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© Published under licence by IOP Publishing Ltd.Materials, consisting of Jahn-Teller (JT) ions, such as cuprates and manganites, display many outstanding properties, including high temperature superconductivity and colossal magnetoresistance. There, the role of JT effect, although widely recognized, is still elusive. Here we show that these materials have vibronic excitations, related to local deformations rotating around JT ions in the dynamic limit, arising from linear electron-vibrational coupling in the "Mexican hat" potential profile. Their energy depends on total angular momentum, which is quantized, as in quantum rotors. We found them in the representative JT compound of orthorhombic manganites, LaMnO3. Since the "Mexican hat" potential energy surface is double-valued, they show up near the ground and excited states of JT ions. Recently, by using spectroscopic ellipsometry technique, we showed that they appear in the excited state in the form of sidebands, accompanying the electron transition between the JT split orbitals at neighboring Mn3+ ions. Here, by using Raman scattering technique, we show that they also exist near the ground state. The found quantum rotor excitations may play an important role in many unusual properties observed in these materials.