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Applied Physics Letters

High-efficiency Ka-band frequency multiplier based on the nonlinear kinetic inductance in a superconducting microstrip

Daniel Cunnane, Henry George LeDuc, Nikita S. Klimovich, Farzad Faramarzi, Andrew D. Beyer, Peter K. Day

Published Jan 8, 2024• 8 citations
Publisher

Abstract

Local oscillator sources have become a major technological deficit approaching the terahertz frequencies. For applications, where a narrow linewidth is necessary, such as coherent remote sensing, the best solution to signal generation is frequency multiplication, where phase locking can be easily achieved using the fundamental source. We present an alternative to existing frequency multiplier technologies for cryogenic applications. The device is a superconducting waveguide that has kinetic inductance dependent on the rf current through the device. The nonlinear kinetic inductance is anomalous to a nonlinear optical medium, where the Kerr effect causes 3- or 4-wave mixing, as demonstrated in microwave parametric amplifiers utilizing the same nonlinear effect. In 4-wave mixing, three photons at the fundamental frequency are mixed to generate a single photon at the third harmonic. Dispersion engineering is used to achieve wideband phase matching and phase out harmonics higher than the third. The device length is designed to be the point where most photons are up-converted to the third harmonic. Simulations of these devices lead to expected efficiencies as high as 90%. We report results from a NbTiN frequency multiplier from 34.2 to 104 GHz with efficiency better than 50%.

DOI
10.1063/5.0191743

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Local oscillator sources have become a major technological deficit approaching the terahertz frequencies. For applications, where a narrow linewidth is necessary, such as coherent remote sensing, the best solution to signal generation is frequency multiplication, where phase locking can be easily achieved using the fundamental source. We present an alternative to existing frequency multiplier technologies for cryogenic applications. The device is a superconducting waveguide that has kinetic inductance dependent on the rf current through the device. The nonlinear kinetic inductance is anomalous to a nonlinear optical medium, where the Kerr effect causes 3- or 4-wave mixing, as demonstrated in microwave parametric amplifiers utilizing the same nonlinear effect. In 4-wave mixing, three photons at the fundamental frequency are mixed to generate a single photon at the third harmonic. Dispersion engineering is used to achieve wideband phase matching and phase out harmonics higher than the third. The device length is designed to be the point where most photons are up-converted to the third harmonic. Simulations of these devices lead to expected efficiencies as high as 90%. We report results from a NbTiN frequency multiplier from 34.2 to 104 GHz with efficiency better than 50%.
Traveling-wave parametric amplifiers based on superconducting NbTiN films are being developed that provide gain over nearly an octave of bandwidth at microwave frequencies. The amplifiers are non-linear transmission lines, where the nonlinearity comes from the current dependence of the kinetic inductance. Amplification results from three and four-wave mixing processes, and phase matching over a wide frequency range is achieved by engineering the dispersion characteristics of the transmission line. Recent noise measurements over a wide frequency band demonstrate that the added noise of these amplifiers is close to one half photon, consistent with the quantum limit for a phase preserving amplifier. We will discuss applications of this class of amplifier to astronomical instruments.
Traveling-wave parametric amplifiers may be fabricated from superconducting films that exhibit highly nonlinear kinetic inductance. The coplanar waveguide of such a microwave device, extending to a meter or more in length but compacted to reside on a chip of the order of a square centimeter, is engineered with periodic variations in its width. These width variations, or loadings, alter the dispersion characteristics of a nonlinear current propagating along the waveguide, changing its group velocity and modulation behavior. A strong pump and a small signal injected into one end of the waveguide mix parametrically in the presence of the nonlinear kinetic inductance. Engineered dispersion induces the favorable conditions of overall phase matching, leading to generation of idler products as well as signal amplification of wide bandwidth, high dynamic range, and low noise, making the device of particular use in quantum computing and photon detection. The authors present a theoretical framework in which signal gain may be calculated solely from loading design. This involves construction of a metamaterial band theory of the engineered dispersion, which is used as a basis to describe the mixing of nonlinear traveling waves.
Superconducting quantum circuits are typically operated at low temperatures (mK), necessitating cryogenic low-noise, wideband amplifiers for signal readout ultimately also compatible with room temperature electronics. While existing implementations partly meet these criteria, they suffer from certain limitations, such as rippled transmission spectra or limited dynamic range, some of which are caused by the lack of proper impedance matching. We develop a microstrip kinetic inductance traveling wave amplifier, exploiting the nonlinear kinetic inductance of tungsten-silicide for wave-mixing of the signal and a pump, and engineer the impedance to 50 Ω, while decreasing the phase velocity, with benefit for the amplification. Despite losses, pumping on our device amplifies the signal by 15 dB over a 2 GHz bandwidth.
We have fabricated a wide-bandwidth, high dynamic range, low-noise cryogenic amplifier based on a superconducting kinetic inductance traveling-wave device. The device was made from NbTiN and consisted of a long, coplanar waveguide on a silicon chip. By adding a DC current and an RF pump tone we are able to generate parametric amplification using three-wave mixing. The devices exhibit gain of more than 15 dB across an instantaneous bandwidth from 4 to 8 GHz. The total usable gain bandwidth, including both sides of the signal-idler gain region, is more than 6 GHz. The noise referred to the input of the devices approaches the quantum limit, with less than 1 photon excess noise. Compared to similarly constructed four-wave mixing amplifiers, these devices operate with the RF pump at ~20 dB lower power and at frequencies far from the signal. This will permit easier integration into large scale qubit and detector applications.
Microwave parametric amplifiers operating at the quantum noise limit have become indispensable tools for a range of cryogenic quantum technologies. These amplifiers are typically constructed from nonlinear Josephson junctions, which limit the ability to amplify high-power signals. This study reports a device based instead on the weakly nonlinear kinetic inductance intrinsic to a superconducting film of niobium titanium nitride. The amplifier offers large phase-sensitive gain and high power handling, plus a simple design and fabrication process. As it contains no junctions, it is robust to electrostatic discharge and potentially operable under high temperatures and large magnetic fields.
Parametric amplification is essential for quantum measurement, enabling the amplification of weak microwave signals with minimal added noise. While Josephson-junction-based amplifiers have become standard in superconducting quantum circuits, their magnetic sensitivity, limited saturation power, and sub-kelvin operating requirements motivate the development of alternative nonlinear platforms. Here we demonstrate a two-mode kinetic-inductance parametric amplifier based on a pair of capacitively coupled Kerr-nonlinear resonators fabricated from NbTiN and NbN thin films. The distributed Kerr nonlinearity of these materials enables nondegenerate four-wave-mixing amplification with gains approaching 40 dB, gain-bandwidth products up to 6.9 MHz, and 1-dB compression powers two to three orders of magnitude higher than those of state-of-the-art Josephson amplifiers. A coupled-mode theoretical model accurately captures the pump-induced modification of the hybridized modes and quantitatively reproduces the observed signal and idler responses. The NbN device exhibits a significantly larger Kerr coefficient and superior gain-bandwidth performance, highlighting the advantages of high-kinetic-inductance materials. Our results establish coupled kinetic-inductance resonators as a robust platform for broadband, high-power, and magnetically resilient quantum-limited amplification, offering a scalable route for advanced readout in superconducting qubits, spin ensembles, quantum dots, and other microwave-quantum technologies.