  Water plays a crucial role both in the interstellar medium and on Earth. To
constrain its formation mechanisms and its evolution through the star formation
process, the determination of the water deuterium fractionation ratios is
particularly suitable. Previous studies derived HDO/H$_2$O ratios in the warm
inner regions of low-mass protostars. We here report a detection of the D$_2$O
1$_{1,0}$-1$_{0,1}$ transition toward the low-mass protostar NGC1333 IRAS2A
with the Plateau de Bure interferometer: this represents the first
interferometric detection of D$_2$O - and only the second solar-type protostar
for which this isotopologue is detected. Using the observations of the HDO
5$_{4,2}$-6$_{3,3}$ transition simultaneously detected and three other HDO
lines previously observed, we show that the HDO line fluxes are well reproduced
with a single excitation temperature of 218$\pm$21 K and a source size of
$\sim$0.5 arcsec. The D$_2$O/HDO ratio is $\sim$(1.2$\pm$0.5) $\times$
10$^{-2}$, while the use of previous H$_2^{18}$O observations give an
HDO/H$_2$O ratio of $\sim$(1.7$\pm$0.8) $\times$ 10$^{-3}$, i.e. a factor of 7
lower than the D$_2$O/HDO ratio. These results contradict the predictions of
current grain surface chemical models and indicate that either the surface
deuteration processes are poorly understood or that both sublimation of grain
mantles and water formation at high temperatures ($\gtrsim$230 K) take place in
the inner regions of this source. In the second scenario, the thermal
desorption of the grain mantles would explain the high D$_2$O/HDO ratio, while
water formation at high temperature would explain significant extra production
of H$_2$O leading to a decrease of the HDO/H$_2$O ratio.
