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European Conference on Antennas and Propagation

Optimized Design Parameters for a Flux-Driven SNAIL-Based Traveling-Wave Parametric Amplifier

Michael Haider, Yongjie Yuan, Christian Jirauschek

Published Mar 17, 2024• 0 citations
Publisher

Abstract

We present an analytic approach for finding optimized design parameters for flux-driven traveling-wave parametric amplifiers with superconducting nonlinear asymmetric inductive elements. The parameter to be optimized, i.e., the gain coefficient, is extracted from a Hamiltonian quantum model for three-wave mixing flux-driven amplifiers. Analytic expressions for the nonlinear coefficients up to the third order in the current-phase relation are derived. The minimum potential energy is determined by finding the roots of a polynomial function. Candidates for optimal operation points are identified by minimizing the residual cross-phase modulation while at the same time maximizing the gain coefficient. Finally, the gain of a traveling-wave parametric amplifier implementation with optimized parameters is evaluated using a quantum model, including substrate losses and chromatic dispersion.

DOI
10.23919/eucap60739.2024.10501275

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We present an analytic approach for finding optimized design parameters for flux-driven traveling-wave parametric amplifiers with superconducting nonlinear asymmetric inductive elements. The parameter to be optimized, i.e., the gain coefficient, is extracted from a Hamiltonian quantum model for three-wave mixing flux-driven amplifiers. Analytic expressions for the nonlinear coefficients up to the third order in the current-phase relation are derived. The minimum potential energy is determined by finding the roots of a polynomial function. Candidates for optimal operation points are identified by minimizing the residual cross-phase modulation while at the same time maximizing the gain coefficient. Finally, the gain of a traveling-wave parametric amplifier implementation with optimized parameters is evaluated using a quantum model, including substrate losses and chromatic dispersion.
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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.
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Three-wave mixing is a key process in superconducting quantum information processing, being involved in quantum-limited amplification and parametric coupling between superconducting cavities. These operations can be implemented by superconducting nonlinear asymmetric inductive element (SNAIL)-based devices that present a Kerr-free flux-bias point where unwanted parasitic effects, such as Stark shift, are suppressed. However, with a single flux-bias parameter, these circuits can only host one Kerr-free point, limiting the range of their applications. In this Letter, we demonstrate how to overcome this constraint by introducing the gradiometric SNAIL, a doubly flux biased superconducting circuit in which both effective inductance and Kerr coefficient can be independently tuned. Experimental data show the capability of the gradiometric SNAIL to suppress the Kerr effect in a three-wave mixing parametric amplifier over a continuum of flux bias points corresponding to a 1.7 GHz range of operating frequencies.
Superconducting quantum computing is at the forefront of demonstrating quantum advantages for revolutionary applications in science and technology. One key component for the readout of qubit state information is given by superconducting traveling-wave parametric amplifiers (TWPAs) due to their low power dissipation and unprecedented quantum-limited noise performance. This work presents a black-box circuit quantum electrodynamic model for TWPAs with arbitrary superconducting nonlinear elements. A unified Hamiltonian description for directly pumped and flux-driven amplifiers is derived, and analytic results for the gain and the added quantum noise are presented, closely matching recent experimental realizations. We also offer an optimization strategy for nonlinear elements for large gain and low noise based on the proposed black-box quantum model. The results of this article will be helpful in the design and multitarget optimization of new and improved quantum-limited low-noise amplifiers.