Frequency spectrum of a superconducting metadevice

We report on a systematic analysis of the frequency spectrum of a system often considered for quantum computing purposes, metadevice applications, and high-sensitivity sensors, namely a superconducting loop interrupted by Josephson junctions, the core of an rf-SQUID. We analyze both the cases in which a single junction closes the superconducting loop and the one in which the single junction is replaced by a superconducting interferometer. Perturbation analysis is employed to display the variety of the solutions of the system and the implications of the results for the present interest in fundamental and applied research are analyzed. Copyright c © EPLA, 2016 Introduction. – Research on metamaterials and metadevices is receiving much attention from both fundamental science and applications [1,2]. The “functional” features of devices when these are thought to perform specific tasks in response to electromagnetic stimuli, are particularly rich in their required multi-disciplinary understanding. Excellent reviews covering several aspects of the developments of this new topic have already appeared [3,4]. Condensed-matter systems which could operate at specific electromagnetic wavelengths performing particular operations occupy a somewhat privileged role and, within this framework, superconducting systems have already been considered by several groups [5,6]. Josephson junction systems, having the ability to provide active response in a continuum range of wavelengths in the microwave and millimeter wave range of the electromagnetic spectrum, have been considered [7] due to the inherent ac-Josephson relationship, which uniquely relates frequency (ν) to voltage V , namely hν = 2eV , where h is Planck’s constant and e the elementary charge. The ratio h/2e = Φ0 = 2.07× 10−15 Wb is the flux quantum [8]. A superconducting loop interrupted by a Josephson junction, the core of the rf-SQUID [8], is a system combining two fundamental phenomena in superconductivity, (a)Also at: CNR-SPIN Institute Genova, Italy. namely flux quantization and Josephson effect; these loops have been extensively investigated since the discovery of the Josephson effect [8]. An rf-SQUID core exploits the Josephson sensitivity to the electromagnetic field thereby achieving unprecedented magnetic-flux sensitivities. Today’s rf-SQUID relies just on a superconducting ring made by planar thin films interrupted by a tunnel junction, a device which is not beyond the reach of contemporary medium-level technological facilities. The interest for the rf-SQUID core, relevant in macroscopic quantum tunneling [9], in quantum computation [10] and metamaterial research [6], has often required operation of the system under the application of external microwaves, or pulsed-microwave bursts, and we believe that is relevant for tracing a detailed spectrum of proper modes in the system. Our analysis will be carried out in two steps: in the next section we trace the properties of a superconducting loop interrupted by a single Josephson junction while in the third section we analyze the case in which the single Josephson junction of the loop is replaced by a two-junction interferometer. This system was first investigated by Blackburn and Smith [11] and then taken as a basis for barrier-modulated Josephson macroscopic quantum tunneling devices [12,13]. Metadevice applications based on rf-SQUIDs, and two-dimensional arrays of rf-SQUIDs cores, have been recently reported [14].