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arXiv:1309.7557 · Superconductor Science and Technology

Design and experimental study of superconducting left-handed transmission lines with tunable dispersion

Е. А. Овчинникова, S. Butz, P. Jung, V. P. Koshelets, Lyudmila V. Filippenko, Alexander S. Averkin, S. V. Shitov, Alexey Vladimirovich Ustinov

Published Oct 7, 2013• 16 citations
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Abstract

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.

DOI
10.1088/0953-2048/26/11/114003

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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.
To control phase velocity in superconducting transmission lines using short electrical pulses, a few approaches are being developed. A new design is developed for left-to-right (L2R) and right-to-left (R2L) tunable transmission lines based on a CPW with embedded paired resonators containing dc-SQUIDs. Experimental layouts are designed according to rules of 2-μm Nb-Al/AlOx-Nb technology for Jc≈ 0.1 kA/cm2and compared numerically with a scheme-model containing 40 cells at frequencies up to 20 GHz. Characteristic impedance of new dispersive transmission lines is increased above 30 Ohm; a thin-film attenuator is integrated for suppression of standing waves. A stop-band is found for R2L line demonstrating slower phase velocity; this transmission gap is due to effect of shorter wavelength (up to 100 times) reaching electrical length of the paired resonators cell (70 μm). In case of L2R line with faster phase velocity, the transmission band can be almost flat, if simultaneous tuning of frequency for all paired resonators is provided. No negative phase velocity is found in the simulations; however, the increment of differential phase velocity is positive for R2L near edge of the stop-band and negative near the resonance for L2R case.
Left-handed (LH) superconducting transmission lines, built with series capacitors and shunt inductors instead of the series inductors and shunt capacitors of a conventional right-handed (RH) line, have a spectrum with a nonzero lower band edge and modes that become sparse at high frequencies. We study the dynamical Casimir effect in a LH line terminated by a flux-modulated SQUID and compare it with an RH line built from the same elements and with a long coplanar waveguide terminated by the same SQUID. We derive the quantum Hamiltonian and show that the coupling between two modes factorizes into their amplitudes at the SQUID. Together, the LH spectrum and the mode dependence of this coupling determine which modes are populated and how fast. With equal elements, the LH coupling grows with frequency and exceeds the RH one above a crossover pump frequency set by the cell inductance and capacitance, and only the LH line has resonances above the RH band edge. Pumping two modes at once lets a weakly coupled mode borrow coupling from a strongly coupled one, while crossings of resonance lines populate three or four modes without increasing the growth rate. Compared with the coplanar waveguide, the LH line has a similar coupling but keeps the created particles in the target mode, whereas the nearly equidistant waveguide spreads them over many pairs and needs more pump energy.
We propose tunable superconducting split-ring resonators (SRRs) employing nonlinear Josephson inductance. A fraction of SRR is replaced by Nb-AlOx-Nb Josephson tunnel junctions connected in parallel and forming a superconducting quantum interference device, whose inductance is sensitive to the external dc magnetic field. Due to the lumped nature of the Josephson inductance, the SRR can be made very compact, and its resonance frequency can be tuned by applying magnetic field. We present the model, results of extensive electromagnetic-simulation and experimental data for the SRR weakly coupled to a transmission line within frequency range of 11–13 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.
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.
The authors report on a novel microwave phase shifter featuring rapid electronic adjustment, continuous phase control true time delay operation, high device fault tolerance, and very broadband operation. By coupling a large number of superconducting quantum interference devices (SQUIDs) to a superconducting microstrip transmission line, a variable magnetic medium in which the wave velocity is controlled electronically is created. The authors have measured 60 degrees phase shift at 10 GHz, and wideband operation from 5 to 15 GHz for an 8-cm-long Nb transmission line coupled to 1600 SQUIDs, each containing a single Nb/AlO/sub x//Nb tunnel junction. The observed phase shift corresponds to a change in wave velocity of about 1 part in 60.>