Persistence of small polarons into the superconducting doping range of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>Ba</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:mi>x</mml:mi></mml:mrow></mml:ms

Bipolaronic superconductivity is an exotic pairing mechanism proposed for materials like <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:msub><a:mi>Ba</a:mi><a:mrow><a:mn>1</a:mn><a:mo>−</a:mo><a:mi>x</a:mi></a:mrow></a:msub><a:msub><a:mi mathvariant="normal">K</a:mi><a:mi>x</a:mi></a:msub><a:msub><a:mi>BiO</a:mi><a:mn>3</a:mn></a:msub></a:mrow></a:math> (BKBO); however, conclusive experimental evidence for a (bi)polaron metallic state in this material remains elusive. Here, we combine resonant inelastic x-ray and neutron total scattering techniques with advanced modeling to study the local lattice distortions, electronic structure, and electron-phonon <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mo>(</c:mo><c:mi>e</c:mi><c:mtext>−</c:mtext><c:mi>ph</c:mi><c:mo>)</c:mo></c:math> coupling in BKBO as a function of doping. Data for the parent compound <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mrow><d:mo>(</d:mo><d:mi>x</d:mi><d:mo>=</d:mo><d:mn>0</d:mn><d:mo>)</d:mo></d:mrow></d:math> indicate that the electronic gap opens in predominantly oxygen-derived states strongly coupled to a long-range ordered breathing distortion of the oxygen sublattice. Upon doping, short-range breathing distortions and sizable <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mi>e</e:mi></e:math>-ph coupling persist into the superconducting regime <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"><f:mrow><f:mo>(</f:mo><f:mi>x</f:mi><f:mo>=</f:mo><f:mn>0.4</f:mn><f:mo>)</f:mo></f:mrow></f:math>. Comparisons with exact diagonalization and determinant quantum Monte Carlo calculations further support this conclusion. Our results provide compelling evidence that BKBO’s metallic phase hosts a liquid of small (bi)polarons derived from local breathing distortions of the lattice, with implications for understanding the low-temperature superconducting instability.