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International Congress on Advanced Electromagnetic Materials in Microwaves and Optics

Superconducting transmission lines with pulse-controlled dispersion

S. V. Shitov, A. I. Yahya, Alexey Vladimirovich Ustinov

Published Sep 1, 2016• 0 citations
Publisher

Abstract

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.

DOI
10.1109/metamaterials.2016.7746390

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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.
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.
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.
This paper reports the design, fabrication, and measurements of optically tunable superconducting microwave resonators and delay lines. The devices are comprised of superconducting coplanar waveguide (CPW) transmission lines fabricated from a 100 nm-thick YBCO film, interrupted by 3- and 5-m YBCO meander structures of the same thickness on top of an LAO substrate. The CPW is tested at 77 K up to a frequency of 50 GHz, where it exhibits a transmission loss of about 0.12 dB/mm. The measurements are done in a cryogenic microwave probe station, where all the calibrations have been performed at 77 K. It has been observed that the resonance frequencies of the superconducting resonators can be changed by more than 2 GHz under the optical illumination at a wavelength of 1550 nm. The delay lines also exhibit a phase retardation of up to 90 at the same operating conditions.
Superconducting microwave transmission lines can be designed to have lower loss, lower dispersion, and lower phase velocity than conventional metal lines. These properties make superconducting transmission lines attractive for use in many devices and systems such as filters and analog to digital converters. The problem with designing microwave circuits which utilizes these lines is that accurate circuit models do not exist. This paper present models for the microwave transmission line parameters (phase velocity, attenuation, and characteristic impedance) of superconducting lines as a function of temperature and geometry. An experiment to verify these models is also presented.
We have studied the propagation of subpicosecond electrical pulses on coplanar superconducting Nb transmission lines. Pulses with 0.6 ps full width at half maximum were generated by photoconductively shorting a\sim 10 \mum region between two charged 1 to 5 μm lines separated by a 2 to 10 μm gap. The propagating pulses were sampled by the delayed shorting of a fast phototconductive switch between a sampling probe and one of the transmission lines at variable distances away from the generation point. Silicon-on-sapphire wafers served as the transmission line substrate, with the 0.5 μm thick Si layer heavily damaged by an oxygen implant to provide the subpicosecond carrier life time for the excitation and probe switches. Measurements and analyses of pulses propagated up to 8 mm distance at temperatures from 2 K to 10 K showed a threshold for strong attenuation and dispersion at a frequency reflecting the onset of pair breaking in the superconducting transmission lines. The results at least qualitatively confirm the superconducting microstrip transmission line calculations of Kautz based on Mattis and Bardeen's formulae for the complex conductivity of superconductors.
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.