We present the results of our ALMA Cycle 4 high-spatial-resolution (0.04-0.07) observations, at HCN J=3-2 and HCO+ J=3-2 lines, of the nucleus of NGC 1068, the nearby prototypical type 2 active galactic nucleus (AGN). Our previous ALMA observations identified the compact emission of these lines at the putative location of the torus around a mass-accreting supermassive black hole. We now report that we have detected the rotation of this compact emission, with the eastern and western sides being redshifted and blueshifted, respectively. Unlike the previously reported CO J=6-5 emission, both the morphological and dynamical alignments of the HCN J=3-2 and HCO+ J=3-2 emission are roughly aligned along the east-west direction (i.e., the expected torus direction), suggesting that these molecular lines are better probes of a rotating dense molecular gas component in the torus. The western part of the torus exhibits larger velocity dispersion and stronger emission in the HCN J=3-2 and HCO+ J=3-2 lines than the eastern part, revealing a highly inhomogeneous molecular torus. The dense molecular gas in the torus and that of the host galaxy at 0.5-2.0 from the AGN along the torus direction are found to be counter-rotating, suggesting an external process happened in the past at the NGC 1068 nucleus.
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