[Date] November 28 (Mon) - December 2 (Fri), 2011: [Place] Kyoto University Clock Tower Centennial Hall, Kyoto, JAPA

Anna Leese de Escobar

Berggren, Susan

In, Visarath

Longhini, Patrick

Palacios, Antonio

Kyoto University Research Information Repository

Title<Contributed Talk 25>Modeling Coupled Serial Non-Uniformbi-SQUIDsAuthor(s)Longhini, Patrick; Berggren, Susan; Palacios, Antonio; In,Visarath; Anna Leese de EscobarCitationIUTAM Symposium on 50 Years of Chaos : Applied andTheoretical (2011): 72-73Issue Date2011-12URL http://hdl.handle.net/2433/163124RightType BookTextversionpublisherKyoto UniversityC25 72 IUTAM Symposium on SO Years of Chaos: Applied and Theoretical Kyoto, Japan, November 28- December 2, 2011 Modeling Coupled Serial Non-Uniform hi-SQUIDs Patrick Longhini \Susan Berggren2 , Antonio Palacios2, Visarath In\ Anna Leese de Escobar1 1 Space and Naval Warfare Systems Center, 53560 Hull Street, San Diego, CA 92152-5001, USA. patrick.longhini@navy.mil 2Nonlinear Dynamics Group Department of Mathematics & Statistics San Diego State University, San Diego, CA 92182, USA. In this work we study, analytically and computationally, the behaviour of a non-uniform array of Superconducting Quantum Interference loops with three Josephson Junctions or hi-SQUID [1]. We show that the average voltage response of the coupled system to an external magnetic field is greatly increased compared to that of a single element. The non-uniformity is related to the distribution of loops sizes of each hi-SQUID, which is similar to the SQIF (Superconducting Quantum Interference Filter) design [2]. However, the single hi-SQUID has the ability to improve linearity by tuning t e current across an additional shunting junction. In addition, it has been reported that the SQIF is at least one order of magnitude greater than the values reported for the known SQUIDs [3]. The focus of this work is to investigate in great detail a serially connected hi-SQUID array. Computer simulations confirm that a voltage response with an 'anti-peak' profile can be obtained with high linearity arou d zero flux. Applications of this device include: geological equipment, biomedical equipment such as MRI machines, and applications to homeland defence such as mine detection. Background A basic SQUID is made of two Josephson junctions symme ically connected in a closed loop. A Josephson junction is made by sandwiching a thin layer of a nonsuperconducting material between two layers of superconducting material. The construction of a single hi-SQUID differs from a conventional two-junction de SQUID (junctions J~, J2) by adding a third Josephson junction (J3) as is shown in Figure 1(a). Figure 1 (b) demonstrates that the additional junction (J3) can improve the linearity of the V-B response by choosing an optimal ic3, where ic3 is related to the critical current for junctions J 1 and J2• When operating below the critical temperature the material changes from the normal state, where it has electrical resistance, to the superconducting state, where there is essentially no resistance to the flow of direct electrical current. Detecting and measuring the change from one state to the other is the basic application of Josephson junctions. Readout electronics have used many approaches such as the commonly used flux-locked loop (FLL) and other alternate readouts that seek to improve dynamic range. ·~ . . . ~ .. (a) (b) Figure 1: Single hi-SQUID (a) Schematic diagram of a single hi-SQUID. (b) Average voltage response vs. the external magnetic flux (Fe) and varying the current across the third junction (J3) by the parameter ic3• IUTAM Symposium on 50 Years of Chaos: Applied and Theoretical Kyoto, Japan, November 28 - December 2, 2011 Serial Array of hi-SQUIDs In this research work we demonstrate, through numerical simulations, that there is a significant increase the dynamic range and linearity of the voltage response by using a non-uniform serial hi-SQUID design (shown in Figure l(a)). The main difference from the single hi-SQUID is the mutual inductances between elements. Also, each hi-SQUID element is design with a different loop size (bk) fork= 1, ... , N, where N is the number of elements connected in series. Interestin ly, there exists an optimized value of ic3 (i.e., relation to the current across the third junction J3b fork= 1, ... , N) where the serial hi-SQUID achieves its greatest linearity. Generally, a serial array of N SQUIDs is believed to deliver a significant power increase, such that the dynamic range increase as N 112 • Similarly, serial arrays of hi-SQUIDs can be implemented to not only increase the dynamic range but also to improve the linearity around the anti-peak voltage profile. This 'anti-peak' is useful for readout mechanisms and the device can be used as an absolute magnetometer, i.e., it has the ability to measure the intensity of a magnetic field without reference to other magnetic instruments. If (a) .'.) (b) Figure 2: Serial hi-SQUID (a) Schematic diagram of a serial hi-SQUID. (b) Average voltage response vs. the external magnetic flux (Fe) and varying the current across the third junction (J3) by the parameter ic3• Conclusions We demonstrate numerically the existence of a unique 'anti-peak' at zero magnetic flux by constructing a non-uniform serially connected hi-SQUID array. Essentially, with an optimal distribution of loops sizes and critical current ic3 we can improve the dynamics range and linearity of the device. The array n lead to future improvements for low noise amplifiers (LNA) and electrically small antennas that can provide acceptable gain. Acknowledgements We gratefully acknowledge support from the Office of Naval Research (Code 30). References [1] V.K. Komev, 1.1. Soloviev, N.V. Klenov, and O.A. Mukh nov, Bi-SQUID: a novel linearization method for de SQUID voltage response, Superconductor Science and Technology, VOl 22, Issue 1 , pp. 114011 (2009) [2] Ch. Haussler, J. OppenHinder, and N. Schopohl, Journal of Applied Physics, Vol. 89, Issue 3, pp. 1875-1879 (2001); [3] Shadrin, A.V., Constantinian, K.Y., and Ovsyannikov, G.A.; Techinical Physics Letters; Vol. 33, No.3, pp.192-195 (2007) 73 

<Contributed Talk 25>Modeling Coupled Serial Non-Uniform bi-SQUIDs

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<Contributed Talk 25>Modeling Coupled Serial Non-Uniform bi-SQUIDs

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