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IEEE Transactions on Applied Superconductivity

The effect of mutual coupling between RF SQUID's in distributed Josephson inductance phase shifters

Willem Jakobus Perold

Published Jan 1, 1994• 1 citation
Publisher

Abstract

A brief overview of the principles behind the behavior of the recently reported distributed Josephson inductance phase shifter is given. Simulation results of a typical phase shifter are presented. A model for the mutual flux coupling between adjacent RF SQUID sections is derived and the results are used to predict the effect of the coupling on the phase shift of the device. Distortion of the output signal is related to the time variation of the dynamic inductance of the transmission line.>

DOI
10.1109/77.317836

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A brief overview of the principles behind the behavior of the recently reported distributed Josephson inductance phase shifter is given. Simulation results of a typical phase shifter are presented. A model for the mutual flux coupling between adjacent RF SQUID sections is derived and the results are used to predict the effect of the coupling on the phase shift of the device. Distortion of the output signal is related to the time variation of the dynamic inductance of the transmission line.>
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We implement a broadly tunable phase shifter for microwaves based on superconducting quantum interference devices (SQUIDs) and study it both experimentally and theoretically. At different frequencies, a unit transmission coefficient, |S21| = 1, can be theoretically achieved along a curve where the phase shift is controllable by the magnetic flux. The fabricated device consists of three equidistant SQUIDs interrupting a transmission line. We model each SQUID embedded at different positions along the transmission line with two parameters, capacitance and inductance, the values of which we extract from the experiments. In our experiments, the tunability of the phase shift varies from 0.07 × π to 0.14 × π radians along the full-transmission curve with the input frequency ranging from 6.00 GHz to 6.28 GHz. The reported measurements are in good agreement with simulations, which is promising for future design work of phase shifters for different applications.
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Radio frequency superconducting quantum interferometers (RF-SQUIDs) are structural elements of nonlinear media used in superconducting metamaterials and superconducting low-noise parametric amplifiers. An expression for the effective Josephson inductance as a function of the external microwave signal power in a two-tone excitation mode is derived. This formula is applied to calculate the effective inductance of a Josephson junction embedded in an RF-SQUID under microwave radiation. The analytically calculated dependences of the resonant frequency and effective Josephson inductance of a non-hysteresis RF-SQUID on microwave power are in good agreement with experimental results.
We introduce a magnetic-flux-tunable phase shifter for propagating microwave photons, based on three equidistant superconducting quantum interference devices (SQUIDs) on a transmission line. We experimentally implement the phase shifter and demonstrate that it produces a broad range of phase shifts and full transmission within the experimental uncertainty. Together with previously demonstrated beam splitters, this phase shifter can be utilized to implement arbitrary single-qubit gates for qubits based on propagating microwave photons. These results complement previous demonstrations of on-demand single-photon sources and detectors, and hence assist in the pursuit of an all-microwave quantum computer based on propagating photons.
We realize tunable coupling between two superconducting transmission line resonators. The coupling is mediated by a non-hysteretic rf SQUID acting as a flux-tunable mutual inductance between the resonators. We present a spectroscopic characterization of the device. In particular, we observe couplings g/2πg/2\pig/2π ranging between −320 MHz and 37 MHz. In the case of g≃0g \simeq 0g≃0 , the microwave power cross transmission between the two resonators is reduced by almost four orders of magnitude as compared to the case where the coupling is switched on.