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

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/(2e)(2) is approximately equal to 6.5 kΩ] 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.

Collective modes in the fluxonium qubit

“…[18], the ground capacitance C a g we estimate here is about three times bigger. Since the calculations throughout the paper are based on the original estimate of [18], they could underestimate, e.g., the dispersive shifts and the decay rates by almost one order of magnitude; we will return to this point when estimating the dephasing rate in Sec. VIII.…”

“…For example, in Ref. [18] an array of 80 junctions was placed in parallel to a (resonator) capacitor and the 9 lowest resonant frequencies were measured. The system is described by the Hamiltonian H in Eq.…”

“…More recently, renewed attention has been given to the physics of collective modes, whose frequency can be significantly lowered below the constituent Josephson junctions plasma frequency due to ground capacitances; in particular, the interplay between collective modes and quantum * g.catelani@fz-juelich.de phase slips in rings has been studied [14][15][16], as well as the localizing effect of disorder in the junction parameters [17]. Long junction arrays can have a large inductance, proportional to the number of elements, and for quantum computation applications such superinductors [18] have been proposed as elements of topologically protected qubits [19], for example, the 0-π qubit [20,21]. An alternative design for a superinductor has also been realized [22] and recently implemented in a qubit circuit [23].…”

Approaching ultrastrong coupling in transmon circuit QED using a high-impedance resonator

“…Moving to a λ/4 resonator makes the current architecture sufficient in terms of resonator impedance. The impedance could be further increased using a high kinetic inductance based resonator [42] or by using an array of Josephson junctions [43].…”

Phase sticking in one-dimensional Josephson junction chains

“…Recently it was demonstrated that chains in this regime can be used as so called superinductors which have a high frequency impedance much larger than the quantum resistance 19,20 . There have been several successful experiments of the observation of quantum phase-slips in chains with large Josephson energy 21,22 .…”