We have designed an automatic differentiation-based strategy to generate optical trap arrays that change smoothly over time. Instead of repeatedly regenerating the holograms for each time step, we derive the differential form of the phase dynamics that enables the continuous evolution of the trap coordinates. This differential form is derived from the implicit differentiation of the fixed point of the Gerchberg-Saxton algorithm, which is computationally efficient. We carried out numerical and laboratory experiments to demonstrate its effectiveness at improving the phase continuity and reducing the computational burden compared to traditional pure interpolation techniques. By combining the method with the spatial light modulator, the method is promising for the dynamic manipulation of particles in real experiments.

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• Analog computation
• Holography
• Optical lattices & traps
• Optical quantum information processing
• Atomic systems
• Spatial light modulators
• Machine learning
• Optical computing