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

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