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Quantum phase transitions, which are driven by quantum fluctuations, mark afrontier between distinct quantum phases of matter. However, our understandingand control of such phenomena is still limited. Here we report an atomic scalecontrol of quantum phase transition between two different topological quantumclasses of a well-defined {\pi}-conjugated polymer controlled by their length.We reveal that a pseudo Jahn-Teller effect is the driving mechanism of thephase transition, being activated above a certain polymer chain length. Inaddition, our theoretical calculations indicate the presence of long-timecoherent fluctuations at finite temperature between the two quantum phases ofthe polymer near the phase transition. This work may pave new ways to achieveatomic scale control of quantum phase transitions, in particular in organicmatter.

Atomic scale control and visualization of topological quantum phase transition in {\pi}-conjugated polymers driven by their length