Extended Data Fig. 2: Measuring the optical spectral diffusion correlation timescale of a ¹⁷¹Yb ion.

a, Optical spectral diffusion on timescales longer than the optical lifetime is measured using a delayed echo pulse sequence. First, a superposition between the \(| 0\rangle \) and \(| e\rangle \) states, \(|\psi \rangle =1/\sqrt{2}(|0\rangle +|e\rangle )\), is used to probe the initial optical frequency, ω(0). A free evolution time, τ, yields the state \(|\psi \rangle \approx 1/\sqrt{2}(|0\rangle +|e\rangle {e}^{-i\omega (0)\tau })\). Next, the state is mapped to the qubit manifold, \(|\psi \rangle \approx 1/\sqrt{2}(|0\rangle +|1\rangle {e}^{-i\omega (0)\tau })\), and stored for a duration T_W using an XY-8 pulse sequence with an odd number of pulses (2N + 1) that have a separation of 2τ_s = 5.8 μs. During this wait time the optical frequency undergoes spectral diffusion with correlation timescale τ_c (red line). Finally, the optical frequency is probed for a second time by mapping the qubit state back on to the optical transition. After a free evolution time, τ, the quantum state is \(|\psi \rangle \approx 1/\sqrt{2}(|0\rangle +|1\rangle {e}^{-i[\omega ({T}_{W})-\omega (0)]\tau })\). When the wait time is much less than the optical correlation timescale (T_W ≪ τ_c), ω(T_W) − ω(0) ≈ 0 and coherence is preserved. However, when T_W ≫ τ_c, ω(T_W) and ω(0) are uncorrelated, optical coherence isn’t rephased and the measurement contrast reduces. b, Experimental results plotting the final state coherence, C, against wait time, T_W, with logarithmic y axis and fixed τ = 1.5 μs. We fit a decay profile with form \(\log (C)=a-b(1-{e}^{-{T}_{W}/{\tau }_{c}})-({T}_{W}/{T}_{2,s})\) (solid line) where a, b and τ_c are free parameters, and T_2,s is the spin XY-8 coherence time, obtained from independent measurements. Note that the initial coherence contrast, a, is limited by optical decay during the two free evolution periods of duration τ. The red and green regions correspond to decays attributed to optical decorrelation and spin decoherence, respectively. We extract an optical frequency correlation timescale of τ_c = 1.42 ± 0.04 ms.