Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Physics B Atomic Molecular and Optical Physics

Dynamical behaviour of the entanglement between two spatially separated atoms under the influence of dissipation

Hui-Ping Cui, Jian Zou, J G Li, Bin Shao

Published Apr 18, 2007• 11 citations
Publisher

Abstract

We consider two two-level atoms, which are located in two independent dissipative cavities. The two atoms are initially prepared in the singlet state. We investigate the influence of dissipation on the entanglement between the two atoms. In the case of resonance the degree of the entanglement can fall abruptly to zero, which is the so-called sudden death of entanglement. It is noted that when two atoms are in a common environment, the singlet state is a decoherence-free state. When the dispersive limit is fulfilled, the degree of entanglement between the two atoms is oscillating at first, then it arrives at a steady value, which increases with the increase of the damping constant κ; when both fields are initially in the vacuum state, the entanglement between the two atoms will not decay.

DOI
10.1088/0953-4075/40/9/s08

Related papers

Dynamic Behavior of Entanglement Between Two Spatially Separated Atoms in Two Dissipative and Driven Cavity Fields

Cui Hui-Ping, Jian Li, Liu Jin +1 more

We consider two two-level atoms, interacting with two independent dissipative cavities, each of which is driven by an external source. The two cavity fields are both initially prepared in the coherent states, and the two two-level atoms are initially prepared in the singlet state |Ψ − ⟩ = (|eg⟩ – |ge⟩)/√2. We investigate the influence of the damping constant κ, the intensity of the external sources F, and the relative difference of the atomic couplings r on the entanglement between the two atoms. In the dispersive approximation, we find that the entanglement between the two atoms decreases with the time evolution, and the decreasing rate of entanglement depends on the values of F/κ, κ/ω, and r. For the given small values of F/κ and κ/ω, on the one hand, the increasing of r favors entanglement decreasing of the atomic system, on the other hand, when r → 1 the entanglement decreasing becomes slower. With the increasing of the value of κ/ω, the influence of r on the decreasing rate of entanglement becomes smaller, and gradually disappears for the big value of κ/ω.

Communications in Theoretical Physics•Mar 1, 2009•1 citation

Influence of dissipation on the entanglement ofNtwo-level atoms located in one cavity orNcavities

Lin Li, Jian Zou, Jungang Li +2 more

We investigate the influence of dissipation on the entanglement among N identical two-level atoms. We analyse the situation of N two-level atoms in a dispersive cavity or in N dispersive cavities, both in W-like and in GHZ states for N atoms. By considering the Jaynes–Cummings model in the dispersive regime, and a master equation formalism, we compute the time evolution of the entanglement of the atoms, in a variety of situations. We find that, depending on whether the atoms are located in one or N cavities, and on their initial entangled state, the subsequent dynamics will be very different, specifically, exponential decay to coherent oscillations, exponential decay to steady values, or collapse and revival.

Journal of Physics B Atomic Molecular and Optical Physics•Apr 7, 2008•1 citation

Two atoms in dissipative cavities in dispersive limit: entanglement sudden death and long-lived entanglement

Jian-Song Zhang, Ai-Xi Chen, M Abdel-Aty

We investigate the entanglement dynamics and coherence of two two-level atoms interacting with two coherent fields of two spatially separated and dissipative cavities. It is in particular shown that entanglement sudden death is obtained within a short interaction time. However, after a long interaction time a long-lived entanglement is shown; that is, the initial entanglement of two atoms could be partially preserved. In addition, the coherence of the two atoms will not be lost during the evolution.

arXiv:0912.4617•Journal of Physics B Atomic Molecular and Optical Physics•Dec 21, 2009•37 citations

Entanglement dynamics of a pure bipartite system in dissipative environments

Rabia Tahira, Manzoor Ikram, Tasnim Azim +1 more

We investigate the phenomenon of sudden death of entanglement in a bipartite system subjected to dissipative environments with arbitrary initial pure entangled state between two atoms. We find that in a vacuum reservoir the presence of the state where both atoms are in excited states is a necessary condition for the sudden death of entanglement. Otherwise entanglement remains for an infinite time and decays asymptotically with the decay of individual qubits. For pure 2-qubit entangled states in a thermal environment, we observe that the sudden death of entanglement always happens. The sudden death time of the entangled states is related to the temperature of the reservoir and the initial preparation of the entangled states.

