We present a multi-wavelength integral field spectroscopic study of the low-z LIRG IRAS F11506-3851, on the basis of VIMOS and SINFONI (ESO-VLT) observations. The morphology and the 2D kinematics of the gaseous (neutral and ionized) and stellar components have been mapped using the NaD doublet, the H$alpha$ line, and the near-IR CO(2-0) and CO(3-1) bands. The kinematics of the ionized gas and the stars are dominated by rotation, with large observed velocity amplitudes and centrally peaked velocity dispersion maps. The stars lag behind the warm gas and represent a dynamically hotter system, as indicated by the observed dynamical ratios. Thanks to these IFS data we have disentangled the contribution of the stars and the ISM to the NaD feature, finding that it is dominated by the absorption of neutral gas clouds in the ISM. The neutral gas 2D kinematics shows a complex structure dominated by two components. On the one hand, the thick slowly rotating disk lags significantly compared to the ionized gas and the stars, with an irregular and off-center velocity dispersion map. On the other hand, a kpc-scale neutral gas outflow is observed along the semi-minor axis of the galaxy, as revealed by large blueshifted velocities (30-154 km/s). We derive an outflowing mass rate in neutral gas of about 48 $dot{M_{rm w}}$/yr. Although this implies a global mass loading factor of 1.4, the 2D distribution of the ongoing SF suggests a much larger value of mass loading factor associated with the inner regions (R$<$200 pc), where the current SF represents only 3 percent of the total. All together these results strongly suggest that we are witnessing (nuclear) quenching due to SF feedback in IRAS F11506-3851. However, the relatively large mass of molecular gas detected in the nuclear region via the H2 1-0 S(1) line suggests that further episodes of SF may take place again.
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