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arXiv:1612.00365 · Physical review. B./Physical review. B

Theory of multiwave mixing within the superconducting kinetic-inductance traveling-wave amplifier

Robert P. Erickson, David P. Pappas

Published Mar 6, 2017• 37 citations

Abstract

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.

DOI: 10.1103/physrevb.95.104506

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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.

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.

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.

Travelling wave parametric amplifiers (TWPAs) made from highly non-linear reactive superconducting thin films have been demonstrated to be a potentially viable quantum-noise-limited amplifier technology for various fundamental physics platforms, including microwave/mm/sub-mm astronomy, dark matter search experiments, neutrino mass experiments, and qubit readout. We present a kinetic inductance TWPA consisting of a patterned titanium nitride film on a sapphire substrate, which comprises a coplanar waveguide (CPW) with a continuous, smoothed periodic loading (PL) structure that modulates the characteristic impedance of the CPW in a double sinusoidal fashion. This double sinusoidal modulation creates much stronger dispersion features than a conventional PL design, which allows for phase matching and pump harmonic suppression over a much shorter transmission length, potentially leading to reduced losses. In this paper, we shall discuss in detail the design of our TWPA and present the predicted gain-bandwidth characteristics from electromagnetic simulations.

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.

We present a detailed simulation and design framework for realizing traveling wave parametric amplifiers (TWPAs) using the nonlinear kinetic inductance of disordered superconductors -- in our case niobium-titanium-nitride (NbTiN). These kinetic inductance TWPAs (KITs) operate via three-wave mixing (3WM) to achieve high broadband gain and near-quantum-limited (nQL) noise. Representative fabricated devices -- realized using an inverted microstrip (IMS), dispersion-engineered, artificial transmission line -- demonstrate power gains above 25 dB, bandwidths beyond 3 GHz, and achieve ultimate system noise levels of 1.1 quanta even when operated with no magnetic shielding. These performance metrics are competitive with state-of-the-art Josephson-junction-based TWPAs but involve simpler fabrication and able to providing three orders of magnitude higher dynamic range (

IIP_1 = -68

dBm,

IIP_3 = -55

dBm), and high magnetic field resilience -- making KITs an attractive technology for highly multiplexed readout of quantum information and superconducting detector systems.

We report on the implementation of a near-quantum-limited, traveling-wave parametric amplifier that uses three-wave mixing (3WM). To favor amplification by 3WM, we use superconducting nonlinear asymmetric inductive element (SNAIL) loops, biased with a dc magnetic flux. In addition, we equip the device with dispersion engineering features to create a stopband at the second harmonic of the pump and suppress the propagation of the higher harmonics that otherwise degrade the amplification. With a chain of 440 SNAILs, the amplifier provides up to 20 dB gain and a 3-dB bandwidth of 1 GHz. The added noise by the amplifier is found to be less than one photon.