Microwave Characterization of Josephson Junction Arrays: Implementing a Low Loss Superinductance

Nicholas A. Masluk, Ioan M. Pop, Archana Kamal, Zlatko K. Minev, and Michel H. Devoret

Phys. Rev. Lett. 109, 137002 – Published 27 September 2012

Abstract

We have measured the plasma resonances of an array of Josephson junctions in the regime $E_{J} ≫ E_{C}$ , up to the ninth harmonic by incorporating it as part of a resonator capacitively coupled to a coplanar waveguide. From the characteristics of the resonances, we infer the successful implementation of a superinductance, an electrical element with a nondissipative impedance greater than the resistance quantum [ $R_{Q} = h / (2 e)^{2} ≃ 6.5 k Ω$ ] at microwave frequencies. Such an element is crucial for preserving the quantum coherence in circuits exploiting large fluctuations of the superconducting phase. Our results show internal losses less than 20 ppm, self-resonant frequencies greater than 10 GHz, and phase-slip rates less than 1 mHz, enabling direct application of such arrays for quantum information and metrology. Arrays with a loop geometry also demonstrate a new manifestation of flux quantization in a dispersive analog of the Little-Parks effect.

Received 21 June 2012

DOI:https://doi.org/10.1103/PhysRevLett.109.137002

Authors & Affiliations

Nicholas A. Masluk^*, Ioan M. Pop, Archana Kamal, Zlatko K. Minev, and Michel H. Devoret

Department of Applied Physics, Yale University, 15 Prospect Street, New Haven, Connecticut 06511, USA

^*nicholas.masluk@yale.edu

Quantum Superinductor with Tunable Nonlinearity

M. T. Bell, I. A. Sadovskyy, L. B. Ioffe, A. Yu. Kitaev, and M. E. Gershenson

Phys. Rev. Lett. 109, 137003 (2012)

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Vol. 109, Iss. 13 — 28 September 2012

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Images

Figure 1
(a) Schematic representation of an array of Josephson junctions. Capacitances of islands to ground and across tunnel junctions are denoted with $C_{0}$ and $C_{J}$ , respectively. The junction inductance is given by $L_{J}$ . (b) SEM image of the Josephson junction array fabricated using the bridge-free technique [20, 21]. (c) Optical image of an $L C$ resonator. The large pads implement the resonator capacitance as well as coupling capacitances to the coplanar waveguide feedline. An array of Josephson junctions between the pads implements the superinductance. The ground plane is patterned with flux-trapping holes. (d) Low-frequency model for the device shown in (c). The phase-slip element (split diamond) in series with the superinductance represents the collective contribution of phase slips through all junctions in the array. The characteristic energy of the phase-slip element is denoted by $E_{S}$ .Reuse & Permissions
Figure 2
(a) Typical microwave transmission data for an 80-junction resonator measured with order one photon circulating power; the solid line is the theoretical prediction corresponding to $Q_{int} > 37 000$ . Inset: Temperature dependence of the internal quality factor of the resonator. The dashed line is a guide for the eye. (b) Same measurement as in (a) for a 160-junction array loop; the solid line corresponds to $Q_{int} > 56 000$ . Parameters for the low-frequency model in Fig. 1d are $C_{c} = 1.6 fF$ , $C_{R} = 7.2 fF$ , and $L_{R} = 150 nH$ for (a) and $C_{c} = 1.8 fF$ , $C_{R} = 11 fF$ , and $L_{R} = 76 nH$ for (b).Reuse & Permissions
Figure 3
(a) Shift of the lowest frequency mode of the 80-junction resonator upon application of a probe tone. Because of the weak nonlinearity of the array (theory predicts of order $10 MHz / photon$ [33]), shifts occur when the probe tone matches a plasmonic resonance of the array (marked with red arrows). (b) Measured plasma mode frequencies of the 80-junction array: The blue square represents the fundamental resonant frequency of the resonator (4.355 GHz), and red circles indicate the plasma modes pointed out by red arrows in (a). The black crosses denote the calculated plasma frequencies. The gray curve represents the dispersion relation without including corrections due to the coupling capacitors (open boundary conditions), and markers show corresponding plasma frequencies. The inset in (b) shows the voltage profile along the array for the first three plasma modes.Reuse & Permissions
Figure 4
(a) Lowest mode frequency versus applied flux bias for resonator with 160-junction array loop. Flux bias is swept up and down over the course of several hours. Gray curves represent quasiclassical predictions for resonator frequencies at different integer values of flux quanta in the array loop. The only adjustable parameter is the number of junctions, found to be $150 \pm 10$ . (b) Same measurement as in (a) over a smaller flux range, but before each measurement a high power pulse at one of the plasma modes is applied in order to reset the resonator to the lowest flux state.Reuse & Permissions

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