Anomalous periodicity in superpositions of localized periodic patterns

Interference between overlapping periodic patterns gives rise to important phenomena, such as Moiré fringes, appearing when the patterns have different periods or orientations. Here we present a novel phenomenon, applicable to both the classical and quantum regimes, where two one-dimensional localized periodic patterns with the same period interfere to create fringes with anomalous periodicity. We analyze the effect theoretically and demonstrate it with atomic matter waves. When a central parameter of the system is scanned continuously, we observe a discontinuous but piecewise-rigid periodicity of the resulting fringes. We show that this is a universal phenomenon that emerges from a superposition of two spatially shifted localized periodic patterns of any source or nature when they interfere with a global phase difference. The rigidity of the spectrum becomes even more robust for a coherent superposition of non-overlapping wavepackets, although the conventional interferometric visibility drops to zero. The effect is expected to appear in space and time, as well as in the momentum distribution of quantum particles.