Context : Doppler tomography of emission line profiles in low mass X-ray binaries allows us to disentangle the different emission sites and study the structure and variability of accretion disks . Aims : We present UVES high-resolution spectroscopic observations of the black hole binary A0620–00 at quiescence . Methods : These spectroscopic data constrain the orbital parameters P _ { orb } = 0.32301405 ( 1 ) d and K _ { 2 } = 437.1 \pm 2.0 { km } \ > { s } ^ { -1 } . These values , together with the mass ratio q = M _ { 2 } / M _ { 1 } = 0.062 \pm 0.010 , imply a minimum mass for the compact object of M _ { 1 } \sin ^ { 3 } i = 3.15 \pm 0.10 \hbox { M } _ { \odot } , consistent with previous works . Results : The H \alpha emission from the accretion disk is much weaker than in previous studies , possibly due to a decrease in disk activity . Doppler imaging of the H \alpha line shows for the first time a narrow component coming from the secondary star , with an observed equivalent width of 1.4 \pm 0.3 Å , perhaps associated to chromospheric activity . Subtracting a K-type template star and correcting for the veiling of the accretion disk yields to an equivalent width of 2.8 \pm 0.3 Å . A bright hot-spot is also detected at the position where the gas stream trajectory intercepts with the accretion disk . Conclusions : The H \alpha flux associated to the secondary star is too large to be powered by X-ray irradiation . It is comparable to those observed in RS CVn binaries with similar orbital periods and , therefore , is probably triggered by the rapid stellar rotation .