Cryogenic Analog Microwave Variable Attenuator Using rf-SQUIDs for Quantum Systems

Abstract

We present the design, fabrication and testing of a low-temperature superconducting (LTS) analog microwave variable attenuator. The two-port circuit includes two <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$90^{\circ }$</tex-math></inline-formula> hybrid couplers and a phase shifter to realize a variable attenuation at the output port. The wideband analog phase shifter is implemented using LTS microstrip transmission line (TL) coupled to an array of radio frequency superconducting quantum interference devices (rf-SQUIDs). The phase shift is achieved by passing a dc current through a TL adjacent to the SQUID-loaded microstrip line which controls the flux through the rf-SQUIDs. The proposed variable attenuator shows more than 30 dB of precise analog flat attenuation tuning range over 8 GHz to 12 GHz with a dc control current ranging from 0 mA to 4.5 mA. The device exhibits a wideband operation with variable attenuation seen not only in the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">X-</i> band but also in <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Ku-</i> band. The device is fabricated using a multilayer niobium-based superconducting process SFQ5ee by MIT Lincoln Laboratory, and has a compact footprint of 1.3 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathrm{mm}^{2}$</tex-math></inline-formula> . To the best of our knowledge, this is the first implementation of a variable attenuator using distributed rf-SQUIDs. This device has implications in a variety of applications such as cryogenic receivers and qubit circuit measurements.