Quantum Dynamics Of Coupled Quantum Dot And Bose-Einstein Condensate

This doctoral thesis is devoted to studying the quantum dynamics of two kinds of physical systems in the presence of external fields. One is the interacting electrons in the quantum dot system. The other is the dilute atomic Bose-Einstein condensate. In chapter two, we study the dynamics of two interacting electrons in a double quantum dot driven by a time-dependent field. With the help of the Floquet formalism, we find that the Floquet states of the system undergo a series of level crossing and avoided crossing which originate from the dynamical symmetry of the system Hamiltonian. Essential changes of the dynamical behavior of the system are found numerically. In particular two electrons initially localized in one of the dots are found to be localized forever at the crossing between the quasienergies which are developed from the unperturbed nearly- degenerate levels. We also find that due to the structure exchange of the Floquet states at the avoided crossing, the dynamical localization can be built up little by little near the multi-photon resonances. In addition, we also study in chapter one the transmission dynamics of a driven two-level system dissipated by the two leads. Using the nonequilibrium Green function, we derive an analytical transmission formula for an electron incident from the left lead, through the double quantum dot, to the right lead. The Landauer-type conductance and current are also given. A discussion of the internal tunneling dynamics reveals crucial effects of the localization and delocalization. In chapter three, we study the laser field-induced entanglement of the excitons in a coupled quantum dot. We show that excitons in coupled quantum dot are ideal candidates for reliable preparation of entangled states in solid-state systems. An optically controlled exciton transfer process is shown to lead to the generation of Bell and Greenberg-Home- Zelinger states in systems comprising two and three coupled dots, respectively. In addition, we also show that a linear configuration of three quantum dots can also used to generate the maximally entangled GHZ states with arbitrary phase. In chapter four, the dynamical population oscillations between two atomic Bose- Einstein condensates are investigated within the rotating wave approximation. Analytical expressions for the population imbalance between the traps in the number state and coherent states have been derived, which predict different revivals periods. Thus the true quantum state of the condensates may be unambiguously determined by detecting the atom intensity evolution for one trap. Also in this chapter we study the dynamics of a two- component Bose-Einstein condensate dressed by an oscillatory laser field. We find that when the driving strength and frequency are satisfied to be in particular relation, the condensate initially localized in one of the two internal states can stay localized in the following time evolution. In chapter five we study the dynamical response of a spinor Bose condensate under the influence of external magnetic fields which have both a random and a time varying systematic component. We find that the external noise may eventually destroy the Rabi oscillation and dynamical localization. The destruction of the Rabi oscillation due to the noise is much easier than that of the dynamical spin localization.