We investigate the coupling factor φ _µ that quantifies the magnetic flux Φ per magnetic moment µ of a point-like magnetic dipole that couples to a superconducting quantum interference device (SQUID). Representing the dipole by a tiny current-carrying (Amperian) loop, the reciprocity of mutual inductances of SQUID and Amperian loop provides an elegant way of calculating ϕμ(r,eˆμ) vs. position r and orientation eˆμ of the dipole anywhere in space from the magnetic field BJ(r) produced by a supercurrent circulating in the SQUID loop. We use numerical simulations based on London and Ginzburg–Landau theory to calculate φ _µ from the supercurrent density distributions in various superconducting loop geometries. We treat the far-field regime ( r≳a= inner size of the SQUID loop) with the dipole placed on (oriented along) the symmetry axis of circular or square shaped loops. We compare expressions for φ _µ from simple filamentary loop models with simulation results for loops with finite width w (outer size A > a), thickness d and London penetration depth λ _L and show that for thin ( d≪a ) and narrow (w < a) loops the introduction of an effective loop size aeff in the filamentary loop-model expressions results in good agreement with simulations. For a dipole placed right in the center of the loop, simulations provide an expression ϕμ(a,A,d,λL) that covers a wide parameter range. In the near-field regime (dipole centered at small distance z above one SQUID arm) only coupling to a single strip representing the SQUID arm has to be considered. For this case, we compare simulations with an analytical expression derived for a homogeneous current density distribution, which yields excellent agreement for λL>w,d . Moreover, we analyze the improvement of φ _µ provided by the introduction of a narrow constriction in the SQUID arm below the magnetic dipole.

中文翻译：

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磁矩与超导量子干涉装置的耦合

我们研究耦合因子φ _µ 量化每个磁矩的磁通量 Φµ与超导量子干涉装置（SQUID）耦合的点状磁偶极子。通过微小的载流（安培）环路来表示偶极子，SQUID 和安培环路的互感互感提供了一种优雅的计算方法 φμ（r,e^μ） 与位置 r 和方向 e^μ 空间中任意位置的偶极子的磁场 乙J（r） 由 SQUID 回路中循环的超电流产生。我们使用基于 London 和 Ginzburg-Landau 理论的数值模拟来计算φ _µ 来自各种超导回路几何形状的超电流密度分布。我们对待远场制度（ r≳A= SQUID 环的内部尺寸），偶极子放置在（沿）圆形或方形环的对称轴上。我们比较表达式φ _µ 来自简单的丝状环路模型以及有限宽度环路的模拟结果w（外部尺寸A > A）， 厚度d和伦敦渗透深度λ _L并表明对于薄 ( d≪A ）和狭窄（w < A) 循环引入有效循环大小 A有效值 丝状环模型表达式中的结果与模拟结果非常一致。对于放置在环路中心的偶极子，模拟提供了一个表达式 φμ（A,A,d,λL） 涵盖了广泛的参数范围。在近场区域（偶极子以小距离为中心z在一个 SQUID 臂上方），只需考虑与代表 SQUID 臂的单个条带的耦合。对于这种情况，我们将模拟与针对均匀电流密度分布导出的解析表达式进行比较，这与以下结果非常吻合： λL>w,d 。此外，我们还分析了改进φ _µ 通过在磁偶极子下方的 SQUID 臂中引入狭窄的收缩来提供。