Context. The origin of the enormous luminosities of the two opaque nuclei of Arp 220, the prototypical ultra-luminous infrared galaxy, remains a mystery because we lack observational tools to explore the innermost regions around the nuclei. Aims. We explore the potential of imaging vibrationally excited molecular emission at high angular resolution to better understand the morphology and physical structure of the dense gas in Arp 220 and to gain insight into the nature of the nuclear powering sources. Methods. The Atacama Large Millimeter/submillimeter Array (ALMA) provided simultaneous observations of HCN, HCO + , and vibrationally excited HCN v 2 = 1 f emission. Their J = 4-3 and 3-2 transitions were observed at a matching resolution of ∼0.5 , which allows us to isolate the emission from the two nuclei. Results. The HCN and HCO + lines within the ground-vibrational state poorly describe the central ∼100 pc region around the nuclei because there are strong effects of cool absorbing gas in the foreground and severe line blending that is due to the prolific molecular emission of Arp 220. Vibrationally excited emission of HCN is detected in both nuclei with a very high ratio relative to the total L FIR , higher than in any other observed galaxy and well above what is observed in Galactic hot cores. HCN v 2 = 1 f is observed to be marginally resolved in ∼60 × 50 pc regions inside the dusty ∼100 pc sized nuclear cores. Its emission is centered on our derived individual nuclear velocities based on HCO + emission (V WN = 5342 ± 4 and V EN = 5454 ± 8 km s −1 , for the western and eastern nucleus, respectively). With virial masses within r ∼ 25-30 pc based on the HCN v 2 = 1 f line widths, we estimate gas surface densities (gas fraction f g = 0.1) of 3 ± 0.3 × 10 4 M pc −2 (WN) and 1.1 ± 0.1 × 10 4 M pc −2 (EN). The 4−3/3−2 flux density ratio could be consistent with optically thick emission, which would further constrain the size of the emitting region to >15 pc (EN) and >22 pc (WN). The absorption systems that may hide up to 70% of the HCN and HCO + emission are found at velocities of −50 km s −1 (EN) and 6, −140, and −575 km s −1 (WN) relative to velocities of the nuclei. Blueshifted absorptions are the evidence of outflowing motions from both nuclei. Conclusions. Although vibrationally excited molecular transitions could also be affected by opacity, they may be our best tool to peer into the central few tens of parsecs around compact obscured nuclei like those of Arp 220. The bright vibrational emission implies the existence of a hot dust region radiatively pumping these transitions. We find evidence of a strong temperature gradient that would be responsible for both the HCN v 2 pumping and the absorbed profiles from the vibrational ground state as a result of both continuum and self-absorption by cooler foreground gas.