Third harmonic-mediated amplification in TWPA

TL;DR

This work redefines the role of third-harmonic generation in Josephson Traveling-Wave Parametric Amplifiers by showing that phase-matched THG can substantially increase both gain and bandwidth in a plasma-oscillation-based TWPA. The authors extend the coupled-mode theory to include the pump's third harmonic and relevant sidebands, and validate the predictions with time-domain simulations and dispersion analyses, identifying a narrow pump-frequency sweet-spot around $f_p \approx 8.5$–$8.64\,\mathrm{GHz}$ where THG is most effective. The extended CME-3 model reveals that THG mediates new amplification pathways involving the sidebands, providing a quantitative explanation for the observed gain enhancement and the sweet-spot. These findings offer design principles for higher-performance, wider-bandwidth JTWPAs, with potential impact on quantum measurements requiring low-noise, broadband amplification.

Abstract

In Josephson Traveling-Wave Parametric Amplifiers, higher-order harmonics of the pump tone and its sidebands are commonly present and typically regarded as parasitic. Consequently, most design efforts have focused on suppressing these harmonics. In spite of that, motivated by transient simulations, we extend the coupled-mode theory and demonstrate that, contrary to conventional belief, the third harmonic can enhance amplifier performance, improving both gain and bandwidth. We show that the recently developed plasma oscillation-based amplifier is particularly well-suited for exploiting this effect. Their dispersion relation enables us to observe the phenomenon in transient numerical simulations using JoSIM and WRspice. These simulations reveal improvement of the amplifier's performance, specifically the doubling of the bandwidth and an increase in the gain.

Figures (9)

• Figure 1: (a) Schematic of PTWPA implemented in JoSIM and WRspice. It consists of an array of N identical unit cells (UC). $Z_{in/out} =\text{50 } \Omega$. (b) Schematic of PTWPA unit cell. Capacitor $C_{p} = \textrm{394 fF}$ (blue), responsible for plasma oscillation, is placed in parallel to every $5^{th}$ Josephson junction (black crosses) to modify dispersion. Parameters of RSCJ model of junctions are:$\; I_{c} =2~\mu\textrm{A}, R = 550~\Omega, C_{JJ} =\textrm{12 fF}$. All ground capacitances have equal values: $C_{g} = \textrm{71.5 fF}$. In simulations, the whole circuit contains $N = 240$ unit cells. In CME calculations, we considered $dz = 5~\mu$m. (c) Dispersion curves for PTWPA unit cell; real (black) and imaginary part (orange) of $k$, respectively, obtained by ABCD matrix method. The wave vector is normalized to $2\pi/dz$, where $dz$ is the distance between adjacent junctions. DC current was set to $I_{d} = 0.8~\mu\textrm{A}$. Linear dispersion approximation utilized in CME to study the amplification process is shown as a grey dashed line. For third harmonic (green arrow) an additional phase shift $\theta$ is introduced for phase matching. Sidebands are indicated by purple and blue arrows.
• Figure 2: (a) PTWPA transmission spectra ($S21$) for single pump tone simulated in JoSIM as a function of signal frequency. (b) Strong signal transmission (green and red lines) and THG conversion gain (dashed lines). Parameters of the simulation are: $I_{p} = 1.6~\mu\textrm{A}$ (red line), $I_{p} = 1~\mu\textrm{A}$ (green line), $I_{p} = 0.01~\mu\textrm{A}$ (blue line), and $I_{d} = 0.8~\mu\textrm{A}$.
• Figure 3: Power flow of propagating plane waves for relevant modes under three pump configurations simulated in JoSIM, each corresponding to a different third-harmonic generation efficiency: $f_{p} = 8.5 \textrm{ GHz}, I_{p} = 1.8~\mu\textrm{A}$ (dashed line); $f_{p} = 8.64 \textrm{ GHz}, I_{p} = 1.6~\mu\textrm{A}$ (solid line); $f_{p} = 8.8 \textrm{ GHz}, I_{p} = 1.7~\mu\textrm{A}$ (dotted line). Respective modes are a) $f_{3p}$ (black lines), $f_{2p}$ (gray lines), $f_{s}$ (green lines), $f_{p+s}$ (purple lines); b) $f_{s}$ (green lines), $f_{2p-s}$ (red lines), $f_{p-s}$ (orange lines). The remaining parameters of the simulation are: $f_{s} = 4.8 \textrm{ GHz}; I_{s} = 0.01~\mu\textrm{A}, I_{d} = 0.8~\mu\textrm{A}$.
• Figure 4: Gain (a) and reflections (b) simulated in JoSIM for three pump configuration cases presented in Fig. \ref{['fig:Power_propagation_JoSIM']}. Parameters of the simulation are: $f_{p} = 8.5 \textrm{ GHz}, I_{p} = 1.8~\mu\textrm{A}$ (green dashed line), $I_{p} = 1.6~\mu\textrm{A}$ (brown dashed line); $f_{p} = 8.64 \textrm{ GHz}, I_{p} = 1.6~\mu\textrm{A}$ (green solid line); $f_{p} = 8.8 \textrm{ GHz}, I_{p} = 1.7~\mu\textrm{A}$ (green dotted line), $I_{p} = 1.6 ~\mu\textrm{A}$ (brown dotted line); $I_{s} = 0.01~\mu\textrm{A}, I_{d} = 0.8~\mu\textrm{A}$.
• Figure 5: (a) Node evolution of the pump tone calculated from the basic CME including: pump, signal, and idler (red); addition of a non–phase-matched third harmonic (green dashed); and addition of a phase-matched third harmonic (green solid). (b) Thick solid lines represent signal gain according to CME with various modes: 3WM theory with signal, idler, pump (red), with additional 4WM idler $2f_p-f_s$ (purple), or with additional $f_p+f_s$ tone (blue), and with both sidebands (orange). Process with both sidebands and third harmonic not phase matched (green dashed line), and phase matched third harmonic (green solid line). Thin green lines are evolutions of the respective $f_{3p}$ mode. (c) Dependence of the negative normalized imaginary parts of the eigenvalues (black and grey curves) of matrix describing the simplified CME (left axis) on the third harmonic amplitude and corresponding signal gain (green line) - right axis. The calculations used parameters: $f_p=9~$GHz, $f_s=4.8~$GHz, and $I_p=I_d=0.4I_c$, which for $I_{c} = 2 ~\mu\textrm{A}$ corresponds to $I_p=I_d = 0.8 ~\mu\textrm{A}$, same as in transient simulations.