Phantom energy in the nonlinear response of a quantum many-body scar state

Quantum many-body scars are notable as nonthermal states that exist at high energies. Here, we use attractively interacting dysprosium gases to create scar states that are stable enough be driven into a strongly nonlinear regime while retaining their character. We uncover an emergent nonlinear many-body phenomenon, the effective transmutation of attractive interactions into repulsive interactions. We measure how the kinetic and total energies evolve after quenching the confining potential. Although the bare interactions are attractive, the low-energy degrees of freedom evolve as if they repel each other: Thus, their kinetic energy paradoxically decreases as the gas is compressed. The missing ``phantom'' energy is quantified by benchmarking our experimental results against generalized hydrodynamics calculations. We present evidence that the missing kinetic energy is stored in very high-momentum modes.