Extended Data Fig. 4: Coherence characterization in spin-echo measurements.
From: Quantum thermalization and Floquet engineering in a spin ensemble with a clock transition
a, The spin-echo sequence with a final π/2 analyzer pulse with a variable phase angle θ. The phase angle θ defines the rotation axis of the π/2 pulse relative to the initial π/2 pulse. While maintaining a fixed free evolution time τ, θ is varied from 0 to 2π to quantify the residual coherence of the spin ensemble. b, Photoluminescence signals from the spin system exhibit a sinusoidal oscillation as θ is swept, from which coherence is extracted as the contrast of the oscillation. c, Coherence decay profiles as a function of evolution time τ for the cases of large J ≈ 2π × 0.35 MHz and small J ≈ 2π × 0.19 MHz. d, Comparison of long-time decoherence dynamics between experiment and simulation under the spin-echo dynamics. The numerical simulations with calibrated parameters (solid lines) show excellent agreement with the experiments (markers) over extended long times for both the small J (orange) and large J (blue) cases.
