Broadband Magnetless Isolation in a Flux-Pumped, Dispersion-Engineered Transmission Line

Abstract

Isolators are commonly found in the amplification chain of microwave setups to shield sensitive devices such as superconducting qubits from noise and back-scattered signals. Conventional ferrite-based isolators are bulky, lossy and rely on strong magnetic fields, which pose challenges for their co-integration in large-scale superconducting devices. Although several magnetless approaches based on parametric modulation have been explored to overcome these limitations, none has yet experimentally demonstrated wideband isolation on par with ferrite devices. Here, we propose a compact modulation-based isolator that achieves large isolation bandwidth using a dispersion-engineered transmission line. The engineered line forms an effective two-mode system that enables broadband isolation by supporting adiabatic mode conversion over a wide instantaneous bandwidth. Numerical simulations show that this architecture can provide more than 20 dB isolation across 4 - 8 GHz, matching the performance of ferrite-based isolators. Moreover, we propose an on-chip superconducting device implementation that shows promise against parameter variations and enables a scalable path for co-integration with future large-scale superconducting systems.

Figures (9)

• Figure 1: Broadband isolation in a modulated waveguide(a) Nonreciprocal frequency up-conversion realized with a propagating parametric modulation $m(x,t)$ whose wavenumber and amplitude are adiabatically varied in space. (b) The propagating parametric modulation breaks time-reversal symmetry and produces direction-dependent coupling (green arrow) between modes of the waveguide. When phase-matched (solid lines), the modulation produces both amplification and conversion with the modes at $\omega_\Delta$ and $\omega_\Sigma$, respectively. In the reverse direction (dashed lines), the modulation is not phase-matched and parametric coupling is strongly suppressed. (c) At lower frequencies, dispersion engineering prevents parametric coupling to the modes $\omega_\Delta$ below the bandgap which suppresses the undesired amplification process. At higher frequencies, the engineered dispersion curve limits the coupling to higher modes so that only the two modes at $\omega_{\mathrm{s}}$ and $\omega_\Sigma$ are parametrically coupled. These two modes hence form an effective two-mode system (TMS) and periodically exchange photons with wavelength $\Lambda$. (d) The adiabatic modulation is swept through the phase-matching conditions and converts the right-propagating signal (solid lines) in the bandwidth of interest (in red) to higher-frequency modes (in blue) without converting back which provides high isolation over the whole operating bandwidth ($\text{BW}$). In the reverse direction (dashed lines), parametric coupling is negligible, resulting in low insertion loss.
• Figure 2: Adiabatic mode conversion(a) The population of the lower dressed mode $A_2^+$ is converted from mode $A^{+}_{\omega_{\mathrm{s}}}$ to mode $A^{+}_{\omega_{\Sigma}}$ by adiabatically sweeping the mixing angle $\Theta$ from $0$ to $\pi/2$ (solid arrow), avoiding coupling to $A^+_{1}$ (dotted arrow). (b) Example of a quasi-adiabatic spatial variation of the modulation's amplitude $|m(x)|$ and wavenumber $k_{\mathrm{m}}(x)$, with $|m| = m_0 \left[1-\left(1-2x/L\right)^2\right]$ and $k_{m} = k_{\mathrm{m}0}\left[1-0.2\left(1-2x/L\right)\right]$. (c) Comparison of the isolation bandwidth obtained with Eq. \ref{['eq:CoupledTLSRotatingFrame']} for a device with and without the adiabatic modulation profile shown in (b).
• Figure 3: Circuit schematic of the proposed isolator.(a) The pump propagating in the upper pump line modulates the inductance of the lower signal line where the signals of interest propagate. (b) Every unit cell in the signal line comprises a symmetric DC-SQUID, i.e. with $L_{\mathrm{J}1}=L_{\mathrm{J}2}$ and $C_{\mathrm{J}1}=C_{\mathrm{J}2}$, whose inductance is modulated by the magnetic flux threading the loop, including a contribution $\Phi_{\mathrm{DC}}$ from an external static magnetic field $B_{\mathrm{DC}}$ and a varying contribution $\Phi_{\mathrm{AC}}$ from the pump’s oscillating magnetic field. (c) The equivalent inductance $L_0(x,t)$ of every unit cell in the signal line hence varies over time and space as the pump propagates on the adjacent pump line.
• Figure 4: Dispersion engineering and isolation bandwidth. The bandgap below $\omega_{\mathrm{L}}$ suppresses parametric coupling to lower-frequency modes for any signal within the isolation bandwidth $\text{BW}$, up to $\omega_{\mathrm{max}}<\omega_{\mathrm{L}}+\omega_p$, . At higher frequencies, the curvature of the dispersion relation, induced by the line's Bragg frequency $\omega_0$ and/or the SQUIDs' plasma frequency $\omega_{\mathrm{J}}$, creates a phase-mismatch $\Delta k_{\Sigma}^+$ between $\omega_s$ and $\omega_\Sigma$ which limits the isolation obtained for modes close to $\omega_{\mathrm{max}}$.
• Figure 5: Transmission spectrum obtained by HB simulation (colored lines) and from Eq. \ref{['eq:CoupledModes']} (gray lines), for different number of unit cells $N$. In the isolating direction (solid lines), longer transmission lines provide higher isolation since the variations in modulation happen at a slower rate, which provides more adiabatic mode conversion and lower $|S_{21}|$. In the passing direction (dashed lines), the phase-mismatch is large and the parametric coupling is negligibly small regardless of the devices size leading to $|S_{12}|< 0.02 \text{ dB}$.