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arXiv:2406.19751

Mixing of counterpropagating signals in a traveling-wave Josephson device

Matthieu Praquin, Vincent Lienhard, Anthony Giraudo, Aron Vanselow, Zaki Leghtas, Philippe Campagne-Ibarcq

Published Jun 28, 2024• 0 citations
arXivHTMLPDF

Abstract

Light waves do not interact in vacuum, but may mix through various parametric processes when traveling in a nonlinear medium. In particular, a high-amplitude wave can be leveraged to frequency convert a low-amplitude signal, as long as the overall energy and momentum of interacting photons are conserved. These conditions are typically met when all waves propagate in the medium with identical phase velocity along a particular axis. In this work, we investigate an alternative scheme by which an input microwave signal propagating along a 1-dimensional Josephson metamaterial is converted to an output wave propagating in the opposite direction. The interaction is mediated by a pump wave propagating at low phase velocity. In this novel regime, the input signal is exponentially attenuated as it travels down the device. We exploit this process to implement a robust on-chip microwave isolator that can be reconfigured into a reciprocal and tunable coupler. The device mode of operation is selected in situ, along with its working frequency over a wide microwave range. In the 5.5-8.5 GHz range, we measure an isolation over 15 dB on a typical bandwidth of 100 MHz, on par with the best existing on-chip isolators. Substantial margin for improvement exists through design optimization and by reducing fabrication disorder, opening new avenues for microwave routing and processing in superconducting circuits.

DOI
10.48550/arxiv.2406.19751

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Light waves do not interact in vacuum, but may mix through various parametric processes when traveling in a nonlinear medium. In particular, a high-amplitude wave can be leveraged to frequency convert a low-amplitude signal, as long as the overall energy and momentum of interacting photons are conserved. These conditions are typically met when all waves propagate in the medium with identical phase velocity along a particular axis. In this work, we investigate an alternative scheme by which an input microwave signal propagating along a 1-dimensional Josephson metamaterial is converted to an output wave propagating in the opposite direction. The interaction is mediated by a pump wave propagating at low phase velocity. In this novel regime, the input signal is exponentially attenuated as it travels down the device. We exploit this process to implement a robust on-chip microwave isolator that can be reconfigured into a reciprocal and tunable coupler. The device mode of operation is selected in situ, along with its working frequency over a wide microwave range. In the 5.5-8.5 GHz range, we measure an isolation over 15 dB on a typical bandwidth of 100 MHz, on par with the best existing on-chip isolators. Substantial margin for improvement exists through design optimization and by reducing fabrication disorder, opening new avenues for microwave routing and processing in superconducting circuits.
Light waves do not interact in vacuum but can mix in nonlinear media. A strong pump wave can thus convert the frequency of a weaker signal, provided energy and momentum are conserved. These conditions are typically satisfied when all waves propagate with comparable phase velocity along a given axis. Here, we investigate an alternative scheme by which a microwave signal propagating along a one-dimensional Josephson metamaterial is converted into a counter-propagating wave through interaction with a slower pump. In this regime, the input wave is exponentially attenuated, enabling an on-chip microwave isolator reconfigurable into a reciprocal, tunable coupler. The device’s operating mode and working frequency can be selected in situ over a broad microwave range. We measure isolation exceeding 5 dB in the 5-8.5 GHz range and 10 dB in the 7-8.5 GHz range, with a typical 200 MHz bandwidth. Further improvements are expected through design optimization and reduced fabrication disorder, opening new possibilities for microwave routing and processing in superconducting circuits. Wave-mixing is investigated in a Josephson traveling-wave device supporting two modes of propagation. A phase-matched conversion process between counterpropagting waves is leveraged to implement a robust on-chip circulator and tunable coupler.
Superconducting traveling-wave parametric amplifiers have emerged as highly promising devices for near-quantum-limited broadband amplification of microwave signals and are essential for high quantum-efficiency microwave readout lines. Built-in isolation, as well as gain, would address their primary limitation: lack of true directionality due to potential backward travel of electromagnetic radiation to their input port. Here, we demonstrate a Josephson-junction-based traveling-wave parametric amplifier isolator. It utilizes third-order nonlinearity for amplification and second-order nonlinearity for frequency upconversion of backward propagating modes to provide reverse isolation. These parametric processes, enhanced by a novel phase matching mechanism, exhibit gain of up to 20~dB and reverse isolation of up to 30~dB over a static 3~dB bandwidth greater than 500~MHz, while keeping near-quantum limited added noise. This demonstration of a broadband truly directional amplifier ultimately paves the way towards broadband quantum-limited microwave amplification lines without bulky magnetic isolators and with inhibited back-action.
Josephson traveling-wave parametric amplifiers (JTWPAs) are promising platforms for realizing broadband quantum-limited amplification of microwave signals. However, substantial gain in such systems is attainable only when strict constraints on phase matching of the signal, idler, and pump waves are satisfied---this is rendered particularly challenging in the presence of nonlinear effects, such as self- and cross-phase modulation, which scale with the intensity of propagating signals. In this work, we present a simple JTWPA based on ``left-handed'' (negative-index) nonlinear Josephson metamaterial, which has phase matching native to its design, precluding the need for any complicated circuit or dispersion engineering. The resultant efficiency of the four-wave-mixing process can implement gains in excess of 20 dB over few-gigahertz bandwidths with much shorter lines than previous implementations. Furthermore, the intrinsic phase matching considerably simplifies the JTWPA design and operation compared to the previous implementations based on ``right-handed'' (positive-index) Josephson metamaterials, making the proposed architecture particularly appealing for integration with large superconducting architectures. The left-handed Josephson transmission line introduced here constitutes an alternative modality in distributed Josephson circuits, and forms a crucial piece of the unified framework that can be used to inform the optimal design and operation of broadband microwave amplifiers.
We report on the design and performance of an on-chip microwave circulator with a widely (GHz) tunable operation frequency.Nonreciprocity is created with a combination of frequency conversion and delay, and requires neither permanent magnets nor microwave bias tones, allowing on-chip integration with other superconducting circuits without the need for high-bandwidth control lines.Isolation in the device exceeds 20 dB over a bandwidth of tens of MHz, and its insertion loss is small, reaching as low as 0.9 dB at select operation frequencies.Furthermore, the device is linear with respect to input power for signal powers up to hundreds of fW (≈10 3 circulating photons), and the direction of circulation can be dynamically reconfigured.We demonstrate its operation at a selection of frequencies between 4 and 6 GHz.
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.
High-fidelity qubit measurement is a critical element of all quantum computing architectures. In superconducting systems, qubits are typically measured by probing a readout resonator with a weak microwave tone that must be amplified before reaching the room temperature electronics. Superconducting parametric amplifiers have been widely adopted as the first amplifier in the chain, primarily because of their low noise performance, approaching the quantum limit. However, they require isolators and circulators to route signals up the measurement chain and to protect qubits from amplified noise. While these commercial components are wideband and simple to use, their intrinsic loss, size, and magnetic shielding requirements impact overall measurement efficiency and scalability. Here we report a parametric amplifier that achieves both broadband forward amplification and backward isolation in a single, compact, non-magnetic circuit that could be integrated on chip with superconducting qubits. The approach relies on a nonlinear transmission line that supports traveling-wave parametric amplification of forward propagating signals, and isolation via frequency conversion of backward propagating signals. This traveling-wave parametric amplifier and converter has the potential to reduce the readout hardware overhead when scaling up the size of superconducting quantum computers.