Many-body dynamical localization in Fock space

We investigate the emergence of many-body dynamical localization (MBDL) in the Fock space of an interacting two-mode bosonic system subject to periodic driving. Using a mapping to the paradigmatic kicked-top model, we analyze the interplay between classical chaotic diffusion and quantum interference effects. While the mean-field (classical) dynamics exhibits bounded ergodic diffusion along the population imbalance axis, the quantum dynamics reveals strong suppression of transport in Fock space, in close analogy with Anderson localization in disordered lattices. We characterize the localization length, its scaling with particle number and driving parameters, and reveal the spectral crossover from random-matrix to Poisson statistics as the many-body ensemble localizes. We highlight the connection between MBDL and discrete time crystals. Our findings offer a promising avenue to study the Anderson transition in Fock space.