Outflows driven by active galactic nuclei (AGN) are expected to have a significant impact on the host galaxy evolution, but it is still debated how they are accelerated and propagate on galaxy-wide scales. This work addresses these questions by studying the link between X-ray, nuclear ultra-fast outflows (UFOs) and extended ionised outflows, for the first time in two quasars close to the peak of AGN activity ($zsim2$), where AGN feedback is expected to be more effective. As targets, we selected two multiple-lensed quasars at $zsim1.5$, HS 0810+2554 and SDSS J1353+1138, known to host UFOs and observed with the near-IR integral field spectrometer SINFONI at the VLT. We performed a kinematical analysis of the [O III]$lambda$5007 optical emission line, in order to trace the presence of ionised outflows. We detected spatially resolved ionised outflows in both galaxies, extended more than 8 kpc and moving up to $v>2000$ km/s. We derived mass outflow rates of $sim$12 M$_{sun}$/yr and $sim$2 M$_{sun}$/yr for HS 0810+2554 and SDSS J1353+1138. Comparing with the co-hosted UFO energetics, the ionised outflow energetics in HS 0810+2554 is broadly consistent with a momentum-driven regime of wind propagation, while in SDSS J1353+1138 it differs by a factor of $sim$100 from theoretical predictions, requiring either a massive molecular outflow or a high variability of the AGN activity to account for such a discrepancy. By additionally considering our results with those from the small sample of well-studied objects (all local but one), with both UFO and extended (ionised/atomic/molecular) outflow detections, we found that in 10 out of 12 galaxies the large-scale outflow energetics is consistent with the theoretical predictions of either a momentum- or an energy-driven scenario. This suggests that such models explain relatively well the acceleration mechanism of AGN-driven winds on large scales.
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