Coherent transfer via parametric control of normal-mode splitting in a superconducting multimode resonator

Abstract

Microwave storage and retrieval are essential capabilities for superconducting quantum circuits. Here, we demonstrate an on-chip multimode resonator in which strong parametric modulation induces a large and tunable normal-mode splitting that enables microwave storage. When the spectral bandwidth of a short microwave pulse covers the two dressed-state absorption peaks, part of the pulse is absorbed and undergoes coherent energy exchange between the modes, producing a clear time-domain beating signal. By switching off the modulation before the beating arrives, we realize on-demand storage and retrieval, demonstrating an alternative approach to microwave photonic quantum memory. This parametric-normal-mode-splitting protocol offers a practical route toward a controllable quantum-memory mechanism in superconducting circuits.

Figures (5)

• Figure 1: (a) Optical micrograph of the resonator together with a diagram of the measurement setup. The symbols $\omega_\Phi$, $\Phi$, and $\omega_p$ denote the parametric modulation tone, the DC flux bias, and the probe tone, respectively. Att. and Amp. denote the attenuator and the amplifier. (b) Resonance frequency of each mode $\omega_r^{(n)}$ as a function of the DC flux $\Phi$. The red dashed lines represent the theoretical fits. (c) Reflection coefficient $|r_c|$ (blue) as a function of the probe frequency $\omega_p$ when the resonator is biased at $\Phi = 0.33\Phi_0$. The red dashed line denotes the theoretical fit.
• Figure 2: Normal-mode–splitting spectrum under parametric modulation with a fixed flux-modulation amplitude. $|r_c|$ is plotted as a function of the modulation frequency $\omega_\Phi$ and the probe frequency $\omega_p$, where $\omega_p$ is tuned near resonance with (a) mode 2 and (b) mode 3.
• Figure 3: (a) False-color spectroscopy of $|r_c|$ and (b) the corresponding simulation, plotted as functions of $g_\Phi$ and the probe frequency $\omega_p$. The modulation frequency $\omega_\Phi/2\pi=1.664$ is chosen near the detuning between modes 2 and 3. (c) Line cut of the experimental data at $g_\Phi/2\pi=6.6$ MHz, which is denoted by the blue line. The red dashed curve indicates the theoretical fit. (d) Extracted $g_\Phi$ and detuning $\Delta_\Phi$ as functions of the flux-modulation amplitude $\delta\Phi$. The empty circles represent the fitting results from (a). The red dashed lines show the linear fit for $g_\Phi$ and the quadratic fit for $\Delta_\Phi$.
• Figure 4: A short Gaussian pulse is injected into the resonator with a fixed modulation frequency $\omega_\Phi/2\pi=1.664$ GHz while varying the coupling strength $g_\Phi$. The measured output voltage $V_{\mathrm{out}}$ is plotted as a function of $g_\Phi$ and time. (a) Experimental results. (b) Simulation results.
• Figure 5: On-demand storage and retrieval of the beating signal. The measured output voltage $V_{\mathrm{out}}$ is plotted as a function of the storage time $T_s$ and time. The upper panel shows the control sequence of the parametric modulation.