Full Counting Statistics Of Transport Electrons Through Quantum-dot System

Spin-orbit (SO) coupling, which leads to the connection between the spin degree of freedom and orbital motion, has become a hot area of research in solids, since it yields fascinating phenomena in asymmetric time inversion systems. It turns out to be a new branch of electronics known as spin-tronics, in which the central issue is to develop the spin-dependent electronic devices. Usually the spin degree of freedom is manipulated by ferromagnets and external magnetic fields, while electric controlling of spintronic devices can be realized by SO coupling in semiconductor heterostructures, which results in a spin field-effect transistor. The spin-dependent relaxation processes in nanostructures are also important issues in relation with the quantum computing and information. The SO coupling has very profound effects on the transport properties in mesoscopic systems such as quantum dot (QD) and two-dimensional Fermigas, which have attracted considerable attentionboth theoretically and experimentally. Moreover the coupling strength is turnable in practical experiments by the gatevoltage and thus spin-dependent currents can be realized.The QPC of conduction electrons has been an active research field for decades in the mesoscopic trans-port systems with the measuring of magnetic-flux-dependent current through an Aharonov-Bohm (AB) interferometer. An AB interference experiment in the Coulomb blockade regime has been reported utilizing a bare AB ring with a quantum dot (QD) embedded within one arm of the ring. The coherent properties provide new insight into the state of current transport in the dot. The two-particle interference has been investigated as a direct result of quantum exchange statistics in the absence of two-particle inter -action. The experimental realization of two-electron interference reproduces the original Hanbury Brown and Twiss experiments and has become a central study of multiple-particle wave functions. The QPC also has a great influence on the shot-noise properties from the viewpoint of transport electron-correlation. In fact, the quantum coherence of conduction-electron through different channels is caused physically by the phase accumulation of spatial motion from the electrode to QD.Firstly, We study the full counting statistics of transport electrons through a semiconductor two-level quantum dot with Rashba spin-orbit coupling, which acts as a nonabelian gauge field and thus induces the electron transition between two levels along with the spin flip.By means of the quantum master equation approach, shot noise and skewness are obtained at finite temperature with two-body Coulomb interaction. We particularly demonstrate the crucial effect of spin-orbit coupling on the super-Poissonian fluctuation of transport electrons, in terms of which the SO coupling can be probed by the zero-frequency cumulants.While the charge currents are not sensitive to the spin-orbit coupling.Secondly, we demonstrate a new type of quantum phase coherence, which is generated by the two-body interaction. This conclusion is based on quantum master equation analysis for the full counting statistics of electron transport through two parallel quantum-dots with antiparallel magnetic fluxes in order to eliminate the Aharonov-Bohm interference of either single-particle or non-interacting two-particle wave functions. The interacting two-particle QPC is realized by the flux-dependent oscillation of the zero-frequency cumulants including the shot noise and skewness with a characteristic period. The accurately quantized peaks of cumulant spectrum may have technical applications to probe the two-body Coulomb interaction.Finally, We investigate the multiple stable macroscopic quantum states of a Bose-Einstein condensate in an optomechanical cavity with pump-cavity field detuning and atom-photon interaction. The spin-coherent-state variational method is useful in exploring the multistability since it has the advantage of including both normal and inverted pseudospin states. In the blue detuning regime the usual transition from normal to superradiant phases still exists, however, when the atom-field coupling increases to a certain value, called the turning point, the superradiant phase collapses due to the resonant damping of the mechanical oscillator. As a consequence, the system undergoes at this point an additional phase transition to the normal phase of the atomic population inversion state. In particular, the superradiant phase disappears completely at strong photon-phonon interaction, resulting in the direct atomic population transfer between two atomic levels. Moreover, the coupling-induced collapse and revival of the superradiant state are also found in the red detuning region.