Incoherent Measurement of a Sub-10 kHz Optical Linewidth

Quantum state lifetimes T_{2}, or equivalently homogeneous linewidths Γ_{h}=1/πT_{2}, are a key parameter for understanding decoherence processes in quantum systems and assessing their potential for applications in quantum technologies. The most common tool for measuring narrow optical homogeneous linewidths, i.e., long T_{2}, is the measurement of coherent photon echo emissions, which however gives very weak signal when the number of emitters is small. This strongly hampers the development of nanomaterials, such as those based on rare earth ions, for quantum communication and processing. In this work, we propose, and demonstrate in an erbium doped crystal, a measurement of photon echoes based on incoherent fluorescence detection and its variance analysis. It gives access to T_{2} through a much larger signal than direct photon echo detection, and, importantly, with a laser which is incoherent over the measurement timescale, on the order of a few T_{2}. Our results thus open the way to efficiently assess the properties of a broad range of emitters and materials for applications in quantum nanophotonics.