Sampled-detuning optimal control for robust entanglement generation in dipole-coupled atoms
High-fidelity entangled-state generation in driven two-atom systems is often optimized at a nominal transition frequency, which can produce control pulses that are fragile against detuning errors and experimental imperfections. To address this limitation, we develop a sampled-detuning quantum optimal-control approach in which different detuning values are treated as control scenarios driven by a common laser field. Time-domain equality constraints, including zero pulse area and fixed fluence, are incorporated directly into the pulse update. The resulting constraint-projected update provides a common ascent direction for the sampled detuning objectives while preserving the imposed pulse constraints. Numerical simulations show that the optimized robust pulses maintain a high target-state population over a wider detuning interval than resonant Gaussian pulses and conventional single-objective optimal pulses. The results further reveal a fluence-bandwidth trade-off for robust plateau formation. Frequency-domain analysis indicates that the enhanced robustness is associated with optimized off-resonant spectral components, and the robustness window can be tuned by selecting the sampled-detuning training range.