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| Format: | Preprint |
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2025
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| Online-Zugang: | https://arxiv.org/abs/2512.14155 |
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| _version_ | 1866911660018499584 |
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| author | Amadi, Precious Ogbonda Pewkhom, Paphon Kalasuwan, Pruet Ali, Norshamsuri Aljunid, Syed Alwee Endut, Rosdisham |
| author_facet | Amadi, Precious Ogbonda Pewkhom, Paphon Kalasuwan, Pruet Ali, Norshamsuri Aljunid, Syed Alwee Endut, Rosdisham |
| contents | We examine how the informational properties of a confined single ion response in a Paul trap modified by optical-lattice. We focus on the ground and first excited motional states and show that Fisher information, Shannon entropy, and Fisher-Shannon complexity track the effective frequency $ω_{\mathrm{eff}}=ω\sqrt{1-κ}$ of the potential. We show that the Fisher information and Shannon entropy reflect an effective frequency-driven redistribution of information between conjugate spaces. Our results show that the Fisher-Shannon complexity measure remains invariant under effective frequency control. The invariance demonstrates that optical modulation of $κ$ rescales localization, without altering the harmonic structure of the motional states. These results establish a controlled information-theoretic baseline for lattice-assisted Paul traps. Beyond the harmonic limit, retaining the quartic lattice correction introduces non-Gaussian wavefunction features through state-dependent mixing of higher eigenstates, which breaks the mutual compensation between Fisher information and Shannon entropy that sustains the invariant. The departure of $P'$ from its harmonic reference value intensifies with $κ$ and is stronger for the excited state, which confirms that the Fisher-Shannon complexity invariance is a distinctive property of the small-oscillation harmonic regime. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_14155 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fisher Information Measures under Lattice Combined Paul Trap Amadi, Precious Ogbonda Pewkhom, Paphon Kalasuwan, Pruet Ali, Norshamsuri Aljunid, Syed Alwee Endut, Rosdisham Quantum Physics We examine how the informational properties of a confined single ion response in a Paul trap modified by optical-lattice. We focus on the ground and first excited motional states and show that Fisher information, Shannon entropy, and Fisher-Shannon complexity track the effective frequency $ω_{\mathrm{eff}}=ω\sqrt{1-κ}$ of the potential. We show that the Fisher information and Shannon entropy reflect an effective frequency-driven redistribution of information between conjugate spaces. Our results show that the Fisher-Shannon complexity measure remains invariant under effective frequency control. The invariance demonstrates that optical modulation of $κ$ rescales localization, without altering the harmonic structure of the motional states. These results establish a controlled information-theoretic baseline for lattice-assisted Paul traps. Beyond the harmonic limit, retaining the quartic lattice correction introduces non-Gaussian wavefunction features through state-dependent mixing of higher eigenstates, which breaks the mutual compensation between Fisher information and Shannon entropy that sustains the invariant. The departure of $P'$ from its harmonic reference value intensifies with $κ$ and is stronger for the excited state, which confirms that the Fisher-Shannon complexity invariance is a distinctive property of the small-oscillation harmonic regime. |
| title | Fisher Information Measures under Lattice Combined Paul Trap |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2512.14155 |