• Entangling operations in nonlinear two-atom Tavis-Cummings models
• Disappearance of entanglement: a topological point of view
• Entanglement generation by interaction with semiclassical radiation
• Generating non-classical states from spin coherent states via interaction with ancillary spins
• Quantum-state transfer between atom and cavity field in Jaynes-Cummings model
• Perfect revivals of Rabi oscillations and hybrid Bell states in a trapped ion
• Comparison of the semiclassical and quantum optical field dynamics in a pulse-excited optical cavity with a finite number of quantum emitters
• Photon echoes for a system of large negative spin and few photons