Fig. 4: Measurement of photoluminescence (PL) lifetime from ion arrays.

a PL lifetimes of the Tm³⁺ ions as a function of wavelength in the periodic array, indicating the lifetime shortening near the atomic resonance as a result of cooperative resonances. The solid curve is a fit using a double-Lorentzian function with center wavelengths and widths matching that of scattering profile from the disordered array (Fig. 3a). The inset shows two PL decay curves of the Tm³⁺ ions: one away from the atomic resonance (red), the other close with the resonance (blue). τ is the exponential time constant of the PL decay curve; b PL lifetimes of the Tm³⁺ ions as a function of wavelength in the sample with disordered ion array, showing the lifetime is mainly unchanged near the atomic resonance; We note that the slight difference in quality factors of rings used in a and b causes small differences in Purcell-enhanced emission in the two cases and therefore the off-resonant lifetimes are not exactly the same. The shaded regions indicate the predicted cavity resonances based on measurement of the cavity spectrum obtained from a different experiment run while taking into the account the uncertainly due to the drift in the cavity resonances; c PL lifetimes of the Tm³⁺ ions as a function of input resonant pump power in the periodic array at a fixed wavelength of 794.4 nm. The lifetime linearly changes with the pump power that is a proxy for ion numbers in the array. Above some critical power, the lifetime remains unchanged as the pump saturates the ions. The y-intercept of the linear fit is ~224 μs. The lifetime data in a and b are taken with the pump power in the saturation region of c. Error bars defined here represent 95% confidence interval.