Evidence of Memory Effects in the Dynamics of Two-Level System Defect Ensembles Using Broadband, Cryogenic Transient Dielectric Spectroscopy

TL;DR

TLS defects limit coherence in superconducting circuits, motivating a broadband, cryogenic probe. The authors introduce Broadband Cryogenic Transient Dielectric Spectroscopy (BCTDS), a modular 3D waveguide–based approach operating in the $3$--$6$ GHz band at $T \approx 10\ \mathrm{mK}$ to drive ensembles of TLS defects and analyze their post-pulse emission via $\chi''(\omega)$. They observe memory effects and Floquet-like dressed-state features, with material dependence showing enhanced TLS density in thin AlOx and surface-resist layers; longer drive durations yield sharper spectral features and more pronounced ring-downs that agree with driven many-body simulations. The method provides a noninvasive, broadband toolkit to map TLS distributions and dipole moments across materials, informing fabrication, passivation, and material choices for low-loss quantum devices across quantum technologies and materials science.

Abstract

Two-level system (TLS) defects in dielectrics cause decoherence in superconducting circuits, yet their origin, frequency distribution, and dipole moments remain poorly understood. Current probes, primarily based on qubits or resonators, require complex fabrication and measure defects only within narrow frequency bands and limited mode volumes, restricting insight into TLS behavior in isolated materials and interfaces. We introduce Broadband Cryogenic Transient Dielectric Spectroscopy (BCTDS), a broadband 3D waveguide technique that enables probing of TLS ensembles at cryogenic temperatures. Complementary to the dielectric dipper method, this approach probes a broader spectrum and reveals interference of drive-induced sidebands in TLS ensembles. The broadband, power-tunable nature of BCTDS makes it well suited for studying dressed-state physics in driven TLS ensembles, including multi-photon processes and sideband-resolved dynamics. By analyzing Fourier-transformed time-domain signals, BCTDS reveals eigen-mode frequencies of undriven TLS ensembles through characteristic V-shaped features and uncovers memory effects arising from interactions and broadband excitation. The modular method can be applied throughout device fabrication, informing mitigation strategies and advancing the design of low-loss materials with broad implications for quantum technologies and materials science.

Figures (13)

• Figure 1: Overview of TLS defects and how they can be probed. (a) Double-well representation of TLS defects under a drive $\Omega$, described by the standard tunneling model. (b) Candidate TLS defects and their likely locations in superconducting circuits. (c) Comparison of traditional TLS defect spectroscopy using 2D qubits and resonators and our proposed broadband 3D waveguide approach. The concept of image (b) is inspired by Lisenfeld2019.
• Figure 2: Broadband waveguide design. (a) Photograph of upper and lower WR-229 to SMA adapter components and clamp with sapphire samples (marked by the black box). These components are assembled to create the closed 3D aluminum waveguide used in this work. (b) HFSS simulated and measured transmission ($S_{21}$) and reflection ($S_{11}$) spectra of the waveguide containing samples at room temperature, demonstrating a waveguide cutoff of around 3 GHz and broadband transmission from 3-6 GHz.
• Figure 3: Dielectric spectroscopy of different samples. We send a 30 ns pulse (marked by black dashed lines) and readout over a 0.8 $\mu$s window (shown in subpanels (ii) with the color scale clipped to reveal weak transient features). Room temperature experiments for empty waveguide (a) and waveguide with solvent-cleaned sapphire samples (b) show no detectable response. The horizontal band around 4.4 GHz is due to electronic noise. Measurements (c)-(f) are performed at 10 mK, revealing coherent transient dielectric response features arising from TLS defects. Measurements (c) and (d) feature the same setups as (a) and (b), at 10mK. (e) The same samples as (b) with a 2 nm aluminum oxide layer deposited via ALD. (f) The same samples as (b) with spin-coated Shipley 1813 photoresist. Transient response in (e)-(f) shows prominent features in the ring-down, which we attribute to increased TLS defect density. Subpanels (i) show the average driven dielectric response and the extracted lifetimes ($\tau$) of the ring-downs, using an exponential fit. We include the FFT of the pulse in the inset in (dii) and mark the FWHM of the pulse, $\Delta$f, with a vertical white line, which has approximately the same bandwidth as the prominent spectral features.
• Figure 4: Dielectric response of 2 nm aluminum oxide sample under different pulse lengths. (a) 20 ns pulse. (b) 50 ns pulse. (c) 200 ns pulse. Similar to Fig. \ref{['fig:sample_compare']}, subpanels (ii) show the driven and transient dielectric response, while subpanels (i) show the average of the driven dielectric response and the extracted lifetimes ($\tau$) of the transient dielectric response. As the pulse length increases, the bandwidth (marked by the short vertical white lines) of the pulse decreases, resulting in sharper emissions. Absorption in the pulsing region often corresponds to an emission around the same frequency, after the pulse is turned off.
• Figure 5: Transient dielectric response of Shipley 1813 photoresist on sapphire. We use the same data as Fig. \ref{['fig:sample_compare']}(f). (aii) Logarithmic magnitude of the transient dielectric response. (bii) Magnitude of Fast Fourier transform (FFT) of the logarithmic amplitude. (cii) Log of the two-time correlation function g$^{(2)}$ map of the transient spectrum, defined by Eq. \ref{['eq:g2']}. (dii) $\chi"$ computed from g$^{(2)}$ using Eq. \ref{['eq:chi_imag_IQ']}. We highlight transitions from positive to negative $\chi"$ with the cyan contour in (dii). Subpanels (i) show linecuts at $\omega/2\pi = 3.322$ GHz, marked by dashed line in (ii), highlighting distinct memory effects in the form of collapse and revivals in the ringdown (a), sharp spectral features in the FFT (b), non-exponential decay, bunching, and oscillations indicative of non-Markovian dynamics (c), and non-monotonic and negative $\chi"$ (d). The negative regions are consistent with the bright FFT features in (bii). It should be noted that $\chi"$ oscillates around zero near $\omega/2\pi = 3$ GHz primarily due to weak signals and not necessarily indicating memory effects. A short horizontal white line is added to indicate pulse bandwidth $\Delta$f.