The stability of entanglement of two atoms in a cavity is analyzed in this work. By studying the general Werner states we clarify the role of Bell-singlet state in the problem of suppression of disentanglement due to spontaneous emission. It is also shown explicitly that the final amount of entanglement depends on the initial ingredients of the Bell-singlet state.PACS numbers: 03.65.Yz 03.65.Ud 03.65.TaOne of the specific features of quantum world is the existence of quantum coherence which forms the basis of describing wide varieties of phenomena including superconductivity and Bose-Einstein condensation of cold atoms. During the last decade, another aspect of quantum coherence, namely, quantum entanglement[1], has been recognized as the essential element of quantum computing [2]. In order to realize quantum information processing, stability of entanglement of quantum subsystems is one of the important problems that requires careful analysis. Instabilities of quantum entanglement can be generated through different mechanisms [3]. In general, an entangled state of a closed system can be disentangled by its own dynamics [4]. On the other hand, due to decoherence, system and environment interaction might not preserve initially entangled state. However, decoherence can also be a dynamical effect if one includes the quantum fluctuation of vacuum. In fact, such fluctuation is the origin of spontaneous emission which can reduce entangled state to separable state via photon emission.The recent work of Yu and Eberly [5] has discussed the finite-time disentanglement via spontaneous emission. In their system two non-interacting atoms are coupled to two separate cavities(environments). As a result, the dynamical evolution of the atoms are independent and, depending on initial state, the effect of spontaneous emission can drive the system to disentangled in finite time. However it is not clear if the disentangle phenomenon will persist if the atoms are allowed to interact. Intuitively, it is easy to imagine that for two atoms interacting in a lossless cavity, the photon emits by one atom during spontaneous emission can be absorbed by the other. As a result, entanglement might be preserved through this mechanism. In fact the above photon process is equivalent to the interaction between atoms by exchanging photon. Furthermore it is also more practical for constructing the quantum circuit inside one cavity instead of distribute the atoms in different separate ones. Consequently, it is inevitable to include the effects of interaction among atoms for any discussions on disentanglement via spontaneous emission. This problem has also been * Electronic address: fmliu@phys.ncku.edu.tw † Electronic address: chiachu@phys.ncku.edu.tw addressed in the interesting work by Tanaś and Ficek[6]. By putting two atoms inside the same cavity they showed that the entanglement exhibits oscillatory behavior, and the amount of entanglement is directly related to the population of the slowly decaying Bell-singlet state in the long time limit. Their ...

Analysis on the generation of spin entanglement from non-relativistic QED is presented. The results of entanglement are obtained with relativistic correction to the leading order of ( v c ) 2 . It is shown that to this order the degree of entanglement of a singlet state does not change under time evolution whereas the triplet state can change.

Ground state instabilities of the spin-boson model is studied in this work. The existence of sequential ground state instabilities is shown analytically for arbitrary detuning in the two-spin system. In this model, extra discontinuities of concurrence(entanglement measure) are found in the finite system, which do not appear in the on-resonant model. The above results remain intact by including extra boson modes. Moreover, by including extra modes, it is found that ground state entanglement can be obtained and enhanced even in the weak coupling regime.

In this work we provide analytic results of infinite one-dimensional cellular automaton(CA). By realizing symbolic products, we investigate a subclass of infinite CA and prove analytically that within this subclass the only allowed attractors are homogenous, steady and periodic states for arbitrary initial configuration. Our method also provide exact enumeration of these attractors and it is shown explicitly in a particular model.

By using the Rashba Hamiltonian, the evolution of entanglement of two spin-1 2 charged particles in a homogeneous electric field is investigated. It is shown that Bell states become disentangled within finite time and there exist unentangled spin states that stay unentangled during evolution. The correlations among spin-spin, momentum-momentum, and spin-momentum entanglements are discussed in detail. Moreover, a state is constructed to illustrate the fact that spin-momentum entanglement is solely a dynamical effect that can arise without any entanglement of the other degree of freedom. The results are also extended to the mixed states where Werner states are treated.