Dynamical blockade in SU(1,1) quantum batteries via a neural network

In this study, we investigate the charging dynamics of a multiqubit quantum battery, characterized by the SU(2) algebra and driven by a finite-dimensional SU(1,1) bosonic charger. To enable systematic exploration of the parameter space, we develop and validate a neural-network surrogate model that replicates the exact quantum dynamics with high fidelity, yielding computational savings of up to 2 orders of magnitude compared with direct simulation. The dynamical blockade described below is the central physical result of this work, and the surrogate model is the computational means by which we characterize it across the full parameter space. Our framework reveals a many-body charging blockade: when the battery dimensions are comparable to the charger's excitation number, charging efficiency falls well below its kinematic limit despite ample energy remaining in the charger. We identify the physical underpinnings of this blockade as the saturation of the charger's emission rate, which confines the system to a low-excitation subspace before the battery can access its most absorptive states. This mechanism is intrinsic to finite chargers and absent in conventional infinite-mode models. This blockade is robust across a range of Bargmann indices and persists in a standard Dicke charger, confirming that it is a general feature of finite-dimensional charging rather than a property specific to the SU(1,1) algebra. We further show that a large number of charger excitations improves efficiency and reduces variance at the same time, whereas the blockade regime degrades both metrics together. These findings identify a many-body constraint on collective quantum charging and provide guidelines for designing high-performance quantum energy storage systems.