Fig. 4. Pure dephasing of single photon state.

a Visualisation of the time-resolved HOM experiment (not to scale for better visualisation). The black solid line symbolises the single-photon wavefunction, while the black dashed line represents its envelope. For short times close to 0 ns, laser noise photons are observed (red pulse). This contribution is conveniently filtered out by only accepting detection events posterior to the start gate delay t_Start. In our visualisation, the photon wave function experiences a phase kick at a time delay of about 10 ns, due to phonon scattering in the V1 excited state. By having a variable stop gate time t_Stop, we effectively control the integration window Δt = t_Stop − t_Start. This allows us to infer the time scale of pure dephasing. b Uncorrected HOM pattern at T = 5.0 K for t_Start = 3.5 ns and Δt = 4 ns. Owing to the short time gating, the raw visibility increases to V₀ = 0.85 ± 0.04, which matches the theoretical expectation (0.80 ± 0.01) considering only experimental imperfections (see Supplementary Note 3). Dots are data and lines are visual guides. c Corrected HOM visibility at t_Start = 3.5 ns and varying Δt and at three different temperatures. For Δt → 0 ns, visibilities approach unity, as pure dephasing is completely suppressed. Dots are data (red circles: 5.0 K, blue cross marks: 5.9 K, and green triangles: 6.8 K), and lines with associated colours are fits for data at each temperature according to Eq. (1). d Temperature-dependent pure dephasing rate ${\gamma }_{\max }^{\prime }$ (red circles) and associated spectral diffusion amplitude ${\mathrm{\Gamma }}_0^{\prime }$ (black squares). The red line is the fit considering the model described with Eq. (2). The black line is a guide to the eye. Error bars in c and d correspond to one standard error.