| Entanglement and Bell non-locality are the fundamental concept of the quantum mechanics,because they have very important practical applications and play an essential role in quantum information,such as quantum dense coding,quantum teleportation,quantum error-correcting code,quantum control,quantum simulation,quantum entanglement network,and so on.The relationships between entanglement and Bell non-locality in various quantum environment is the hot topic,and many important advances have been made in the course of their research,but most of the previous research work was based on considering the Markovian environments or Non-Markovian environments,dipole-dipole interaction and the initial state of the atom itself,the spatial motion of the atoms is seldom considered in their research,therefore we investigate the relationships between entanglement and Bell non-locality under the premise of the atoms'spatial motion in this paper.As we all know,entanglement is the key part of quantum correlation,so that people think entanglement is completely equivalent to quantum correlation for a long time,until people find some quantum systems without entanglement but they can perform a task exponentially faster than any classical algorithm in the deterministic quantum computation with one qubit(DQC1).Thus,people realized that entanglement is not identical to quantum correlation,it is only one kind of quantum correlation.Therefore,it has prompted people to classify the correlation from the perspective of measurement,and thus proposed the concept of quantum discord.Due to the calculation of quantum discord need a lot of optimization procedure,the calculation of quantum discord become more difficult with the increase of the dimension of the quantum system,thus we can only get the analytic expressions of quantum discord for some special quantum state.Therefore,people proposed the concept of geometric measure of quantum discord which can used to replace the original quantum discord.In the process of calculating the geometric measure of quantum discord,few people take into account the spatial motion,in this paper,by considering the spatial motion of the atoms,the relationships between the geometric measure of quantum discord and Bell non-locality are studied.In conclusion,on the premise of considering the degree of freedom of atomic spatial motion,we investigate the relationships between entanglement and Bell non-locality,the relationships between geometric measure of quantum discord and Bell non-locality in thispaper,the conclusions are summarized as follows:First of all,by taking into account the spatial degrees of freedom of the two atoms,we investigate the Bell non-locality and entanglement dynamics of two atoms interacting with a vacuum multi-mode noise field,and the atomic internal states is initially in a Werner-like state,the conclusions are as follows:(1)Bell non-locality decreases with time and then dies suddenly,while entanglement always approaches zero gradually,and there is no sudden death of entanglement.(2)we have shown that the survival time of entanglement is much more longer than that of the maximum violation of CHSH-Bell inequality,furthermore we have also presented that the Bell non-locality sudden death happens earlier than entanglement decay.Furthermore,we have compared the survival time of quantum correlation between the two Werner-like states.(3)We have also shown that for the two Werner-like internal states,the maximum violations of CHSH-Bell inequality and concurrence change sensitively with the purity,only when the initial purity of the states is high enough,a violation of the CHSH-Bell inequality(p ? 0.71)and entanglement(p ? 1/3)is achieved.(4)Though the spatial degrees of freedom of the two atoms have been taken into account,yet we notice that the dissipation factor GAU(-?t)×[1-exp(-?t/2)]2 of z induced by the vacuum noise field is much larger than the dissipation factor exp(-?)of z,with ?=(?x02+h2t2/4m2?x02)×(?0/c+i?/2c)2 induced by the spatial motion of the two atoms,therefore,the influence of the two atoms' spatial motion may be omitted.Secondly,we study the time evolution of Bell non-locality and entanglement of a pair of atoms for two kinds of Werner-like internal states in an ideal single-mode ring cavity.After theoretical calculations and numerical analysis,we have obtained some importantconclusions:(1)For one of the Werner-like states,we call that W'±,we note that Bell non-locality and entanglement have the phenomena of both sudden death and sudden birth.However,for another type of Werner-like states,we call that W±,we note that although Bell non-locality still has the phenomena of sudden death and sudden birth,yet the entanglement gradually decays to zero over time.(2)We also notice that the preservation of entanglement is much longer than that of Bell-inequality violation.(3)Both entanglement and Bell non-locality obviously depend on the factor that describes the atoms' spatial motion-the width of the atomic wave packet.The width of the wave packet can prolong the survival time of Bell non-locality and entanglement.The wider the width of the wave packet,the longer the survival time of Bell non-locality and entanglement.(4)Both entanglement and Bell non-locality obviously depend on the purity of the initial state of the atom.Only when the purity of the initial state is greater than a certain value,does the entanglement and Bell non-locality begin to occur.Finally,we study the dynamics of geometric measure of quantum discord(GMQD)and Bell-nonlocality of a two-qubit system in an ideal single-mode ring cavity for two kinds of extended Werner-like(EWL)internal states,the study draws the followingconclusions:(1)The results show that with the increase of the entanglement parameter ?,the GMQD and Bmax(?)-2 increase first,and suffer a declining procession after they attain the maximum values.When the initial entanglement parameter is equal to(?)/2,the EWL state is reduced to the Werner-like(WL)state,at which time the violation of the geometric measure of quantum discord and Bell inequality reach a maximum value.(2)Only when the purity of the initial state is greater than a certain value does the violation of the Bell inequality and geometric measure of quantum discord begin to occur.Moreover,both of them increase with the increase of purity.(3)The larger the width of the wave packet,the longer the geometric measure of quantum discord and the Bell inequality violation,that is,the width of the wave packet can extend the lifetime of the two.(4)For one of the EWL states,we call that W'±,we note that the geometric measure of quantum discord and Bell non-locality both have the phenomena of sudden death and sudden birth.However,for another type of extended Werner-like states,we call that W±,we note that although Bell non-locality still has the phenomena of sudden death and sudden birth,yet the geometric measure of quantum discord gradually decays to zero over time.(5)we have shown that the survival time of the geometric measure of quantum discord is much more longer than that of the maximum violation of CHSH-Bell inequality,which means that the geometric measure of quantum discord is more robust than Bell non-locality in describing quantum correlation.Moreover,we have also compared the survival time of quantum correlation between the two EWL states. |
PDF Full Text Request