Ultracold Atoms In The Micro-Cavity And Quantum Phase Transition

Cavity quantum electrodynamics (Cavity-QED), which desicribes the interaction between the atoms and quantized cavity field, has proved a versatile and controllable platform in quantum optics describing various interesting phenomena. The simplest light-atom system is the Jaynes-Cummings model, which describes the coherent interaction of a quantized electromagnetic field with a single two-level atom. As the number of two-level atoms increases, such as the Dicke or Tavis-Cummings model, collective effects lead to an intriguing many-body phenomena known as a superradiant phase. Moreover, at zero and finite temperature, a state with photon and atomic excitations has a lower energy than the vacuum field and ensemble ground state. This quantum critical phenomenon is associated with entanglement between the atomic ensemble and the field. Several implementation proposals allowing the Dicke superradiant phase transition have been given, including open dynamical systems involving semiconductor quantum wells or quantum dots, open dynamical cavity-QED systems with neutral atoms and ions, and superconducting quantum devices. Arrays of coupled cavities have extended the application of the Dicke model and made it possible to study the strongly interacting many-body systems in condensed matter physics. Substituting free atoms, weakly-interacting ultracold atoms in a Bose-Einstein condensate (BEC) have been loaded into high-finesse optical cavities. It has been got that, accounting for the center of motion of the atoms, it is possible to realize the Dicke model in these BEC-cavity-QED systems where the superradiant phase corresponds to a periodical self-organized supersolid phase of the BEC. Motivated by such BEC-cavity-QED system, we study the generalized Dicke model.In chapter1, we introduct the interaction between a two-level atom and a single mode quantum light field of n-photon process. Using time-depedent unitary transformation, we derive that the non-adiabatic approximate Berry phase is proportional to the average photon number m and inversely proportional to the transition photon-number n. In some special case, the adiabatic and non-adiabatic Berry phases coincide with each other, otherwise there appears an additional non-trivial phase factor.In chapter2, we study the generation of entanglement in an alternative hybrid optomechanical system composed of a two-level atom in an optical cavity with a movable mirror in one end. Using the time-averaging method, we derive an effective Hamiltonian and a tripartite entangled GHZ state is generated by means of the effective Hamiltonian. Based on the master eqution, we get the evolution of density operator over time. It is found that negativity depends strongly on the spontaneous emission rate y of the atom, the mean photon number n and the coupling strength k(i.e.G2/ωm). For appropriate these parameters, the phenomena of entanglement sudden death (ESD) and entanglement sudden birth (ESB)) can be observed.In chapter3-5, it is related to the Dicke model. In recent experimental setup about the BEC-cavity system, we obtain the rich ground-state properties induced by the nonlinear interaction. From phase diagram, we can find that the superradiant-normal quantum phase transition can be well driven by this nonlinear interaction in the blue detuning and two new quantum phase transitions are found in the red detuning, which are from the superradiant phase or the normal phase to a dynamically-unstable phase. It should be pointed out that our predicted quantum phase transitions belong to the intrinsic transitions, which are governed only by the second-order derivative of the ground-state energy and not depicted by considering the conventional Landau’s theory with the breaking of symmetry. The consequence predicted in Keeling’s paper can not happen in the ground state about the concomitant region of the superradiant phase and the normal phase. On the basis of chapter3, chaper4considers the effect of the driving field on the system’s ground-state properties, which shifts the critical position of quantum phase transition. The laser makes it easy to control the driving field in the experiment. In chaper5, a new link to the Dicke-model type quantum phase transition is established by considering a monochromatic nonadiabatic modulation of the atom-field coupling and nonlinear atom-photon interaction as well, which make a notable impact on ground-state properties of many-body quantum system. We use Floquet theory and a generalized rotating wave approximation to obtain the effective Hamiltonian.