The Applications Of Spin Squeezing And Quantum Fisher Information And Quantum Correlation In The Quantum Chaos

Quantum optics is a fast-developing subject, of which the squeezing state is a much studied topic. Recently, the study of spin squeezing has roused much interesting. It was found that the spin squeezing is closely related to the quantum entanglement, and this makes the concept of spin squeezing becomes a cross subject of quantum optical and quantum information. In the classical mechanics, chaos can be well described by Lyapunov exponent, While for the quantum chaos, there was not a fit quantity to describe it. In this thesis, we use the different quantum properties to study the quantum chaos. This thesis falls into 6 chapters, in which Chapter 3 to 5 constitute the major part of our work. In Chapter 1, we give a brief introduction to the research background, the general situation and the application of the theories of quantum entanglement and quantum chaos, and we also give the organization of this thesis at the end of this chapter.In Chapter 2, we mainly introduced the general concepts of quantum entanglement and quantum correlation. At first we give the basic concept and properties of entanglement and several typical quantum measurement. We also give the concept of quantum correlation, which can be well described by quantum discord, and here we give a brief introduction of quantum discord.In Chapter 3, we study the basic theories of spin squeezing, quantum Fisher information and concurrence. In this chapter, we are emphasis on the spin squeezing parameterξT2, which introduced by Toth et al. We study the relation betweenξT2 and the spin squeezing parameter which defined by Kitagawa and Ueda, We also study the relation betweenξT2 and concurrence, and find that there is an explicit expression between the spin squeezing parameterξT2 and concurrence. At the end, we consider the relation between the spin squeezing parameterξT2 and the minimal pairwise correlations, and give the explicit expression between the spin squeezing parameter and the minimal pairwise correlation.In Chapter 4, we study the relation between spin squeezing parameter and concurrence in the one-aixs twisting model. And we find that the concurrence can be well described by the spin squeezing parameterξT2, and the spin squeezing parameter is great effected by the number of particles and the strength of external field. In this chapter, we study the time evolution of quantum discord in this model. If there is no external field, the mean quantum discord connect with the number of particles. If we consider the external field, here, we choose N=3, and find that the mean quantum discord connect with the strength of external field. And we also give the explicit expression of geometric measure of quantum discord in the above two case. And study the evolution of geometric measure of quantum discord and the relation between the mean geometric measure of quantum discord and the number of particles or the strength of external field.In Chapter 5, we study the different quantum properties in the quantum chaos. Here we study the evolutions of different quantum properties in the quantum kicked top, whose initial state classical correspondings are at the fixed point, quasi-period and chaotic cases. At first, we consider the evolution of quantum entanglement with different initial states in this model. Here we choose the linear entropy and concurrence to describe the entanglement, and find that the linear entropy increases to the maximum value very quickly in the chaotic case. While the concurrence exists a very short time, and there is entanglement sudden death in the chaotic case, however when the initial state are at the fixed point and quasi-period, with evolution of concurrence, there are entanglement sudden death and entanglement sudden birth. We also study the evolution of spin squeezing in the quantum kicked top, and find that the maximal spin squeezing direction, which refer to the minimal pairwise correlation, is strongly influenced by quantum chaos. The maximal spin squeezing direction are around the direction which is perpendicular to the mean spin direction in the regular case. While the maximal spin squeezing direction is not concentrated in a certain direction in the chaotic case. Here we consider the evolution of quantum Fisher information in this model, and find the system is more sensitive in the chaotic case. At last, we study the relation between quantum correlation and quantum chaos, and find the quantum correlation is larger in the chaotic case.