  Dark matter detectors that utilize liquid xenon have now achieved tonne-scale
targets, giving them sensitivity to all flavours of supernova neutrinos via
coherent elastic neutrino-nucleus scattering. Considering for the first time a
realistic detector model, we simulate the expected supernova neutrino signal
for different progenitor masses and nuclear equations of state in existing and
upcoming dual-phase liquid xenon experiments. We show that the proportional
scintillation signal (S2) of a dual-phase detector allows for a clear
observation of the neutrino signal and guarantees a particularly low energy
threshold, while the backgrounds are rendered negligible during the supernova
burst. XENON1T (XENONnT and LZ; DARWIN) experiments will be sensitive to a
supernova burst up to 25 (35; 65) kpc from Earth at a significance of more than
5 sigma, observing approximately 35 (123; 704) events from a 27 Msun supernova
progenitor at 10 kpc. Moreover, it will be possible to measure the average
neutrino energy of all flavours, to constrain the total explosion energy, and
to reconstruct the supernova neutrino light curve. Our results suggest that a
large xenon detector such as DARWIN will be competitive with dedicated neutrino
telescopes, while providing complementary information that is not otherwise
accessible.
