  We often infer the state of systems in nature indirectly, for example in high
energy physics by recording the tracks particles leave behind in an ambient
medium. We adapt this principle to energies 9 orders of magnitude smaller, to
classify the final state of exotic molecules after internal conversion of their
electronic state, through their interaction with an ambient quantum fluid, a
Bose-Einstein condensate. The BEC is the ground-state of a million bosonic
atoms near zero temperature, and a single embedded ultra-long range Rydberg
molecule can coherently excite waves in this fluid, which carry tell-tale
signatures of its dynamics. Bond lengths exceeding a micrometer allow us to
observe the molecular fingerprint on the BEC in situ, via optical microscopy.
Interpreting images in comparison with simulations shows that the molecular
electronic state rapidly converts from the initially excited S- and D-orbitals
to a much more complex molecular state (called "trilobite"), marked by a
maximally localized electron. This internal conversion liberates energy, such
that one expects final state particles to move rapidly through the medium,
which is however ruled out by comparing experiment and simulations. The
molecule thus must strongly decelerate in the medium, for which we propose a
plausible mechanism. Our experiment demonstrates a coherent medium that
facilitates and records an electronic state change of embedded exotic molecules
in ultra-cold chemistry, with sufficient sensitivity to constrain velocities of
final state particles.
