Robust Hamiltonian engineering with subensemble control

We study a Hamiltonian engineering protocol based on the global, pulsed control of multiple sub-ensembles of interacting spin systems. This setting is directly relevant to NV centers with different crystalline orientations or multi-species atomic ensembles. Specifically, we aim to realize a target Hamiltonian consisting of desired inter- and intra-species interactions by reshaping a given native spin Hamiltonian via a sequence of pulses. Unlike earlier works, the simultaneous engineering of inter- and intra-species interactions imposes severe constraints, making our task provably computationally hard. Despite its formal hardness, we identify a set of conditions under which a target Hamiltonian can or cannot be synthesized from the native one. Moreover, we introduce efficient numerical strategies for designing pulse sequences that engineer a target Hamiltonian and are robust against common control imperfections. As a specific application, we discuss the generation of two-mode spin squeezing in dual-species atomic ensembles in cavities and optical tweezers. Our results provide a practical toolbox to design novel quantum simulation and sensing experiments with minimal control overhead.