Low-temperature 1/f noise in microwave dielectric constant of amorphous dielectrics in Josephson qubits
Alexander L. Burin, Shlomi Matityahu, Moshe Schechter · 2015 · 30 citationsRead the paper
The analytical solution for the low-temperature $1/f$ noise in the microwave dielectric constant of amorphous films at frequency ${\ensuremath{\nu}}_{0}\ensuremath{\sim}5\phantom{\rule{0.28em}{0ex}}\mathrm{GHz}$ due to tunneling two-level systems (TLSs) is derived within the standard tunneling model including the weak dipolar or elastic TLS-TLS interactions. The $1/f$ frequency dependence is caused by TLS spectral diffusion characterized by the width growing logarithmically with time. Temperature and field dependencies are predicted for the noise spectral density in typical glasses with universal TLSs. The satisfactory interpretation of the recent experiment by J. Burnett et al. [Nat. Commun. 5, 4119 (2014)] in Pt-capped Nb superconducting resonators is attained by assuming a smaller density of TLSs compared to ordinary glasses, which is consistent with the very high internal quality factor in those samples.
What the full text shows
Theory or simulation- The 1/f noise amplitude in the microwave dielectric constant follows a power law increase with decreasing temperature, consistent with experimental observations in superconducting resonators. — T^{-1-η} where η ≈ 0.3 (Low temperatures (T < 0.1K) and microwave frequency ν₀ ≈ 5 GHz)
- The 1/f frequency dependence is caused by TLS spectral diffusion, where the resonance width grows logarithmically with time. — W₀(t) ≈ (π² / 3ℏ) χ k_B T ln(3.3 · AT³t) (Long times t ≥ 1s)
- Increasing the external AC field amplitude reduces the noise and weakens its temperature dependence. — Sxx ∝ T F_{AC}^{-2} in the large field limit (F_{AC} > 1000 V/m)
- The standard tunneling model (STM) with a homogeneous density of states (DOS) can explain the observed noise temperature dependence without requiring an energy-dependent DOS. (T < 0.1K)
- Setup
- Theoretical derivation and numerical calculations using parameters p₀ = 5D, P₀Urms = 5·10⁻⁴, A = 10⁸s⁻¹K⁻³, and ω = 2π · 5GHz; compared against experimental data from Pt-capped Nb superconducting resonators.
- How
- The authors derived an analytical solution for 1/f noise in the microwave dielectric constant using the standard tunneling model (STM), incorporating weak dipolar or elastic TLS-TLS interactions and spectral diffusion.
- Limitations
- The model predicts a stronger field dependence (Sxx ∝ F_{AC}^{-2}) than observed in the large field limit, possibly due to nonequilibrium heating. · The model fails to fit experimental noise temperature dependence at higher temperatures (T > 0.1K). · Accuracy in the very strong field regime is limited by assumptions regarding the phase decoherence rate.
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