The Non-classical Properties Of The Photon-added Pair Coherent State And Its Entanglement

It is necessary to construct some allowable quantum states in quantum mechanics as much as possible, then one shall study their quantum statistical properties and then find some new non-classical properties and the relations among all kinds of non-classical effects as soon as possible. This is a very important and effective approach to studying quantum states. Therefore, in theory it is important practical meaning to constructing some new quantum states and investigating their non-classical properties. In recent years, people extensively know that in quantum mechanics the principle of superposition is the source of all kinds of non-classical effects of quantum states. So some quantum states exhibited remarkable non-classical effects are constructed on the basis of the principle. It is a fundamental way to constructing new quantum states. For example, the superposed states of two coherent states have squeezing and anti-bunching effect, etc. Another way to constructing new quantum state is employing the associated operators on the referenced states, where the states are arbitrary states in principle, usually the vacuum state and coherent state are looked on as the referenced states. For example, the photon-added or photon-subtracted coherent state is constructed by employing the creation operator or annihilation operator on the coherent state by many times. On the other hand, some new quantum states are constructed by virtue of eigenvalue equation of quantum operators. For example, Glauber’s coherent state is defined as the eigenstate of the annihilation operator a.In the first chapter, the non-classical properties of photon added pair coherent state(PAPCS) is examined by numeric solution. The result exhibit that the mean numbers of mode a and b are all increased. We see that the field in the PAPCS exhibits stronger sub-Poissonian character than the field in the pair coherent state, and the larger the value of q, the stronger the sub-Poissonian character. It shows that for the PAPCS the mode are correlated, but the correlation degree is weaker than that of the pair coherent state. The larger the value of q, the stronger the PAPCS correlated. The result exhibits that there is a strong violation of the Cauchy-Schwarz inequality in PAPCS.In the second chapter, we carry out a systematic study of the effect of local photon additions on a pair coherent state, showing that the entanglement generally increases with the number of such operations. We observe that the highest entanglement is achieved when these operations are equally shared between the two modes. By keeping the number of additions fixed on one mode, the entanglement is an increasing function of the number of additions on the other mode. We also observe that the entanglement enhancement effected by photon addition is greater when the parameter ? is low. Finally, we note that adding more photons typically provides a stronger entanglement enhancement than less photons, while less photons perform better in terms of energy efficiency.