论文标题
多维量子电容的理论及其在量子点阵列中旋转和电荷辨别的应用
Theory of multi-dimensional quantum capacitance and its application to spin and charge discrimination in quantum-dot arrays
论文作者
论文摘要
可以通过测量量子电容来区分几个粒子系统的量子状态，可以区分该量子，该量子电容可以用系统能量的第二个导数相对于栅极电压来识别。通过引入量子电容矩阵，此方法在这里概括为多压情况。矩阵形式主义使我们能够确定量子电容对参数空间中电压振荡方向的依赖性，并确定栅极电压的最佳组合。作为一个代表性的示例，该方法应用于用哈伯德模型描述的量子点阵列的情况。在这里，我们首先确定多维电压空间中的潜在相关区域，并在电荷稳定性区域之间的边界（在半经典方法中确定）。然后，我们通过量子电容矩阵定量地表征此类边界。总的来说，这提供了一个程序，可以优化具有不同粒子数和/或总旋转状态的歧视。
Quantum states of a few-particle system capacitively coupled to a metal gate can be discriminated by measuring the quantum capacitance, which can be identified with the second derivative of the system energy with respect to the gate voltage. This approach is here generalized to the multi-voltage case, through the introduction of the quantum capacitance matrix. The matrix formalism allows us to determine the dependence of the quantum capacitance on the direction of the voltage oscillations in the parameter space, and to identify the optimal combination of gate voltages. As a representative example, this approach is applied to the case of a quantum-dot array, described in terms of a Hubbard model. Here, we first identify the potentially relevant regions in the multi-dimensional voltage space with the boundaries between charge stability regions, determined within a semiclassical approach. Then, we quantitatively characterize such boundaries by means of the quantum capacitance matrix. Altogether, this provides a procedure for optimizing the discrimination between states with different particle numbers and/or total spins.
