Tunable and switchable coupling between two superconducting resonators

A. Baust, E. Hoffmann, M. Haeberlein, M. J. Schwarz, P. Eder, J. Goetz, F. Wulschner, E. Xie, L. Zhong, F. Quijandría, B. Peropadre, D. Zueco, J.-J. García Ripoll, E. Solano, K. Fedorov, E. P. Menzel, F. Deppe, A. Marx, and R. Gross

Phys. Rev. B 91, 014515 – Published 30 January 2015

Abstract

We realize a device allowing for tunable and switchable coupling between two frequency-degenerate superconducting resonators mediated by an artificial atom. For the latter, we utilize a persistent current flux qubit. We characterize the tunable and switchable coupling in the frequency and time domains and find that the coupling between the relevant modes can be varied in a controlled way. Specifically, the coupling can be tuned by adjusting the flux through the qubit loop or by controlling the qubit population via a microwave drive. Our measurements allow us to find parameter regimes for optimal coupler performance and quantify the tunability range.

Received 8 May 2014
Revised 12 November 2014

DOI:https://doi.org/10.1103/PhysRevB.91.014515

Authors & Affiliations

A. Baust^1,2,3,*,†, E. Hoffmann^1,2,†, M. Haeberlein^1,2, M. J. Schwarz^1,2,3, P. Eder^1,2,3, J. Goetz^1,2, F. Wulschner^1,2, E. Xie^1,2,3, L. Zhong^1,2,3, F. Quijandría⁴, B. Peropadre^5,6, D. Zueco^4,7, J.-J. García Ripoll⁵, E. Solano^8,9, K. Fedorov^1,2, E. P. Menzel^1,2, F. Deppe^1,2,3, A. Marx¹, and R. Gross^1,2,3,‡

¹Walther-Meißner-Institut, Bayerische Akademie der Wissenschaften, D-85748 Garching, Germany
²Physik-Department, Technische Universität München, D-85748 Garching, Germany
³Nanosystems Initiative Munich (NIM), Schellingstraße 4, 80799 München, Germany
⁴Instituto de Ciencia de Materiales de Aragón and Departamento de Física de la Materia Condensada, CSIC–Universidad de Zaragoza, 50009 Zaragoza, Spain
⁵Instituto de Fisica Fundamental, IFF-CSIC, Calle Serrano 113b, Madrid E-28006, Spain
⁶Department of Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts 02138, United States
⁷Fundación ARAID, Paseo María Agustín 36, 50004 Zaragoza, Spain
⁸Department of Physical Chemistry, University of the Basque Country UPV/EHU, Apartado 644, E-48080 Bilbao, Spain
⁹IKERBASQUE, Basque Foundation for Science, Maria Diaz de Haro 3, 48013 Bilbao, Spain

^*alexander.baust@wmi.badw-muenchen.de
^†A.B. and E.H. contributed equally to this work.
^‡rudolf.gross@wmi.badw-muenchen.de

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Vol. 91, Iss. 1 — 1 January 2015

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Images

Figure 1
(a) False-color image of the sample. Nb ground planes are shown in blue and feed lines in orange. The resonator signal lines reside along the ground plane edges. (b) Coupling capacitor defining the resonators. (c) Resonator coupling area with signal lines (green) and flux qubit (red). Light (dark) green stripes highlight Nb-Al overlap areas. (d) Flux qubit galvanically coupled to both resonators. (e) ${Al/AlO}_{x} / Al$ Josephson junction fabricated using shadow evaporation. (f) Working principle of the coupler and measurement setup.
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Figure 2
(a) Transmission through one resonator depending on the applied magnetic flux with the qubit in the ground state. (b) Cross measurement, with the qubit in the ground state. (c) Through measurement, with the qubit driven with a strong excitation signal. (d) Through measurement, with transmission at the frequency of the lower mode at 4.888 GHz [dashed lines in (a) and (c)] with the qubit in the ground state (blue line) and a saturated qubit (red line). Dashed black lines, switch setting conditions. (e) As (d) for the cross measurement. (f) Magnitude of the total coupling between the resonators extracted from a through measurement near the switch setting condition. Black, qubit in ground state; red, saturated qubit. Inset: Measurement with increased flux resolution around the switch setting condition.
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Figure 3
(a) Pulse pattern for the time-domain probe of the coupler. (b) Typical measured time traces of the output signals of the two resonators. The qubit drive pulse is strong enough to saturate the qubit. Blue, through transmission measurement; red cross transmission measurement. The power levels are referred to the insides of the resonators, i.e., they are scaled such that they are equal when the coupling is on. This assumption is justified because $g_{AB} ≫ γ_{A}, γ_{B}$ . (c) As (b) for intermediate qubit drive pulse power. (d) As (b) for small drive pulse power. (e) Switching efficiency $η$ as a function of the mean resonator drive. (f) Total resonator-resonator coupling as a function of the qubit drive power (referenced to signal generator output) measured for three different resonator populations. The points of the red curve at $- 20$ , $- 24$ , and $- 30 dBm$ are derived from the data of (b), (c), and (d), respectively.
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Figure 4
Two-tone spectroscopy of the sample. The switch modes ${\hat{c}}_{+}$ and ${\hat{c}}_{-}$ and an additional mode $\hat{u}$ at $4.5 GHz$ can be identified. At $ω_{4} / 2 π = 13.1 GHz$ and $ω_{5} / 2 π = 14.3 GHz$ the third harmonics $\hat{v}$ and $\hat{w}$ of these modes are observed.
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Figure 5
Transmission through one resonator as shown in the main text. Dashed lines: Fit of the complete Hamiltonian (A1) to the data.
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