Journal of Physics B Atomic Molecular and Optical Physics•Oct 1, 2008•35 citations

Dynamics of entanglement between two free atoms with quantized motion

F. Lastra, Sascha Wallentowitz

The electronic entanglement between two free atoms initially at rest is obtained including the effects of photon recoil, for the case when quantum dispersion can be neglected during the atomic excited-state lifetime. Unlike previous treatments using common or statistically independent reservoirs, a continuous transition between these limits is observed, which depends on the inter-atomic distance and degree of localization. The occurrence of entanglement sudden death and birth as predicted here deviates from the case where the inter-atomic distance is treated classically by a static value. Moreover, the creation of a dark state is predicted, which manifests itself by a stationary entanglement that even may be created from an initially separable state.

arXiv:0911.3564•Journal of Physics B Atomic Molecular and Optical Physics•Jun 1, 2010•3 citations

Entanglement between two atoms successively passing a thermal cavity taking into account detuning and atomic coherence

Eugene K. Bashkirov

The entanglement between two identical two-level atoms successively passing the thermal cavity has been investigated taking into account the detuning. The case when atoms are initially prepared in the Bell types entangled atomic states has been considered. It has been shown that for vacuum state of the cavity the presence of detuning leads to decreasing of the entanglement amplitude oscillations. We have also derived that for thermal field the increasing of the mean photon number leads to decreasing of the entanglement, but the entanglement increases as the detuning increases. For thermal field and small detuning we have established that the effect of sudden death and birth of entanglement takes place and that for large detuning such effect vanishes.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Apr 14, 2017•0 citations
We consider two two-level atoms, which are located in two independent dissipative cavities. The two atoms are initially prepared in the singlet state. We investigate the influence of dissipation on the entanglement between the two atoms. In the case of resonance the degree of the entanglement can fall abruptly to zero, which is the so-called sudden death of entanglement. It is noted that when two atoms are in a common environment, the singlet state is a decoherence-free state. When the dispersive limit is fulfilled, the degree of entanglement between the two atoms is oscillating at first, then it arrives at a steady value, which increases with the increase of the damping constant κ; when both fields are initially in the vacuum state, the entanglement between the two atoms will not decay.
We consider two two-level atoms, interacting with two independent dissipative cavities, each of which is driven by an external source. The two cavity fields are both initially prepared in the coherent states, and the two two-level atoms are initially prepared in the singlet state |Ψ − ⟩ = (|eg⟩ – |ge⟩)/√2. We investigate the influence of the damping constant κ, the intensity of the external sources F, and the relative difference of the atomic couplings r on the entanglement between the two atoms. In the dispersive approximation, we find that the entanglement between the two atoms decreases with the time evolution, and the decreasing rate of entanglement depends on the values of F/κ, κ/ω, and r. For the given small values of F/κ and κ/ω, on the one hand, the increasing of r favors entanglement decreasing of the atomic system, on the other hand, when r → 1 the entanglement decreasing becomes slower. With the increasing of the value of κ/ω, the influence of r on the decreasing rate of entanglement becomes smaller, and gradually disappears for the big value of κ/ω.
We investigate the influence of dissipation on the entanglement among N identical two-level atoms. We analyse the situation of N two-level atoms in a dispersive cavity or in N dispersive cavities, both in W-like and in GHZ states for N atoms. By considering the Jaynes–Cummings model in the dispersive regime, and a master equation formalism, we compute the time evolution of the entanglement of the atoms, in a variety of situations. We find that, depending on whether the atoms are located in one or N cavities, and on their initial entangled state, the subsequent dynamics will be very different, specifically, exponential decay to coherent oscillations, exponential decay to steady values, or collapse and revival.
We investigate the entanglement dynamics and coherence of two two-level atoms interacting with two coherent fields of two spatially separated and dissipative cavities. It is in particular shown that entanglement sudden death is obtained within a short interaction time. However, after a long interaction time a long-lived entanglement is shown; that is, the initial entanglement of two atoms could be partially preserved. In addition, the coherence of the two atoms will not be lost during the evolution.
We investigate the phenomenon of sudden death of entanglement in a bipartite system subjected to dissipative environments with arbitrary initial pure entangled state between two atoms. We find that in a vacuum reservoir the presence of the state where both atoms are in excited states is a necessary condition for the sudden death of entanglement. Otherwise entanglement remains for an infinite time and decays asymptotically with the decay of individual qubits. For pure 2-qubit entangled states in a thermal environment, we observe that the sudden death of entanglement always happens. The sudden death time of the entangled states is related to the temperature of the reservoir and the initial preparation of the entangled states.
The electronic entanglement between two free atoms initially at rest is obtained including the effects of photon recoil, for the case when quantum dispersion can be neglected during the atomic excited-state lifetime. Unlike previous treatments using common or statistically independent reservoirs, a continuous transition between these limits is observed, which depends on the inter-atomic distance and degree of localization. The occurrence of entanglement sudden death and birth as predicted here deviates from the case where the inter-atomic distance is treated classically by a static value. Moreover, the creation of a dark state is predicted, which manifests itself by a stationary entanglement that even may be created from an initially separable state.
The entanglement between two identical two-level atoms successively passing the thermal cavity has been investigated taking into account the detuning. The case when atoms are initially prepared in the Bell types entangled atomic states has been considered. It has been shown that for vacuum state of the cavity the presence of detuning leads to decreasing of the entanglement amplitude oscillations. We have also derived that for thermal field the increasing of the mean photon number leads to decreasing of the entanglement, but the entanglement increases as the detuning increases. For thermal field and small detuning we have established that the effect of sudden death and birth of entanglement takes place and that for large detuning such effect vanishes.