The spectral characterization of quantum emitter luminescence over broad
wavelength ranges and fast timescales is important for applications ranging
from biophysics to quantum technologies. Here we present the application of
time-domain Fourier transform spectroscopy, based on a compact and stable
birefringent interferometer coupled to low-dark-count superconducting
single-photon detectors, to the study of quantum emitters. We experimentally
demonstrate that the system enables spectroscopy of quantum emitters over a
broad wavelength interval from the near-infrared to the telecom range, where
grating-based spectrometers coupled to InGaAs cameras are typically noisy and
inefficient. We further show that the high temporal resolution of single-photon
detectors, which can be on the order of tens of picoseconds, enables the
monitoring of spin-dependent spectral changes on sub-nanosecond timescales.

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