Two-Level System Spectroscopy from Correlated Multilevel Relaxation in Superconducting Qubits

Transmon qubits are a cornerstone of modern superconducting quantum computing platforms. Temporal fluctuations of energy relaxation in these qubits are widely attributed to microscopic two-level systems (TLSs) in device dielectrics and interfaces, yet isolating individual defects typically relies on tuning the qubit or the TLS into resonance. We demonstrate a novel spectroscopy method for fixed-frequency transmons based on multilevel relaxation: repeated preparation of the second excited state and simultaneous $T_1$ extraction of the first and second excited states reveals characteristic correlations in the decay rates of adjacent transitions. From these correlations we identify one or more dominant TLSs and reconstruct their frequency drift over time. Remarkably, we find that TLSs detuned by $\gtrsim 100,\mathrm{MHz}$ from the qubit transition can still significantly influence relaxation. The proposed method provides a powerful tool for TLS spectroscopy without the need to tune the transmon frequency, either via a flux-tunable inductor or AC-Stark shifts.

💡 Research Summary

This work introduces a novel spectroscopy technique for fixed‑frequency transmon qubits that leverages multilevel relaxation dynamics to identify and track individual two‑level system (TLS) defects without any frequency tuning of the qubit. The authors prepare the transmon repeatedly in its second excited state |2⟩ and, after a variable delay, perform a three‑level readout that simultaneously yields the populations of |0⟩, |1⟩, and |2⟩. By fitting the time‑dependent populations to the analytical solutions of the three‑level rate equations, they extract the decay rates Γ₁₀ (|1⟩→|0⟩) and Γ₂₁ (|2⟩→|1⟩) as functions of time, denoted T₁e=1/Γ₁₀ and T₁f=1/Γ₂₁.

In an ideal harmonic oscillator the relation Γ₂₁=2Γ₁₀ holds, but the experiments reveal significant deviations and, more importantly, strong anti‑correlated fluctuations between T₁e and T₁f over many hours. The authors explain this behavior with a single TLS whose resonance frequency ω_TLS drifts between the two transmon transition frequencies ω₀₁ and ω₁₂ (ω₁₂=ω₀₁+α). The TLS contributes a Lorentzian noise spectral density S(ω)=A·γ_TLS/