Probing non-ergodicity and symmetry via direct measurement of coherent scattering in a shaken rotor

The Coherent Backscattering (CBS) peak is a well-known interferential signature of weak localization in disordered or chaotic systems. More recently, a second interference feature-the Coherent Forward Scattering (CFS) peak-was predicted to emerge in the regime of strong localization. However, it has never been directly observed. Here we report the direct observation of the CFS peak and demonstrate its dual role as a signature of non-ergodicity and as a probe of symmetries in quantum chaotic systems. Using a shaken rotor model realized with a Bose-Einstein condensate (BEC) of ultracold atoms in a modulated optical lattice, we investigate dynamical localization in momentum space. The CFS peak emerges in the position distribution as a consequence of non-ergodic dynamics, while its growth timescale and width reveal the underlying localization length. By finely tuning the modulation, we control time-reversal and parity symmetries and measure their distinct effects on both CBS and CFS peaks in position space. Our results highlight the strong link of both temporal growth and contrast of the coherent scattering peaks with symmetry and localization. This work opens several perspectives for investigating coherent scattering signatures in a many-body context.