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Frequency-Tunable High-Q Superconducting Resonators Via Wireless Control of Nonlinear Kinetic Inductance

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Frequency-Tunable High-Q Superconducting Resonators Via Wireless Control of Nonlinear Kinetic Inductance Frequency-tunable high-Q superconducting resonators via wireless control of nonlinear kinetic inductance Cite as: Appl. Phys. Lett. 114, 192601 (2019); https://doi.org/10.1063/1.5098466 Submitted: 02 April 2019 . Accepted: 22 April 2019 . Published Online: 13 May 2019 Mingrui Xu, Xu Han, Wei Fu, Chang-Ling Zou , and Hong X. Tang ARTICLES YOU MAY BE INTERESTED IN High-Tc superconducting detector for highly-sensitive microwave magnetometry Applied Physics Letters 114, 192602 (2019); https://doi.org/10.1063/1.5090175 Frequency-tunable superconducting resonators via nonlinear kinetic inductance Applied Physics Letters 107, 062601 (2015); https://doi.org/10.1063/1.4927444 Néel vector reorientation in ferromagnetic/antiferromagnetic complex oxide nanostructures Applied Physics Letters 114, 192403 (2019); https://doi.org/10.1063/1.5094604 Appl. Phys. Lett. 114, 192601 (2019); https://doi.org/10.1063/1.5098466 114, 192601 © 2019 Author(s). Applied Physics Letters ARTICLE scitation.org/journal/apl Frequency-tunable high-Q superconducting resonators via wireless control of nonlinear kinetic inductance Cite as: Appl. Phys. Lett. 114, 192601 (2019); doi: 10.1063/1.5098466 Submitted: 2 April 2019 . Accepted: 22 April 2019 . Published Online: 13 May 2019 . Corrected 1 August 2019 Mingrui Xu,1,a) Xu Han,1,a) Wei Fu,1 Chang-Ling Zou,2 and Hong X. Tang1,b) AFFILIATIONS 1Department of Electrical Engineering, Yale University, New Haven, Connecticut 06520, USA 2Key Laboratory of Quantum Information, University of Science and Technology of China, CAS, Hefei, Anhui 230026, China a)Contributions: M. Xu and X. Han contributed equally to this work. b)Electronic mail: [email protected] ABSTRACT Frequency-tunable microwave resonators are in great demand especially in hybrid systems where precise frequency alignment of resonances is required. Here, we present frequency-tunable high-Q superconducting resonators fabricated from thin niobium nitride and niobium tita- nium nitride films. The resonant frequency is tuned by applying a magnetic field perpendicular to the hole structures in the resonator’s inductor wire, whose kinetic inductance is modified by wirelessly induced DC supercurrents. A continuous in situ frequency tuning of over 300 MHz is achieved for a 10 GHz resonator with a moderate magnetic field of 1.2 mT. The planar resonator design and the noncontact tun- ing scheme greatly ease the fabrication complexity and can be widely applied in many hybrid systems for coupling microwave modes with other forms of excitations such as optical photons, phonons, magnons, and spins. Published under license by AIP Publishing. https://doi.org/10.1063/1.5098466 As an essential building block of future quantum technology, patterned because of their simple geometries and hence are a more superconducting microwave resonators have been extensively studied accessible source of nonlinearity. In addition, they are suitable for for interfacing with other forms of excitations, including phonons,1,2 applications that require larger operating power22 or exposure to larger magnons,3,4 spins,5,6 optical photons,7 and superconducting qubits.8 magnetic fields,21 because superconducting materials of high-kinetic- Such hybrid systems leverage the strength of superconducting circuits inductance wires usually have higher critical temperatures (Tc)than and other quantum systems and thus are considered as a promising most accessible Josephson junctions. Exploiting the current depen- approach toward the realization of scalable quantum networks.9 To dence of kinetic inductance,23 frequency-tunable microwave resona- achieve desired coupling between the microwave mode and other exci- tors have been demonstrated by adding an extra circuit to the tations, fine frequency alignment is routinely required. Hence, fre- resonator for injecting a DC current into the microwires.20,24 The quency tunability of microwave resonators can be of great value. In magnetic field dependence of kinetic inductance has also been utilized addition, frequency-tunable microwave resonators have versatile to enable frequency-tunable microwave resonators.19,21 Typically, to applications in superconducting circuits, such as tunable microwave obtain a wide tuning range, a large magnetic field (100 mT) is filters, microwave parametric amplifiers,10–12 magnetometers,13 and needed.21 microwave storage.14 In this article, we present a junction-free, high-Q supercon- Common approaches to realizing frequency-tunable microwave ducting microwave resonator with a frequency tuning range of resonators include the use of Josephson junctions15–18 and high- 3.5% from 10 GHz. In the presence of a moderate magnetic field kinetic-inductance superconducting wires.19–21 The high nonlinearity on the order of milliTesla, supercurrents are induced around the of Josephson junctions permits the large frequency tuning range. hole structures in the resonator due to the magnetic shielding However, the