  We measured basic parameters such as the lifetime, mobility, and diffusion
constant of trapped paraexcitons in cuprous oxide at very low temperatures
(below 1 K) using a dilution refrigerator. To obtain these parameters, we
observed the space- and time-resolved luminescence spectrum of paraexcitons in
strain-induced trap potential. We extracted the lifetime of 410 ns from the
measurements of the decay of the luminescence intensity. By comparing the
experimental results and numerical calculations, we found that the mobility and
the diffusion constant increase as the temperature of the paraexcitons
decreases below 1 K. In particular, we obtained a mobility of 5.1e7 cm^2/V*s at
the corresponding temperature of 280 mK. To the best of our knowledge, this
value is the highest exciton mobility that has been measured. These results
show that the mean free path of the paraexcitons reaches a size (~300 um)
comparable to that of the cloud of trapped paraexcitons (~100 um). From our
analyses, we found that the spatial distribution of the paraexcitons can reach
a distribution that is defined by the statistical distribution function and the
shape of the three-dimensional trap potential at ultra-low temperatures (well
below 1 K). Our survey shows that the ultra-low temperature ensures that the
Bose--Einstein condensation transition in a trap potential can be investigated
by examining the spatial distribution of the density of 1s paraexcitons.
