Simulation and visualization of the interference phenomena inside DC SQUID with interferometric circuit model
Introduction
Direct Current Superconducting Quantum Interference Device (DC SQUID) is an extreme sensitive flux-to-voltage convertor [1], which is essential for the subtle magnetic field measurements, such as biomagnetism [2]. A typical niobium-based low-Tc DC SQUID is shown in Fig. 1, where, two resistively-shunted Josephson junctions are connected with a top-layer strip, and grounded with the bottom-layer plate, forming a superconducting loop coupled with the external flux Φe. It is working as a superconducting interferometer with two correlated Josephson junctions as oscillators [3, 4], which fundamental oscillation frequency fosc is proportional to the DC voltage VS measured at SQUID terminals, i.e., fosc = VS/Φ0 (Φ0 = 2.07 × 10−15 Wb). The internal superconducting quantum interference phenomena inside DC SQUID result in the flux-modulated I-V characteristics, based on which, SQUID achieves the flux-to-voltage characteristic. The interferometric working principle indicates that DC SQUID is a microwave integrated circuit working in Alternating Current (AC) mode, rather than a conventional DC electronic device.
However, the concept of AC microwave interferometric circuit of DC SQUID is not well interpreted. Firstly, DC characteristics instead of the AC characteristics are concerned. Both theoretical and experimental researches emphasize on the static current-voltage characteristics other than the AC characteristics for most of DC SQUID applications [5], [6], [7], [8], users are inclined to treat SQUID with concept of DC transducer like the semiconductor transistors. The second reason is that the conventional lumped-parameter circuit models neglect the geometric information inside SQUID. The interferometric working principle is neither to be demonstrated directly trough measuring the AC characteristic inside SQUID washer nor to be intuitively simulated with the lumped-parameter equivalent circuit, which geometric information is ignored. Three-Dimension (3D) numerical electromagnetic field calculation method is one of the solutions to extract the AC characteristics inside SQUID washer [9, 10], but the simulation will be complicated taking the Josephson equations into consideration.
AC microwave circuit concept of DC SQUID should be emphasized to improve the understandings of its interferometric dynamics and the AC characteristics. This concept can remind the SQUID designers to pay more attention to the microwave circuit design rules in deal with the peripheral coupled coils, which parasitic capacitance and inductance are vital to the macroscopic characteristics [11, 12], and help SQUID users gain more insights to cope with the Electromagnetic Interference (EMI) challenges in practical applications [13, 14].
Therefore, to revisit the interferometric working principle of DC SQUID, we will visualize the interference phenomena through simulations of AC characteristic inside DC SQUID. We will firstly present the equivalent circuit of DC SQUID in form of the microwave interferometer, and then illustrate its interference mechanism with a concise dynamic system model. Finally, the simulation results of AC current and voltage distributions inside SQUID washer are presented and discussed.
Section snippets
Equivalent circuit
In DC SQUID, two Josephson junctions are working as the active oscillators, since the Josephson current inside is the source of oscillation according to the theory of the Josephson's effect [15]. Therefore, we redraw the equivalent circuit of DC SQUID in from of interferometer as shown in Fig. 2a, where, the top layer of SQUID washer shown in Fig. 1 is straightened to a one-dimension superconductor strip by separating two Josephson junctions apart; the Josephson junction driving in each end is
DC characteristics
Based on the dynamic system model, we firstly simulated the static current-voltage and flux-to-voltage characteristics of a typical symmetric DC SQUID as shown in Fig. 4. The SQUID parameters used in simulations are shown in Table 1.
Fig. 4a shows the typical flux-modulated current-voltage characteristics of a symmetric DC SQUID. In this result, uS is the normalized DC voltage VS measured at its terminal which position x=0.5, thus, uS = AVG(ux(0.5,t)) is calculated from the real-time response of
Discussion
Our interferometric circuit and its dynamic system model implement the numerical simulations of both the real-time responses of circuit elements and the geometric interference distributions. The interferometer working principle and the interference phenomena inside DC SQUID are demonstrated and visualized intuitively with simulation results.
Firstly, the interferometric circuit model exhibit the interference working principle inside the DC SQUID using the double-slit interference as reference.
Conclusion
We reconstructed the equivalent circuit of DC SQUID in form of the microwave interferometer by modeling the Josephson junctions as the microwave oscillators, and simulated its working principle with a concise dynamic system model. The reconfigured interferometric circuit and its graphic dynamic system model are intuitive to improve the understanding of DC SQUID working as the microwave interferometer.
Through calculations of AC current and voltage distribution inside the SQUID washer, we
Author statement
I have made substantial contributions to the conception and design of the work; and the acquisition, analysis of data for the work.
I have drafted the work and revised it critically for important intellectual content; and I have approved the final version to be published.
I agree to be accountable for all aspects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved.
All persons who have made substantial
Declaration of Competing Interest
We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted.
Acknowledgements
This work was supported by National Natural Science Foundation of China under Grant 61701486.
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