Fig. 4: Numerically simulated Hahn-echo qubit coherence function \(\langle {\hat{\sigma }}_{y}({t}_{f})\rangle\) corresponding to two charge-noise baths.
From: Intrinsic and induced quantum quenches for enhancing qubit-based quantum noise spectroscopy
The bath spectral functions are generated by an ensemble of two-level fluctuators (TLFs) with \({\hat{H}}_{{{{{{{{\rm{TLF}}}}}}}}}=\epsilon {\hat{{{\Sigma }}}}_{z}+{{\Delta }}{\hat{{{\Sigma }}}}_{x}\), which are coupled to a phonon bath via \({\hat{{{\Sigma }}}}_{x}\) (see49 for details). Two TLF distributions P(ϵ, Δ) are used in the simulation: P(ϵ, Δ) ∝ ϵ/Δ (triangles), and P(ϵ, Δ) ∝ 1/Δ (circles). The qubit–bath coupling strength is chosen such that the qubit coherence time is T2e = 1 μs at T = 10 mK (orange triangles and blue circles). As we increase bath temperature to T = 50 mK, the two models predict qualitative difference in the behavior of the Hahn-echo signal \(\langle {\hat{\sigma }}_{y}({t}_{f})\rangle\) (purple triangles and green circles), which in turn encodes dynamics of the quench phase shift (QPS).
