Fisher information measures under lattice combined Paul trap

The study investigates the informational properties of a confined single ion's response within a Paul trap that has been altered by an optical lattice. The focus lies on the ground and first excited motional states, with findings revealing that Fisher information, Shannon entropy, and Fisher-Shannon complexity correlate with the effective frequency, \(\omega_{\text{eff}} = \omega \sqrt{1-\kappa}\), of the potential.

These metrics demonstrate an effective frequency-driven redistribution of information between conjugate spaces. Crucially, the Fisher-Shannon complexity measure remains constant under effective frequency control, indicating that optical modulation of \(\kappa\) reshapes localization without disrupting the harmonic structure of the motional states.

This establishes a controlled information-theoretic foundation for lattice-assisted Paul traps. The results highlight that when the quartic lattice correction is included, non-Gaussian wavefunction features emerge through state-dependent mixing of higher eigenstates. This disrupts the balance between Fisher information and Shannon entropy that maintains the invariance.

The deviation of \(P'\) from its harmonic reference value increases with \(\kappa\) and is more pronounced for the excited state, confirming that Fisher-Shannon complexity invariance is a unique characteristic of the small-oscillation harmonic regime. Single trapped ions are prominent in quantum optics and quantum information science due to their strong isolation from the environment, precise control over quantum states, and prolonged coherence times.

The confinement of these ions in electromagnetic potentials restricts their motion to quantized vibrational modes, forming distinct harmonic oscillator states. In strong confinement, these vibrational levels are widely spaced, allowing for precise laser-ion interactions that control internal and motional degrees of freedom for cooling, state engineering, and quantum logic operations.

Paul traps provide electromagnetic confinement through a rapidly oscillating radio-frequency quadrupole field, which generates a stable, time-averaged pseudopotential. This pseudopotential's secular motion of a single ion is accurately described by quantized vibrational levels. By focusing on a single trapped ion, researchers examine the pure quantum dynamics of confinement, free from additional interactions and collective effects found in multi-ion chains.

Single atom trapped ion systems are well-isolated from environmental disturbances, enabling high-precision manipulation and measurement of internal and motional states. Various research efforts have utilized single-ion Paul traps for quantum-optical and quantum-dynamical studies, including high-fidelity quantum logic operations, sideband cooling, and long-lived internal state encoding.