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arXiv 1906.00514cond-mat.str-elquant-ph
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隧穿费米边奇点的电荷转移统计和量子比特动力学

Charge transfer statistics and qubit dynamics at tunneling Fermi-edge singularity

V. V. Ponomarenko, I. A. Larkin

摘要:

研究了无自旋电子从单通道发射极通过量子点的相互作用共振能级进入空收集极的隧穿过程,当量子点上电荷变化的库仑屏蔽由发射极通道实现时,系统被映射到一个耗散量子比特的精确可解模型上.在这个模型中,我们用一个广义的林德布拉德方程来描述量子比特密度矩阵的演化,它允许我们计算隧穿电子,从而将量子比特动力学与电荷转移统计联系起来。特别地,其生成函数的系数等于使固定数量的电子隧穿到集电极中的时间相关概率,通过连续电子隧穿之间的量子比特纯态的非厄米哈密顿演化的参数来表示。从生成函数的长时间渐近性,我们计算Fano因子的第二和第三阶(偏度),并建立它们的关系,额外的平均和累积量,分别积累在瞬态过程中的空QD演化超出其线性时间依赖性的电荷。解释了该系统中亚泊松和超泊松散粒噪声的来源,并指出超泊松噪声表明存在非单调振荡瞬态电流和量子比特相干动力学。该机制的生成函数,其中之一符合在大的时间限制与$1/3$分数泊松实现没有真正的分数电荷隧穿的特定的例子进行说明。

英文摘要:

Tunneling of spinless electrons from a single-channel emitter into an empty collector through an interacting resonant level of the quantum dot (QD) is studied, when all Coulomb screening of charge variations on the dot is realized by the emitter channel and the system is mapped onto an exactly solvable model of a dissipative qubit. In this model we describe the qubit density matrix evolution with a generalized Lindblad equation, which permit us to count the tunneling electrons and therefore relate the qubit dynamics to the charge transfer statistics. In particular, the coefficients of its generating function equal to the time dependent probabilities to have the fixed number of electrons tunneled into the collector are expressed through the parameters of a non-Hermitian Hamiltonian evolution of the qubit pure states in between the successive electron tunnelings. From the long time asymptotics of the generating function we calculate Fano factors of the second and third order (skewness) and establish their relation to the extra average and cumulant, respectively, of the charge accumulated in the transient process of the empty QD evolution beyond their linear time dependence. It explains the origin of the sub and super Poisson shot noise in this system and shows that the super Poisson signals existence of a non-monotonous oscillating transient current and the qubit coherent dynamics. The mechanism is illustrated with particular examples of the generating functions, one of which coincides in the large time limit with the $1/3$ fractional Poissonian realized without the real fractional charge tunneling.

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