[论文解读] Lifting of Coulomb Blockade by Alternating Voltages in Small Josephson Junctions with Electromagnetic Environment-Based Renormalization Effects

Godwill Mbiti Kanyolo, Hiroshi Shimada|arXiv (Cornell University)|Nov 21, 2019

Quantum and electron transport phenomena被引用 5

一句话总结

该论文将库仑阻塞的$P(E)$理论扩展至小尺寸约瑟夫森结和长阵列，通过引入电磁环境引起的重正化，利用复响应因子$\Xi(\omega)$实现。研究表明，振荡场会重正化环境阻抗，在热谱中产生能隙，并通过阵列中奇异的任意任何荷孤子-反孤子对实现动态库仑阻塞的探测。

ABSTRACT

The standard theory of Coulomb blockade [$P(E)$ theory] in ultra-small tunnel junctions has been formulated on the basis of phase-phase correlations by several authors. It was recently extended by several experimental and theoretical works to account for novel features ranging from time-reversal asymmetry to electromagnetic environment-based renormalization effects. Despite this progress, the theory remains elusive in the case of one dimensional arrays. Here, we apply path integral formalism to derive the Cooper-pair current and the BCS quasi-particle current in single small Josephson junctions and extend it to include long Josephson junction arrays as effective single junctions. We consider renormalization effects due to the electromagnetic environment in the single junction as well as the array. As is the case in the single junction, we find that the spectrum of applied oscillating electromagnetic fields is renormalized by the same complex-valued factor $\Xi(\omega) = |\Xi(\omega)|\exp i\eta(\omega)$ that modifies the environmental impedance in the $P(E)$ function. This factor acts as a linear response function for applied oscillating electromagnetic fields driving the quantum circuit, leading to a mass gap in the thermal spectrum of the electromagnetic field. The mass gap can be modeled as a pair of exotic particle excitation with quantum statistics determined by the argument $\eta(\omega)$. In the case of the array, this pair corresponds to a bosonic charge soliton/anti-soliton pair injected into the array by the electromagnetic field. Possible application of these results is in dynamical Coulomb blockade experiments where long arrays are used as electromagnetic power detectors.

研究动机与目标

• 将库仑阻塞的$P(E)$理论扩展至包含超小约瑟夫森结中的电磁环境效应。
• 研究振荡电磁场如何在单个结和长阵列中重正化环境阻抗。
• 将由此产生的谱变化建模为电磁场热谱中的能隙。
• 识别在长阵列中由外加场驱动下涌现的奇异准粒子激发——任意任何荷孤子与反孤子。
• 通过长阵列作为电磁功率探测器，实现动态库仑阻塞实验的应用。

提出的方法

• 采用路径积分形式推导单个小约瑟夫森结中的库珀对和BCS准粒子电流。
• 将该形式化方法扩展至将长约瑟夫森结阵列建模为等效单结。
• 引入复值重正化因子$\Xi(\omega) = |\Xi(\omega)|e^{i\eta(\omega)}$，以修改$P(E)$函数中的环境阻抗。
• 将$\Xi(\omega)$视为量子电路中振荡电磁场的线性响应函数。
• 推导出由于该重正化导致的电磁场热谱中的有效能隙。
• 将该能隙识别为一对由$\Xi(\omega)$相位$\eta(\omega)$决定其量子统计特性的奇异粒子激发，解释为阵列中的任意任何荷孤子。

实验结果

研究问题

• RQ1 电磁环境如何在小约瑟夫森结中重正化外加振荡场的谱？
• RQ2 复响应因子$\Xi(\omega)$在修改$P(E)$函数和环境阻抗中的作用是什么？
• RQ3 该重正化如何导致电磁场热谱中出现能隙？
• RQ4 在振荡驱动下，长约瑟夫森结阵列中会涌现出何种奇异准粒子激发？
• RQ5 长约瑟夫森结阵列能否通过动态库仑阻塞作为有效电磁功率探测器？

主要发现

• 电磁环境通过复因子$\Xi(\omega)$诱导外加振荡场谱的重正化，从而修改$P(E)$理论中的$P(E)$函数。
• 该因子$\Xi(\omega)$作为线性响应函数，导致电磁场热谱中出现能隙。
• 能隙对应一对奇异粒子激发，其量子统计特性由$\Xi(\omega)$的相位$\eta(\omega)$决定。
• 在长约瑟夫森结阵列中，这些激发表现为由电磁场注入的任意任何荷孤子-反孤子对。
• 该重正化机制使得长阵列可作为动态库仑阻塞实验中电磁功率的灵敏探测器。
• 该理论框架通过环境诱导重正化的等效单结建模，统一描述了单结与阵列的行为。