We theoretically study the electron transfer properties of a double quantum dot system in dissipative and pure dephasing environments based on a quantum dot contact detector. Theoretical results show that in the dissipative environment, the decoherence caused by the detector would increase the stable value of the average current and Fano factor as functions of time. Meanwhile, we find the existence of the quantum Zeno effect during the process of dynamical evolution. In the case of symmetric DQD, the relaxation caused by the dissipative environment would decrease the amplitude of the average current with time evolution and increase the value of the Fano factor in the long time limit. In the case of asymmetric DQD, the relaxation reduces the peak value of Fano factor over time. In the pure dephasing environment, we find that the frequent measurement would hinder the switch between different current channels during the cotunneling process. This results in a high value of Fano factor. In the case of symmetric DQD, increasing the pure dephasing rate would improve the value of Fano factor. In the case of asymmetric DQD, the dynamical evolution with time is not sensitive to the pure dephasing rate. In addition, it is indicated that the transfer probability of electron in the detector is only affected by the coupling between QPC and DQD. The environments have no effect on the transfer of a single electron in the detector. Our theoretical results provide theoretical references for experimental researchers to study the electron transport properties.
Using the innovative method of the additional Bloch vector, the electron transfer properties of a double quantum dot (DQD) system measured by a quantum point contact (QPC) in a fluctuating environment are investigated. The results show that the environmental noises in transverse and longitudinal directions play different roles in the dynamical evolution of the open quantum systems. Considering the DQD with symmetric energy level, the Fano factor exhibits a slight peak with the increase of transverse noise amplitude σ T, which provides a basis for distinguishing dynamical phenomena caused by different directional fluctuation noises in symmetric DQD structures by studying the detector output. In the case of asymmetric DQD, the dependence of a detector current involving the level displacement is distinct when increasing the transverse noise damping coefficient τ T and the longitudinal noise damping coefficient τε respectively. Meanwhile, the transverse noise damping coefficient τ T could significantly reduce the Fano factor and enhance the stability of the quantum system compared with the longitudinal one. The Fano factors with stable values as the enhancement of noise amplitudes show different external influences from the detector measurement, and provide a numerical reference for adjusting the noise amplitudes in both transverse and longitudinal directions appropriately in a microscopic experimental process to offset the decoherence effect caused by the measurements. Finally, the research of average waiting time provides unique insights to the development of single electron transfer theory in the short-time limit.
The quantum speed limit(QSL) of the double quantum dot(DQD) system has been theoretically investigated by adopting the detecting of the quantum point contact(QPC) in the pure dephasing environment.The ML type of the QSL bound which is based on the trace distance has been extended to the DQD system for calculating the shortest evolving time.The increase of decoherence rate can weaken the capacity for potential speedup(CPS) and delay the evolving process due to the frequently measurement localizing the electron in the DQD system.The system need longer time to evolving to target state as the enhancment of dephasing rate,because the strong interaction between pure dephasing environment and the DQD system could vary the oscillation of the electron.Increasing the dephasing rate can sharp the QSL bound,but the decoherence rate would weaken the former effect and vice versa.Moreover,the CPS would be raised by increasing the energy displacement,while the enhancement of the coupling strength between two quantum dots can diminish it.It is interesting that there has an inflection point,when the coupling strength is less than the value of the point,the increasing effect of the CPS from the energy displacement is dominant,otherwise the decreasing tendency of the CPS is determined by the coupling strength and suppress the action of the energy displacement if the coupling strength is greater than the point.Our results provide theoretical reference for study the QSL time in a semiconductor device affected by numerous factors.
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