Quantum Effects And Their Manipulation In Coupled Cavity-Bose-Einstein Condensate Systems

Cavity quantum electrodynamics (Cavity QED) describes the coherent in-teraction between matter and electromagnetic field confined within a resonator structure, and is considered as a useful platform for quantum information process-ing. A strong coupling regime can be reached experimentally by using high-quality resonators. In the regime, atoms coherently exchange a photon with a single light-field mode many times before dissipation sets in, which is very important for quantum state engineering and quantum information processing. However, the tremendous degree of freedom of atomic gases is very difficult to control. Fortu-nately, the realization of a Bose-Einstein condensate (BEC) in a dilute atomic gas makes up for this deficiency. For a BEC, all atoms occupy the same motional quan-tum state which can substantially reduce the number of degree of freedom. The BEC are even described by a single mode of a matter-wave field. Brennecke et al firstly achieved the strong coupling of a BEC to the quantized field of an ultrahigh-finesse optical cavity and present a measurement of its eigenenergy spectrum. This opens a window to simulate a wealth of new phenomena that can be expected in the many-body physics of quantum gases with cavity-mediated interactions. Re-cently, using a coupled cavity-BEC system has realized the Dick quantum phase transtion(QPT)[Nature464,1301(2010)]. In this thesis, we mainly investigate the quantum effects and their manipulation in the coupled cavity-BEC systems.In chapter1, we introduce background materials about present subject under our consideration as well as the significance of the cavity-BEC systems.In chapter2, we give a brief introduction about cavity-BEC systems. We put emphasis on introducing a Dicke model and its corresponding Dicke QPT, which based on a two-dimensional cavity-BEC systems. Then we have introduced a self- consistent Bose-Habbard model, which described a one-dimensional cavity-BEC systems.In chapter3, we have investigated an impurity-doped cavity-BEC system. We have presented a new generalized Dicke model, an impurity-doped Dicke model to describe the system. It is shown that the impurity atom can induce Dicke QPT from the normalphase to superradiant phase at a critic value of the impurity population. It is revealed that the impurity-induced Dicke QPT can happen in an arbitrary coupling regime of the cavity field and atoms while the Dicke QPT in the standard Dicke model occurs only in the strong coupling regime of the cavity field and atoms. This opens the door to observing the Dicke QPT and studying new physics related to the Dicke QPT in new parameter regimes of the field-atom coupling.In chapter4, we investigate a two qubits-coupled cavity-BEC system. For the two qubits that enter the cavity at the same time and only interact with the cavity filed, the coupled cavity-BEC system is equivalent to a controlled dephasing environment. The dephasing factor is proportional to the photon number fluctu-ation under the ground state of Dick Hamiltonian, which can be adjusted by the pump field. Then we have studied analytically the dynamic behaviors of quantum correlation measured by quantum discord between two uncoupled qubits, which are immersed in the dephasing environment. We show that the quantum discord of the two honinteracting qubits can be greatly amplified for certain initially pre-pared X-type states in the time evolution. Therefore, the coupled cavity-BEC can amplify the the quantum correlation of the two qubits. Finally, we obtain the an-alytical expression of the cavity photon number fluctuation in the full cavity-BEC coupling area. It is found that the cavity photon number fluctuation near the QPT point increases dramatically, which is the physical mechanism of the sensitive QD amplification.In chapter5, we study tunneling dynamics of a two-component BEC coupled with an optical cavity, which are trapped in a dowble-well. We found the optical cavity can induce an effective tunneling strength. When the cavity frequency shifts induced by each component BEC are different, The difference of the effective tunneling strengths between the two-component BEC can be adjusted by the pump field. Then we studied the dynamics of the space separating degree, mixing degree and entanglement about the two-component BEC. It is found the difference of the effective tunneling strengths can induce a lot of novel quantum effects in the tunneling dynamics process, Such as space separation of the two-component BEC, completely transfer of the entanglement between the atomic field modes, etc. Arbitrary mixing degree of two component BEC can be prepared in the tunneling dynamics. This suggests that if one component BEC are considered as impurities, the cavity-double well-two-component BEC system can be used as a quantum impurity-doped device.In chapter6, we present a summary and outlook.