junctions have limited critical current (typically less than effect of superconductors. These screening currents modify the several microamps) and require a relatively complex fabrication pro- kinetic inductance and hence shift the resonant frequency. Since cess. On the other hand, high-kinetic-inductance wires can be easily the screening currents are generated wirelessly in the resonator Appl. Phys. Lett. 114, 192601 (2019); doi: 10.1063/1.5098466 114, 192601-1 Published under license by AIP Publishing Applied Physics Letters ARTICLE scitation.org/journal/apl without additional DC wire connections, the resonator can main- external magnetic field Bext is applied perpendicular to the device tain a high quality factor (Q factor). This wireless frequency tuning plane, screening DC supercurrents scheme can be applied in different hybrid systems for precise in d situ frequency tuning and alignment. Isc Bext (1) Shown in Fig. 1(a) is the frequency-tunable microwave resonator Lsc named “Ouroboros,” because of its resemblance to a snake biting its will be induced circulating around the holes to expel magnetic flux own tail. Ouroboros has been previously exploited for achieving multi- from penetration [illustrated in Fig. 1(c)]. Here, d denotes the width of mode strong coupling with bulk acoustic modes.2 Thedevicesarefab- each hole, and Lsc is the effective geometric inductance per unit length ricated from two types of superconductors: a niobium titanium nitride à for the circulating DC current Isc.ForsmallIsc ðIsc=I 1Þ,the (NbTiN) film sputtered on a silicon substrate and a niobium nitride kinetic inductance increases with it quadratically26 (NbN) film deposited on a sapphire substrate via atomic layer deposi- "# tion.Bothfilmshavethicknessesof50nanometers.Thedevicepat- 2 I terns are defined by one single e-beam lithography step using a sc ; LkðIscÞLk0 1 þ à (2) hydrogen silsesquioxane (HSQ) resist, followed by chlorine dry etch- I ing. The remaining HSQ mask is removed using diluted buffered oxide à where Lk0 is the kinetic inductance at zero current, and I is a charac- etch. The structure of the Ouroboros can be understood as a planar teristic current on the order of the critical current. When the change of LC resonator—an arc-shaped microwire as the inductor and a disk as inductance is small enough DLk 1 , the resonant frequency f the capacitor [see Fig. 1(b)]. Hence, the resonant frequency is inversely LkþLm c D proportional to the square root of the inductance, which is composed linearly shifts with it, fc À1 DLk . Considering Eqs. (1) and (2),we ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1 fc 2 LkþLm of geometric inductance Lm and kinetic inductance Lk, fc ¼ p . ðLmþLkÞC get While the geometric inductance L is fixed after the device is fabri- m D cated, the kinetic inductance L , originating from the kinetic energy of fc 2 k ÀkBext; (3) electrons, can be tuned by current.23,25 To wirelessly induce DC cur- fc 2 rents in the inductor wire of the Ouroboros, hole structures are pat- 1 Lk0 1 d where k ¼ Ã2 2 . As a result, the Ouroboros resonant fre- 2 Lk0þLm I L terned in the inductor wire [see Fig. 1(a) zoomed-in view]. When an quency can be quadraticallysc tuned by the external magnetic field. It is notable that the wireless-tuning scheme is not unique to the Ouroboros structure. It can be easily adapted in other forms of super- conducting resonators. To characterize the resonance and the frequency tunability, each Ouroboros is inductively coupled to a loop antenna made from a coax- ial cable, for sending in and reading out RF signals [Fig. 2(d)]. A super- conducting coil is placed above the Ouroboros to provide a perpendicular magnetic field. The whole setup is then enclosed in a copper box and soaked in liquid helium (T ¼ 4.2 K) for a low tempera- ture measurement. Reflection spectra (S11) of an Ouroboros at differ- ent external magnetic fields are shown in Fig. 2(a). Each Lorenztian shaped dip marks the Ouroboros resonant frequency at a magnetic field. When the magnetic field increases from 0 to 1.2 mT, a continu- ous frequency tuning of 350 MHz from a 10.6 GHz resonance is achieved. The relative frequency tuning and the intrinsic Qin of a set of different devices are shown in Fig. 2(b).Alargerelativetuningrange above 3% is obtained for both devices made from NbN and NbTiN films. Each frequency tuning curve shows a good quadratic depen- dence on the magnetic field Bext, as suggested by Eq. (3). The intrinsic Qin measured at 4.2 K is on the order of a few thousands without sig- nificant deterioration in the presence of the magnetic field. By comparing the tunability of five otherwise identical devices with different hole widths [see curves #1–#5 in Fig. 2(b)], it is evident that a larger hole width leads to more efficient frequency tuning. FIG. 1. (a) Optical micrograph of a tunable Ouroboros resonator with design Compared to the device with hole width d ¼ 10 lm, it takes 5 times parameters labeled in the zoomed-in view on the right. (b) Equivalent circuit less magnetic field for the device with d ¼ 50 lm to obtain the same of the tunable Ouroboros resonator, whose inductance is constituted of both resonant frequency shift of 3%.
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