Generation Of Atomic Entangled States In Cavity QED Systems

Quantum entanglement,as the indispensable key resource in quantum information,is always one of the hot topics.Recently,entangled states have been widely applied in quantum communication,quantum computing,and quantum metrology.In quantum information processing,entangled states need to exist for a certain time for completing a quantum operation.In the real physical world,however,entangled states are fragile.It's because that the interaction between a quantum system and its surrounding environments destroys entangled states and results in disentanglement.Therefore,how to prepare longlived steady quantum entangled states in dissipative environments has become one of the main problems in quantum information.Cavity quantum electrodynamics(cavity QED)systems,as one of the most promising physical systems to realize quantum hardware,have been widely used in quantum information.Especially,cavity QED systems,as an efficient entanglement generator,many methods have been proposed to prepare different photon and atom entangled states in cavity QED systems.The dissipation of cavity QED systems includes atomic spontaneous emission and cavity dissipation,which severely reduces the fidelity of entangled states.And thus the preparation of high-fidelity steady entanglement in cavity QED systems has always been the goal for making efforts.The main contents of this thesis are the preparation of high-fidelity steady atomic entanglement by using different methods.Taking the preparation of two-atom entangled states as the starting point,the research content gradually goes into the preparation of many-atom entangled states.The schemes for preparing two-atom three-dimensional entangled state,three-atom GHZ state,three-atom W state,and many-atom NOON state are proposed.We propose a scheme of preparing three-dimensional entangled states for two atoms via entanglement swapping in non-Markovian cavity QED systems.In this scheme,the three-level atoms are trapped in two distant dissipative cavities,and the transitions are coupled to a cavity mode and a classical driving field,respectively.The interaction between the atom and the cavity field entangles them,and thus the entanglement between the atom and the cavity field can be transformed into the entanglement between the atoms by performing Bell state measurement on photons leaking from the cavities.Entanglement shows an obvious oscillation behavior in non-Markovian environments,due to the memory effect of environments.By properly selecting the detuning of the classical driving fieldand the initial state of the atoms,the atoms are prepared in a steady three-dimensional entangled state.We propose a scheme of preparing GHZ state for three atoms via entanglement swapping and a scheme of preparing W state for three atoms by Lyapunov control in dissipative cavity QED systems.In the scheme of preparing three-atom GHZ state,the four-level atoms are trapped in three distant cavities,and the transitions are coupled to the left and right circularly polarized cavity modes,respectively.The entanglement of atoms is generated by measuring the photons leaking from cavities.By solving the time-dependent Schr?dinger equation,the analytical results for the evolution of the entanglement and the parameter condition for preparing the maximum entanglement are obtained.When the condition is met,the atoms are prepared in a three-particle GHZ state.When the condition isn't met,the entanglement shows an obvious oscillation behavior in non-Markovian environments.In the scheme of preparing three-atom W state,the three-level atoms are trapped in two cavities connected by an optical fiber.According to the Lyapunov control theory,the control fields in closed and open systems are designed.In closed systems,the coupling between the cavity and fiber only affects the time when the fidelity reaches the maximum,but not the amount of the maximum.And thus a high-fidelity three-atom W state is generated successfully even when the coupling strength between the cavity and fiber is extremely weak.In open systems,the fidelity of W state decreases with increasing the decay rate of atom,cavity,and fiber.In the case of strong dissipation,the fidelity of W state can be greatly improved by introducing quantum measurement and quantum feedback.Also,the time optimization of Lyapunov control under the power and intensity constraints is studied.We propose a scheme of preparing many-atom NOON state by atomic collective excitation and a scheme of preparing many-atom NOON state by single-photon measurement in cavity QED systems.In the scheme of preparing NOON state by atomic collective excitation,the atoms are trapped in two cavities coupled via photon-hopping interaction.The atomic NOON state is produced via a phase-shift which depends on the collective atomic excitations.The time of generating the NOON state is independent of the atom number of NOON state,and thus the time of generating the NOON state is unchanged with increasing the atom number of NOON state.Because the cavity field is always in the vacuum state in the whole preparation process,this scheme is insensitive to the cavity dissipation.The atomic excited states are hardly populated under the condition of largedetunings,and thus this scheme can effectively suppress atomic spontaneous emission.In the scheme of preparing NOON state by single-photon measurement,two distant cavities capture N identical three-level atoms,respectively.A beam of weak light containing two frequency components is successively incident and passed through the two cavities,and then is detected in a specific photon state.The atom-light interaction entangles the collective atomic spin state with a corresponding frequency component of a photon transmitted through the cavity,and thus the single-photon measurement of the transmitted light will project the atoms onto a NOON state.In the presence of dissipation,the fidelity of the NOON state decreases with increasing the number of atoms and the decay rate of the cavity.In the case of a large number of atoms or strong dissipation,the second execution of the preparation step of the NOON state is used to improve the fidelity,and the preparation of a high-fidelity many-atom NOON state is realized.