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arXiv:1405.7117 · Physical Review Letters

Frequency Comb Generation in Superconducting Resonators

Robert P. Erickson, Michael R. Vissers, Martin Sandberg, Steven R. Jefferts, David P. Pappas

Published Oct 30, 2014• 39 citations
arXivHTMLPDF

Abstract

We have generated frequency combs spanning 0.5 to 20 GHz in superconducting λ/2 resonators at T=3 K. Thin films of niobium-titanium nitride enabled this development due to their low loss, high nonlinearity, low frequency dispersion, and high critical temperature. The combs nucleate as sidebands around multiples of the pump frequency. Selection rules for the allowed frequency emission are calculated using perturbation theory, and the measured spectrum is shown to agree with the theory. Sideband spacing is measured to be accurate to 1 part in 10(8). The sidebands coalesce into a continuous comb structure observed to cover at least several frequency octaves.

DOI
10.1103/physrevlett.113.187002

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We have generated frequency combs spanning 0.5 to 20 GHz in superconducting λ/2 resonators at T=3 K. Thin films of niobium-titanium nitride enabled this development due to their low loss, high nonlinearity, low frequency dispersion, and high critical temperature. The combs nucleate as sidebands around multiples of the pump frequency. Selection rules for the allowed frequency emission are calculated using perturbation theory, and the measured spectrum is shown to agree with the theory. Sideband spacing is measured to be accurate to 1 part in 10(8). The sidebands coalesce into a continuous comb structure observed to cover at least several frequency octaves.
Frequency-tunable microwave resonators are in great demand especially in hybrid systems where precise frequency alignment of resonances is required. Here, we present frequency-tunable high-Q superconducting resonators fabricated from thin niobium nitride and niobium titanium nitride films. The resonant frequency is tuned by applying a magnetic field perpendicular to the hole structures in the resonator's inductor wire, whose kinetic inductance is modified by wirelessly induced DC supercurrents. A continuous in situ frequency tuning of over 300 MHz is achieved for a 10 GHz resonator with a moderate magnetic field of 1.2 mT. The planar resonator design and the noncontact tuning scheme greatly ease the fabrication complexity and can be widely applied in many hybrid systems for coupling microwave modes with other forms of excitations such as optical photons, phonons, magnons, and spins.
We have designed, fabricated, and tested a frequency-tunable high-Q superconducting resonator made from a niobium titanium nitride film. The frequency tunability is achieved by injecting a DC through a current-directing circuit into the nonlinear inductor whose kinetic inductance is current-dependent. We have demonstrated continuous tuning of the resonance frequency in a 180 MHz frequency range around 4.5 GHz while maintaining the high internal quality factor Qi > 180 000. This device may serve as a tunable filter and find applications in superconducting quantum computing and measurement. It also provides a useful tool to study the nonlinear response of a superconductor. In addition, it may be developed into techniques for measurement of the complex impedance of a superconductor at its transition temperature and for readout of transition-edge sensors.
We present a design and implementation of a frequency-tunable superconducting resonator. The resonance frequency tunability is achieved by flux-coupling a superconducting LC loop to a current-biased feedline; the resulting screening current leads to a change of the kinetic inductance and shift in the resonance frequency. The thin-film aluminum resonator consists of an interdigitated capacitor and thin line inductors forming a closed superconducting loop. The magnetic flux from the nearby niobium current feedline induces Meissner shielding currents in the resonator loop leading to a change in the kinetic part of the total inductance of the resonator. We demonstrate continuous frequency tuning within 160 MHz around the resonant frequency of 2.7 GHz. We show that: (1) frequency up-conversion is achieved when a kilohertz ac modulation signal is superimposed onto the dc bias resulting in sidebands to the resonator tone; (2) three-wave mixing is attained by parametrically pumping the nonlinear kinetic inductance using a strong rf pump signal in the feedline. The simple architecture is amenable to large-array multiplexing and on-chip integration with other circuit components. The concept could be applied in flux magnetometers, up-converters, and parametric amplifiers operating above 4 K when alternative high-critical-temperature material with high kinetic inductance is used.
Using molecular beam epitaxy, we have realized thin films of titanium nitride (TiN) on c-plane sapphire that exhibit the lowest observed full-width at half maximum X-ray rocking curve width of 18 arcsec. Though the (111) oriented TiN exhibits an abrupt and crystalline interface with sapphire, for the first time we observe sub-surface defects in the sapphire substrate, which nucleate structural defects in the epitaxial TiN layer. Using quarter-wavelength coplanar waveguide (CPW) resonators in a 3 \textmu m/6 \textmu m/3 \textmu m gap/strip/gap lines in a hanger geometry, we find the internal quality factor of the TiN resonators to be >106>10^{6}>106 in the single-photon ⟨n⟩∼1\langle n \rangle \sim 1⟨n⟩∼1 limit at 5.8 GHz and 10 mK, rising to >20×106>20 \times 10^{6}>20×106 at ⟨n⟩∼106\langle n \rangle \sim 10^{6}⟨n⟩∼106. The results are of high interest for applications of superconducting TiN in several areas, and provide a path towards epitaxial Josephson junctions with crystalline barriers in the future for high coherence qubits.
Frequency combs are useful in a wide range of applications, such as optical metrology and high-precision spectroscopy. We experimentally study a controllable frequency comb generated in a tunable superconducting coplanar-waveguide resonator in the microwave regime. A two-tone drive is applied on one of the resonance modes of the resonator and comb generation is observed around the resonance frequency of the resonator. Both central frequency and teeth density of the comb are precisely controllable, and the teeth spacing can be adjusted from Hz to MHz. Moreover, we show that a few hundreds of sidebands can be generated using a sufficiently strong drive power and the weakest drive power needed to generate the comb can be reduced to approach the quantum limit. These experimental results can be qualitatively explained via theoretical analysis.