Sub-Planck structure quantification in non-Gaussian probability densities
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| Main Authors: | , , , , , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866908755491291136 |
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| author | Moore, Darren W. Švarc, Vojtěch Singh, Kratveer Kovalenko, Artem Pham, Minh Tuan Číp, Ondřej Slodička, Lukáš Filip, Radim |
| author_facet | Moore, Darren W. Švarc, Vojtěch Singh, Kratveer Kovalenko, Artem Pham, Minh Tuan Číp, Ondřej Slodička, Lukáš Filip, Radim |
| contents | Sub-Planck structures in non-Gaussian probability densities of phase space variables are pervasive in bosonic quantum systems. They are almost universally present if the bosonic system evolves via nonlinear dynamics or nonlinear measurements. So far, identification and comparison of such structures remains qualitative. Here we provide a universally applicable and experimentally friendly method to identify, quantify and compare sub-Planck structures from directly measurable or estimated probability densities of single phase space variables. We demonstrate the efficacy of this method on experimental high order Fock states of a single-atom mechanical oscillator, showing provably finer sub-Planck structures as the Fock occupation increases despite the accompanying uncertainty increase in the phonon, position, and momentum bases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_05898 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Sub-Planck structure quantification in non-Gaussian probability densities Moore, Darren W. Švarc, Vojtěch Singh, Kratveer Kovalenko, Artem Pham, Minh Tuan Číp, Ondřej Slodička, Lukáš Filip, Radim Quantum Physics Sub-Planck structures in non-Gaussian probability densities of phase space variables are pervasive in bosonic quantum systems. They are almost universally present if the bosonic system evolves via nonlinear dynamics or nonlinear measurements. So far, identification and comparison of such structures remains qualitative. Here we provide a universally applicable and experimentally friendly method to identify, quantify and compare sub-Planck structures from directly measurable or estimated probability densities of single phase space variables. We demonstrate the efficacy of this method on experimental high order Fock states of a single-atom mechanical oscillator, showing provably finer sub-Planck structures as the Fock occupation increases despite the accompanying uncertainty increase in the phonon, position, and momentum bases. |
| title | Sub-Planck structure quantification in non-Gaussian probability densities |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2601.05898 |