Investigation Of Non-Markovian Dynamics Of High-dimensional Open Quantum Systems

Quantum non-Markovian dynamics, due to its wide existence in the open quan-tum systems, has received much attention in recent years. The nature of a quantum non-Markovian process is the flow of lost information from the environment back to the open system, which leads to the oscillations of some pivotal physical quantities such as entanglement and quantum trace distance. The study of non-Markovian dynamics of open quantum systems is typically very involved. Most of the previous works about non-Markovian dynamics mainly concentrated on the two-level sys-tems. The high-dimensional open quantum systems have been seldom investigated. However, high-dimensional open quantum systems are extensively existed in nature and they can increase security in quantum cryptography. Further, high-dimensional systems have advantages in fault-tolerant quantum computation and quantum er-ror correction. In this thesis, we mainly investigate the quantum non-Markovianity dynamics of several typical high-dimensional open quantum systems. This thesis is structured as follow.In the first chapter, we mainly introduced some basic theories of the following three subjects:Quantum information, Open quantum system and Quantum deco-herence. Some basic background knowledge are recommended, including quantum trace distance, quantum entanglement and its measure, dynamical maps of quantum process, quantum divisibility, the master equation of Markovian and non-Markovian, quantum decoherence and three typical kind of quantum channels.In the second chapter, we introduced four kind of typical non-Markovianity measurements, namely measurement based on quantum trace distance, measurement based on the entanglement of auxiliary particle, measurement based on quantum correlation and measurement based on quantum divisibility.In the third chapter, we present a paradigmatic method for exactly study-ing non-Markovian dynamics of a multilevel V-type atom interacting with a zero-temperature bosonic bath. Special attention is paid to the entanglement evolution and the dynamical non-Markovianity of a three-level V-type atom. We find that the entanglement negativity decays faster and non-Markovianity is smaller in the regions of resonance than in non-resonance regions. More importantly, the quan-tum interference between the dynamical non-Markovianities induced by different transition channels is manifested, and the frequency domains for constructive and destructive interference are found.In the fourth chapter, we study the entanglement (measured by negativity) evolution and the non-Markovianity for the dynamical process of a spin-S system embedded in dephasing environments. The exact analytical solution is presented which shows that the decoherence function governs the evolutions of coherence, entanglement and the non-Markovianity of the corresponding dynamical processes. For Ohmic and sub-Ohmic reservoirs, the negativity decreases monotonically in time and the corresponding dynamics is Markovian. While for super-Ohmic reservoirs with non-monotonic decoherence function, the negativity appears the phenomenon of revivals and the corresponding dynamics is non-Markovian. The relation between non-Markovianity and the system dimension is studied.The last chapter is the conclusion and outlook of this thesis.