Non-Markovian Dynamics Of An Open Quantum System Coupled To A Waveguide In Photonic Crystals

The quantum decoherence of an open quantum system is a historical problem in quantum mechanics due to the unavoidable interaction with its environment.Traditionally,the backaction of the environment on the system is totally ignored under Markovian approximation,which leads to the Markovian(memoryless)dynamics of the system.Recently,due to the development of quantum technology and quantum devices,the non-Markovian memory effect of the environment on the dynamics of the quantum open system has attracted much attention,which results in the non-Markovian dynamics of the system that generally the initial quantum coherence of the system could be revived or preserved to some extent.Theoretically,the non-Markovian effect of the environment on the system could be enchanced by the increasing the system-environment coupling strength or by suitably designing the geometric structure of the environment to change its the density of stat.In this work,we would like to extend the previous study on a quantum system coupled to a photonic-crystal waveguide with semi-infinite cavity-array structure to the infinite cavity-array structure.We will show the latter structure takes great advantage for the quantum information preservation.The system considered includes one-qubit quantum system and multi-qubit quantum system.Explicitly,the contents are listed as:i)We evaluate exactly the non-Markovian effect on the decoherence dynamics of a qubit coupling with a waveguide in photonic crystals.In our study,we extend the previous investigation that the waveguide is structured as a semi-infinite cavity arrayto the case that it is set as an infinite cavity array.For the infinite cavity array,we utilize the quantity of fidelity to characterize the ability of the system to preserve its initial quantum information.We make a discussion for different initial states of the qubit.Similar to the case of semi-infinite cavity array,we find that the quantum information of the qubit in the long-time scale could also be partially preserved when the qubit-waveguide coupling strength goes beyond a critical value.This is a strong non-Markovian memory effect induced by the strong qubit-waveguide coupling strength.Interestingly,the critical coupling strength for infinite cavity array happens to be zero,which means that in this real physical system,the quantum-to-classical transition behavior of the qubit never occurs.Therefore,by reasonably choosing the structure of the environment,the quantum information of the quantum systems could be more easily preserved.Moreover,we find that the higher probability of the qubit initially in its ground state,the more easily for it to preserve its initial information in the long-time scale,which proves that the quantum open system always tends to stay in its ground state.ii)We study the exact non-Markovian dynamics of a multi-qubit system coupled to a photonic-crystal waveguide with infinite cavity-array structure.A general solution of the evolution state of the system is solved for a general initial state in the single-excitation subspace.With this solution,we find that the non-Markovian effect of the environment on the system could be enhanced not only by increasing the system-environment coupling strength but also by adding the qubit number in the system.The explicit non-Markovian dynamics are discussed under two initial states to see the non-Markovian effect on entanglement preservation and entanglement generation.For initial W state,we find that the strong non-Markovian effect could greatly preserve the initial entanglement.Interestingly,with the inifinite cavity-array structure of the waveguide,it is very easy for the entanglement to be fully preserved in the long-time scale by enhancing the system-environment coupling strength or by increasing the qubit number in the system.For initial separable state with single qubit excited,we find that by increasing the system-environment coupling strength,the strong non-Markovian effect could not obviously enhance the possibility for entanglement generation.Meanwhile,the increase of the qubit number greatly decreases the possibility for entanglement generation.Interestingly,in the large qubit number limit,the strong non-Markovian limit results in the initial excitation trapped.That is,the non-Markovian effect tends to preserve the system in its initial state.