Double quantum dots are one of the promising two-state quantum systems for realizing qubits. In the quest of successfully manipulating and reading information in qubit systems, it is of prime interest to control the charge response of the system to a gate voltage, as filled in by the dynamical charge susceptibility. We theoretically study this quantity for a nonequilibrium double quantum dot by using the functional integral approach and derive its general analytical expression. One highlights the existence of two lines of maxima as a function of the dot level energies, each of them being split under the action of a bias voltage. In the low frequency limit, we derive the capacitance and the charge relaxation resistance of the equivalent quantum RC-circuit with a notable difference in the range of variation for $R$ depending on whether the system is connected in series or in parallel. By incorporating an additional triplet state in order to describe the situation of a double quantum dot with spin, we obtain results for the resonator phase response which are in qualitative agreement with recent experimental observations in spin qubit systems. These results show the wealth of information brought by the knowledge of dynamical charge susceptibility in double quantum dots with potential applications for spin qubits.

中文翻译：

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非平衡双量子点中的动态电荷敏感性

双量子点是实现量子位的有前途的两态量子系统之一。为了在量子位系统中成功地操纵和读取信息，控制系统对栅极电压的电荷响应至关重要，正如动态电荷敏感性所填充的那样。我们利用泛函积分方法从理论上研究了非平衡双量子点的这个量，并推导出了它的一般解析表达式。一个突出显示了作为点级能量函数的两条最大值线的存在，它们中的每一条在偏置电压的作用下被分裂。在低频极限下，我们推导出等效量子 RC 电路的电容和电荷弛豫电阻，其变化范围有显着差异$R$取决于系统是串联还是并联。通过结合一个额外的三重态来描述具有自旋的双量子点的情况，我们获得了谐振器相位响应的结果，该结果与最近在自旋量子位系统中的实验观察结果定性一致。这些结果显示了双量子点中动态电荷敏感性知识带来的丰富信息，具有自旋量子比特的潜在应用。