Bose - Einstein Condensates Of Phase Coherence And Containing System In The Cloth Habitat Study Of The Localization

This paper is of two folds. Firstly, we investigate the relative quantum phase control of two-component Bose-Einstain condanste(BEC). A boson Josephson junction(BJJ) formed in a weakly coupled double-BEC has been discussed intensively. Based on mean-field theory (MFT), which gives rise to the Gross-Pitaevskii equation, interesting phenomena such as macroscopic quantum self-trapping(MQST), and n -phase state, where the time-averaged quantum phase difference across the junction equals n have been predicted. We rederive the EQPM, however, with the potential field description of the effective quantum spin modeled from weakly linked two-component BECs. We find that the n -phase state can be either the degenerate ground state or metastable, even unstable state depending on experimental parameters ofBECs.The life time of the metastable n -phase state is evaluated explicitly in term of the instanton method. Moreover, we obtain the energy band structure, and the band width of the low-lying energy spectrum of the BECs due to the quantum tunneling between degenerate ground states. Thus we are able to investigate the coherent properties of the Bose-Josephson oscillations.Localization control of atoms or electrons is discussed in the second part. Transport of atoms or molecules driven by laser beams through a mesoscopic device have continued to receive considerable attention in recent years. Using Lewis-Riesenfeld theory, we obtain exact solutions of the time-dependent system, then we recover both n -pulse method based on time-evolution operator of the system and STIRAP method in terms of instantaneous eigenstates with the help of time-dependent gauge transformation. Moreover, adiabatic conditions of these two schemes which have been widely investigated and generalized in many papers are discussed. A strict formulation of adiabatic conditions is given, and a new adiabatic condition to induce complete population transfer is found.It is extremely desirable to have a better understanding of the quantum dot (QD) dynamics and to develop a technique to control the localization of electrons which is of possible application in quantum computation and quantum information processing. Tuning of the driving field thus provides a simple mechanism to localize or move spin polarization within an array of quantum dots by adjusting the tunnelling rate between adjacent dots. We study the dynamical spin separation of two interacting electrons confined in the double QDs driven by a static and a rotating magnetic fields. We use an two-site model of Hubbard-type to describe the dynamical system including the Coulomb interaction. With the time-evolution operator obtained by means of SU(2) spin coherent states we are able to derive analytic time-evolution of spin probability-current between the two quantum dots for various initial states.