Spatially Resolved Optical Responses of a High-Kinetic-Inductance Microwave Resonator

TL;DR

The paper investigates how spatially localized optical illumination affects a high-kinetic-inductance superconducting NbTiN nanowire microwave resonator, revealing mode- and position-dependent shifts in resonance frequency and quality factor due to light-induced nonequilibrium phonons and TLS dynamics.Using a laser-scanning microwave spectroscopy setup integrated with a dilution refrigerator, the authors map $1/Q$ and $f_r$ across four resonance modes and four illumination corners, linking optical responses to local electric-field strength and current density.They develop a TLS-based microscopic model with transverse and longitudinal couplings, nonequilibrium TLS populations, and phonon diffusion, supported by analytical calculations and Monte Carlo simulations, to reproduce the observed linear and saturating/blue-red shift behaviors that depend on $|V_{local}|$ and mode.The findings highlight the central role of TLS–phonon interactions under optical drive in determining microwave-optical response, with implications for designing quantum transducers and superconducting detectors, as well as understanding how high-energy particle irradiation and phonon generation can degrade quantum devices.

Abstract

Understanding the optical response of a high-kinetic-inductance microwave resonator is crucial for applications ranging from single-photon detection to quantum transduction between microwave and optical domains, which is gaining significant attention for scaling up quantum computers. However, interactions between the pump light and the superconducting resonator often induce unintended resonance frequency shifts and linewidth broadening. In this study, we measure the local optical response of a NbTiN nanowire resonator using a laser-scanning microwave spectroscopy system integrated with a dilution refrigerator. The optical response of the resonator shows correlation with the resonance modes and position, which is attributed to the two-level system around the resonator. These findings not only contribute to the design and understanding of quantum transducers and single-photon detectors, but also to the understandings of catastrophic high-energy particle irradiation events that generate unintended phonons in quantum devices.

Figures (18)

• Figure 1: Spatially resolved optical illumination experiments. (a) Schematic of the optical illumination experiments. (b) Photograph of the resonator. Areas 1--4 correspond to the four corner of the resonator. (c) Two-dimensional (2D) optical response map of the superconducting nanowire. The 2D optical response map of the resonator is constructed by sweeping the laser illumination position using the galvanometer mirror and extracting the minimum $S_{21}$ amplitude at each coordinate. The blue line probably corresponds to the nanowire.
• Figure 2: Optical response of the resonator across four modes and four positions. (a) $S_{21}$ spectrum of the resonator. The five resonance modes are labeled as the first through fifth modes. Additional resonance modes originate from other resonators located on the same chip. (b) Changes in $1/Q$ and $\Delta f_\mathrm{r}/f_\mathrm{r}$ under laser illumination are plotted for different modes and positions. $Q$ denotes the internal quality factor. Fitting curves for $1/Q$ and $\Delta f_\mathrm{r}/f_\mathrm{r}$ are also shown. The horizontal red dashed line indicates the resonance frequency measured without optical illumination. Three response types based on frequency shifts are: low-frequency shift (red shift), high-frequency shift (blue shift), and subtle shift (purple). Simulated current-density distributions for each position and mode are shown in the inset. The color is normalized by the maximum current density for each mode. The corners are enlarged to highlight the current density in each mode. To prevent current crowding at the corners, the current density is averaged, excluding the corners.
• Figure 3: Relationship between local electric potential and changes in the resonance properties. (Top) Slope of $\Delta(1/Q)$ ($=\gamma$), and (Bottom) slope of $\Delta f_\mathrm{r}/f_\mathrm{r}$ ($=\delta_1$) as a function of the local potential, $|V_\mathrm{local}|$, in each mode and area. The average is calculated over data points with similar $|V_\mathrm{local}|$ values. The vertical and horizontal error bars correspond to the standard deviation of these data points. The fitting curves are the quadratic function ignoring the weight from the standard deviation.
• Figure 4: Schematic of the laser-induced effects and theoretical calculation based on the TLS model. (a) Laser illumination induces (1) quasiparticle generation in the superconductor, (2) nonequilibrium phonon generation, and (3) excitation/relaxation of TLSs via phonon absorption/emission. Some TLS formation mechanisms in the amorphous material are shown Muller2019. (b) $\mathrm{d}\Delta(1/Q)/\mathrm{d}P_\mathrm{opt}$ and (c) $\mathrm{d} (\Delta f_\mathrm{r}/f_\mathrm{r})/\mathrm{d}P_\mathrm{opt}$ as a function of $g$ for different $\xi$. The lines are calculated using the analytical formula, while the dots with error bars are obtained from Monte Carlo simulations. The error bars correspond to the standard deviation over 100 trials. In each figure, the dotted line indicates the experimentally measured value at the voltage antinode of the third mode (7.2 GHz).
• Figure S1: Experimental setup. (a) Schematic of the optical and microwave system integrated with the dilution refrigerator. (1) CCD camera, (2) beamsplitter, (3) galvanometer mirror, (4) objective lens, (5) 3-axis piezo-positioner. (b) Photograph of the experimental system on the mixing chamber plate (MXC). (c) Schematic of the microwave resonator used in the experiment. The laser is focused on the corners of the resonator (Area 1-4).