Quantum Fisher Information Measure in a Strongly Confined Harmonic Paul Trap Lattice System

In this work, we examine how the informational and structural properties of a single ion respond to controlled changes of the effective potential in a Paul trap modified by an optical lattice. We consider the ground state of the system where confinement is strongest. And by treating the trap frequency ω and lattice κ as independent tunning parameters, we show that Fisher information, Shannon entropy, and Fisher-Shannon complexity track the curvature of the effective potential ω_eff=ω² sqrt{1-κ}. The ω and κ sweeps confirm that curvature and not the choice of control parameter determines the behaviour of the system. This gives the trapped-ion platform a clear advantage that the curvature can be engineered without altering the harmonic characteristics of the system. The interplay between ω and κ thus provides a practical route for precision quantum control and offers Information-theoretic framework for experiments that probe confinement, quantization scale, and information flow in engineered ion traps.