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ACTA PHOTONICA SINICA

Entanglement Properties of Two Entangled Atoms Without Rotating Wave Approximation

姜道来 JIANG Dao-lai, 任学藻 Ren Xuezao, 丛红璐 Cong Honglu, 廖旭 Liao Xu

Published Jan 1, 2010• 0 citations

Abstract

Applying the method of coherent-state orthogonalization expansion, the influnences of dipole-dipole interaction and the coupling strength on the entanglement between two atoms of the Tavis-Cummings model without rotating wave approximation(without-RWA) are studied. Compared with the rotating wave approximation(RWA), it is found that the entanglement of the without-RWA agree with that of RWA when the coupling strength is weak. In the strong coupling regime, the sudden death phenomena occurs. The results also show that the stronger the atom-field coupling strength is, the longer the state stays in the disentangled separable state, which means that the length of the time interval for the distanglement depends on the atom-field coupling strength. When the dipole-dipole interacton is taken into account, the entanglement of the two atoms will be enhanced with the increace of dipole-dipole interaction.

DOI: 10.3788/gzxb20103909.1636

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Applying the method of coherent-state orthogonalization expansion, the influnences of dipole-dipole interaction and the coupling strength on the entanglement between two atoms of the Tavis-Cummings model without rotating wave approximation(without-RWA) are studied. Compared with the rotating wave approximation(RWA), it is found that the entanglement of the without-RWA agree with that of RWA when the coupling strength is weak. In the strong coupling regime, the sudden death phenomena occurs. The results also show that the stronger the atom-field coupling strength is, the longer the state stays in the disentangled separable state, which means that the length of the time interval for the distanglement depends on the atom-field coupling strength. When the dipole-dipole interacton is taken into account, the entanglement of the two atoms will be enhanced with the increace of dipole-dipole interaction.

The entanglement property of two identical atoms, initially entangled in Bell states, coupled to a single-mode cavity is considered. Based on the reduced non-perturbative quantum master equation method, the entanglement evolution of the two atoms with decay is investigated beyond the conventional rotating-wave approximation. We show that the counter-rotating wave terms, usually neglected, have a great influence on the disentanglement behaviour of the system. The phenomena of entanglement sudden death and entanglement sudden birth will occur. In addition, we show that the entanglement can be strengthened by introducing the dipole-dipole interaction of the two atoms.

Entanglement evolution of two independent Jaynes-Cummings atoms without the rotating-wave approximation (RWA) is studied by a numerically exact approach. Previous results based on the RWA are essentially modified in the strong-coupling regime ($g\ensuremath{\geqslant}0.1$), which has been reached in the recent experiments on the flux qubit coupled to the

\mathit{LC}

resonator. For the initial Bell state with anticorrelated spins, entanglement sudden death (ESD) is absent in the RWA but does appear in the present numerical calculation without the RWA. Aperiodic entanglement evolution in the strong-coupling regime is observed. The strong atom-cavity coupling facilitates the ESD. The sign of the detuning plays an essential role in the entanglement evolution for strong coupling, which is irrelevant in the RWA. Analytical results based on an unitary transformation are also given, which could not modify the RWA picture essentially. It is suggested that the activation of the photons may be the origin of ESD in this system.

The influences of dipole-dipole interaction and detuning on the entanglement between two atoms with different initial tripartite entangled W -like states in the Tavis–Cummings model have been investigated by means of Wootters' concurrence, respectively. The results show that the entanglement between the two atoms can be enhanced via appropriately tuning the strength of dipole-dipole interaction of two atoms or the detunings between atom and cavity, and the so-called sudden death effect can be weakened simultaneously.

We study the entanglement dynamics of T-C (Tavis-Cummings) model without rotating wave approximation. By using displaced coherent state method, the influence of initial state and coupling strength to concurrence is numerically studied. Our result demonstrates that the entanglement between two atoms always keep maximum when the initial state is antisymmetric while the non-entangled initial state produce entanglement periodically due to the effect of non-rotating terms. We also show that the coupling strength between the cavity field and atoms play a critical role in the entanglement dynamics.