Quantum phase transitions (QPTs) driven by quantum fluctuations are transitions between distinct quantum phases of matter. At present, they are poorly understood and not readily controlled. Here, scanning tunneling microscopy (STM) and noncontact atomic force microscopy (nc-AFM) are used to explore atomic scale control over quantum phase transitions between two different topological quantum states of a well-defined π-conjugated polymer. The phase transition is driven by a pseudo Jahn-Teller effect that is activated above a certain polymer chain length. In addition, theoretical calculations indicate the presence of long-lasting coherent fluctuations between the polymer's two quantum phases near the phase transition, at finite temperature. This work thus presents a new way of exploring atomic-scale control over QPTs and indicates that emerging quantum criticality in the vicinity of a QPT can give rise to new states of organic matter.
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