Extended Data Fig. 1: Hong-Ou-Mandel indistinguishability measurement on photons emitted by two remote ¹⁷¹Yb ions.

a, Experimental setup for Hong-Ou-Mandel (HOM) measurements. Orthogonally polarized photons emitted from the A transitions of two ions with frequency difference ω₂ − ω₁ = Δω₁₂ ≈ 2π × 33 MHz (denoted \(| V,{\omega }_{1}\rangle \) and \(| H,{\omega }_{2}\rangle \)) are incident on a polarizing beamsplitter (PBS). Photon detections on two superconducting nanowire single photon detectors (SNSPD 1 and SNSPD 2 with detection times t₁ and t₂, respectively) are correlated. We maximize the HOM contrast by rotating the half waveplate (λ/2). The ions’ optical frequencies drift on week-long timescales, hence Δω₁₂ is slightly different here compared to Fig. 2. b, After optical excitation of both ions with resonant π pulses, photon coincidences are histogrammed with respect to the detection time difference (Δt = t₂ − t₁) using a 160 ns bin size. We don’t see any signature of HOM interference due to the ≈ 2π × 33 MHz frequency difference, rendering the photons distinguishable. c, Frequency information is erased by reducing the bin size below 1/Δω₁₂. We use a bin size of 4 ns and observe a quantum beat in coincidences, i.e. an oscillation between photon bunching and anti-bunching, at the optical frequency difference. Note that the number of coincidences has been re-normalized by the bin width to provide a direct comparison with b. d, We plot the number of coincidences using a 4 ns bin size but only at the trough of each oscillation (i.e. at the points of maximum anti-bunching), thereby recovering a conventional Hong-Ou-Mandel dip. Dip width is limited by optical Ramsey decoherence of the two ions between consecutive emission events. e, We extract a HOM visibility from the oscillation contrast, this is averaged over a two-sided window with width W i.e. −W/2 < Δt < W/2. For the smallest window size of 6 ns, a 96 ± 2% visibility is achieved. Solid lines are fits to a model detailed in Supplementary Information section III.