Correlating Decoherence in Transmon Qubits: Low Frequency Noise by Single Fluctuators

We report on long-term measurements of a highly coherent, nontunable superconducting transmon qubit, revealing low-frequency burst noise in coherence times and qubit transition frequency. We achieve this through a simultaneous measurement of the qubit’s relaxation and dephasing rate as well as its resonance frequency. The analysis of correlations between these parameters yields information about the microscopic origin of the intrinsic decoherence mechanisms in Josephson qubits. Our results are consistent with a small number of microscopic two-level systems located at the edges of the superconducting film, which is further confirmed by a spectral noise analysis.

Figure 1

(a) Measurement pattern: Single pulse sequences of different measurements (e.g., of $T_1$ and $T_2^{\mathrm{R}}$) are interleaved, resulting in a simultaneous acquisition. The time $\mathrm{\Delta }t$ is the free evolution. The ratio between the number of pulses can differ, and spin echo pulses may be added. The inset in (b) shows an exemplary single trace with fits for $T_1$ (red), $T_2^{\mathrm{R}}$ and the Ramsey detuning $\mathrm{\Delta }{\omega }_{\mathrm{q}}$ (green). (b) Data taken over a course of 19 hours displays fluctuations in $T_1$ and $T_2^{\mathrm{R}}$ (red squares and green stars, left axis), and telegraphlike switching of the qubit frequency $\mathrm{\Delta }{\omega }_{\mathrm{q}}$ (blue dots, right axis). The time resolution corresponds to 10 s of averaging using the pattern shown in (a). For clarity, dephasing times are divided by two. With this measurement we reveal a connection between noise at mHz frequencies and qubit dephasing. (c) Illustration of how the frequency of a single TLS near resonance with the qubit fluctuates due to its coupling to thermally activated TLS (so-called TLF) at energies at or below $k_{\mathrm{B}}T$ (orange shaded area). Depending on the detuning between qubit and TLS, this can cause positive or negative correlations between qubit coherence times and its resonance frequency.

Figure 2

(a) Cross-correlation of the absolute fluctuation strength and relaxation or dephasing rates of the dataset shown in (b). All curves show significant correlation at zero time delay $\tau$, relating fluctuations in qubit frequency on the order of seconds to relaxation and dephasing. (b),(c) Scatterplots of $T_{\mathrm{\Phi }}$ vs Ramsey detuning for two measurements from different cooldowns (identical setup) with drastically different pure dephasing times. The point color indicates the measurement time. In (b) positive, negative, and no correlation occur within the measurement period. In (c) the qubit frequency is relatively stable, bins of pure dephasing times are colored in the vertical histogram, corresponding fits to normal distributions (top panel) are colored accordingly. Lower dephasing times correspond to larger variances in qubit frequency. The standard deviation of the violet curve is indicated exemplarily. On the right, the extracted variances ${\sigma }^2$ are plotted against the corresponding mean values of pure dephasing. A fit to the expected function $T_{\mathrm{\Phi }}\propto 1/{\sigma }^2$ is in agreement with the data. The simulated field distribution at the superconducting film edge of the qubit capacitance is shown in the inset.

Figure 3

Power spectral density of frequency fluctuations $\mathrm{\Delta }{\omega }_{\mathrm{q}}$ (cyan dots) in a long-term measurement of 47 h, revealing significant deviation from $1/f^{\alpha }$ noise (dash-dotted line). A fit (red solid line) is in agreement with the effect of a single thermal TLF (black dashed line) plus $1/f^{\alpha }$. The inset shows a short section of raw data, showing telegraphic noise that is presumably due to frequency switching of a near-resonant TLS coupled to a single thermal fluctuator. The frequency uncertainty is approximately the size of the dots.