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SQUIDs as tunable inductors integrated in the design of filters

Raihan Rafique, Thomas Ohki, Anna Yurievna Herr

Published Jan 1, 2007• 0 citations
OpenAlex

Abstract

This work presents the dc-SQUID based tunable inductance and its relevance into the design of resonators and filters for the qubit application. The SQUID inductance depends on loop inductance, applied magnetic field and bias\ncurrent for a given thermal noise. Tunable resonators and\nfilters have been designed by replacing the inductances of the resonator with a chain of SQUIDs in series. A narrow bandpass filter with variable central frequency is useful for superconducting qubit applications, specifically for improving the line widths of Josephson junction oscillators. We have designed a tunable 3.5 GHz resonator and 2 GHz 7 stage Chebyshev filters to be fabricated in Hypres 4.5 kA/cm2 process. According to simulations, up to 50% of the operating frequency of the designed filter can be varied. We present data that shows a frequency tuning of >2 GHz.

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中国物理B：英文版•Jan 1, 2012•0 citations
This work presents the dc-SQUID based tunable inductance and its relevance into the design of resonators and filters for the qubit application. The SQUID inductance depends on loop inductance, applied magnetic field and bias\ncurrent for a given thermal noise. Tunable resonators and\nfilters have been designed by replacing the inductances of the resonator with a chain of SQUIDs in series. A narrow bandpass filter with variable central frequency is useful for superconducting qubit applications, specifically for improving the line widths of Josephson junction oscillators. We have designed a tunable 3.5 GHz resonator and 2 GHz 7 stage Chebyshev filters to be fabricated in Hypres 4.5 kA/cm2 process. According to simulations, up to 50% of the operating frequency of the designed filter can be varied. We present data that shows a frequency tuning of >2 GHz.
A superconductor bandpass filter with tunable central frequency in the range of 2-3.5 GHz has been implemented using superconducting quantum interference devices (SQUIDs). The filter is designed using two pi-network resonators connected by a transmission line. Both resonators have a SQUID inductor with a tuning range of 65-200 pH, controlled by current magnetically coupled to the SQUIDs. Over a frequency tunability of 1.5 GHz, the filter has a mid-band insertion loss of 0.5-3.0 dB and corresponding maximum unloaded quality factor of 40. Due to the presence of active elements, tunability of the filter depends on the power of the microwave signal. A maximum power of -52 dBm corresponds to a frequency tuning range of 15%. Spectral measurements by controlling the central frequency of the filter with variable pulsewidth shows that the filter can be tuned at a rate of 120 GHz/mus.
In this licentiate thesis design, fabrication, and measurements of tunable superconducting microwave transmission line resonators are described. The resonators are of quarter wavelength type were the tuning is achieved by changing one of the boundary conditions of the resonator through a tunable impedance. As tunable impedance the Josephson inductance in form of SQUIDs is used. The Josephson inductance can then be tuned by applying a magnetic field to the SQUID loop. A tuning range of 750 MHz for a 5 GHz resonator is achieved, and as a figure of merit it can be tuned over 200 line widths. The purpose of the tunable resonators is to use them for dynamic coupling of superconducting quantum bits, this requires that the resonators can be tuned fast on the timescale of the resonator-qubit coupling. To measure tuning speeds faster then the ring up time of the resonators a method that measures the leakage of energy out of a detuned resonator was developed. With this method a frequency shift of the energy stored in the resonator can be measured. A detuning of 330 MHz in less than 10 ns is demonstrated for a 4.5 GHz resonator with a quality factor of 104^44. Working in the few photon limit indicates that the devices can be used to change the frequency of individual photons, this is however still to be demonstrated. As a part of this work the dressed states of a superconducting charge qubit was also studied.
We describe the design of an inductor-capacitor (LC) network to increase the isolation of a dc SQUID phase qubit from its current bias leads and thereby increase the relaxation time T1and coherence time T2. One junction in the SQUID acts as an ideal phase qubit while the second junction and the SQUID loop inductance act as a broadband inductive filter to isolate the first junction from the current bias leads. The LC isolation network provides an additional isolation factor at the junction plasma frequency and allows flexibility in the choice of SQUID parameters. Our thin-film on-chip LC isolation network has a 10 nH inductor and an 80 pF capacitor. The combination of the broadband filter and LC filter provides a maximum nominal isolation factor of about 108at a qubit plasma frequency of about 6.7 GHz. To reduce dielectric loss and two level systems in the qubit junction, we use a relatively small area (4 mum2) Al/AlOx/Al qubit junction built on sapphire and add an external capacitor with 100 nm thick SiNxdielectric layers. Measurements revealed Rabi oscillations with an envelope decay time constant of about 42 ns, and an energy relaxation time of 32 ns, consistent with a loss tangent tan(delta)=7times10-4in the SiNx.
We study the microwave properties of a superconducting tunable coplanar waveguide (CPW). Pairs of Josephson junctions are forming superconducting quantum interference devices (SQUIDs), which shunt the central conductor of the CPW. The Josephson inductance of the SQUIDs is varied in the range of 0.08–0.5 nH by applying a dc magnetic field. The central conductor of the CPW contains Josephson junctions connected in series that provide extra inductances; the magnetic field controlling the SQUIDs is weak enough not to influence the inductance of the chain of the single junctions. The circuit is designed to have left- and right-handed transmission properties separated by a variable rejection band; the band edges can be tuned by the magnetic field. We present transmission measurements on CPWs based on up to 120 Nb–AlO x –Nb Josephson junctions. At zero magnetic field, we observed no rejection band in the frequency range of 8–11 GHz. When applying the magnetic field, a rejection band between 7 GHz and 9 GHz appears. The experimental data are compared with numerical simulations.
We propose a scheme of tunable coupler based on quarter-wave resonator for scalable quantum integrated circuits. The open end of the T-type resonator is capacitively coupled to two Xmon qubits, while another end is an asymmetric dc-SQUID which dominates the inductive energy of coupler resonator. The dc-Current applied through the flux bias line could change the magnetic flux inside the dc-SQUID, so the frequency of coupler resonator can be effectively tuned and the qubit-qubit coupling can be totally switched off. As the increase of junction asymmetry for the dc-SQUID, the coupling of SQUID's effective phase difference and cavity modes become smaller at required working frequency regime of coupler resonator, and this could reduce the descent of the resonator's quality factor. The separation between two cross-capacitor can be larger with help of transverses width of the T-shape resonator, and then the ZZ crosstalk coupling can be effectively suppressed. The asymmetric dc-SQUID is about 5 millimeters away from the Xmon qubits and only needs a small current on the flux bias line, which in principle creates less flux noises to superconducting Xmon qubits.
We present the design of a superconducting flux qubit with a large loop inductance. The large loop inductance is desirable for coupling between qubits. The loop is configured into a gradiometer form that could reduce the interference from environmental magnetic noise. A combined Josephson junction, i.e., a DC-SQUID is used to replace the small Josephson junction in the usual 3-JJ (Josephaon junction) flux qubit, leading to a tunable energy gap by using an independent external flux line. We perform numerical calculations to investigate the dependence of the energy gap on qubit parameters such as junction capacitance, critical current, loop inductance, and the ratio of junction energy between small and large junctions in the flux qubit. We suggest a range of values for the parameters.