  Quantum anomalies are violations of classical scaling symmetries caused by
quantum fluctuations. Although they appear prominently in quantum field theory
to regularize divergent physical quantities, their influence on experimental
observables is difficult to discern. Here, we discovered a striking
manifestation of a quantum anomaly in the momentum-space dynamics of a 2D Fermi
superfluid of ultracold atoms. We measured the position and pair momentum
distribution of the superfluid during a breathing mode cycle for different
interaction strengths across the BEC-BCS crossover. Whereas the system exhibits
self-similar evolution in the weakly interacting BEC and BCS limits, we found a
violation in the strongly interacting regime. The signature of scale-invariance
breaking is enhanced in the first-order coherence function. In particular, the
power-law exponents that characterize long-range phase correlations in the
system are modified due to this effect, indicating that the quantum anomaly has
a significant influence on the critical properties of 2D superfluids.
