Fig. 2

Experimental observation of CBS and CFS peaks in two symmetry classes. Using two periodically modulated kick sequences with different symmetry properties, we measure the time-evolution of the zero-momentum probability density Π₀(t). a The kick sequence with \(\tilde \varphi = 0\) in Eq. (5) has symmetric amplitudes \({\cal K}(t)\) and antisymmetric phases a(t) by reversing time around τ = 3.5 (and 8.5) kicks, so that the system is in the orthogonal symmetry class. b For \(\tilde \varphi = - 3\pi {\mathrm{/}}5\), the sequence has no symmetry, putting the system in the unitary class. c In the orthogonal class, we observe two distinct enhancements of Π₀(t), at times t = 6 (mod. 10) and t = 0 (mod. 10), associated to CBS (green) and CFS (red) peaks, respectively. The CBS peaks have maximum contrast early during the kick sequence, and decrease due to stray decoherence, whereas the CFS peaks start by slowly increasing in contrast, and equalize the CBS at longer times. This constitutes a genuine interferential signature of the emergence of Anderson localization. d The time evolution of Π₀ obtained with a Hamiltonian with broken PT-symmetry clearly shows the disappearance of the CBS peaks in the unitary class. The CFS peaks, insensitive to the symmetry breaking, continue to be present, with a contrast following the same increasing trend at short times