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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2506.20594 |
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| _version_ | 1866912816072491008 |
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| author | Tayler, Michael C D Sabba, Mohamed |
| author_facet | Tayler, Michael C D Sabba, Mohamed |
| contents | We identify a cyclic property of rotation sequences involving piecewise displacements $β$ about arbitrary axes in three dimensions. Specifically, when transformation to the toggling frame is applied successively $m$ times, for $β=2π/m$ the original sequence returns. This main result unites several families of rotation sequences used for error-tuned control across quantum technologies, from NMR and MRI to atomic clocks and atom-scale computing. For the widest class of cycle, $m=2$, we highlight sequence duality where every narrowband $π$-element sequence has a broadband $π$-element counterpart, and vice-versa. Higher cycles ($m>2$) connect to polyhedral models for error-tolerant sequence design, characterized by vertex axes with $m$-fold rotational symmetry. We derive original sequences and outline their applications to spin control and spin decoupling. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_20594 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cyclicity of interaction frame transformations Tayler, Michael C D Sabba, Mohamed Quantum Physics We identify a cyclic property of rotation sequences involving piecewise displacements $β$ about arbitrary axes in three dimensions. Specifically, when transformation to the toggling frame is applied successively $m$ times, for $β=2π/m$ the original sequence returns. This main result unites several families of rotation sequences used for error-tuned control across quantum technologies, from NMR and MRI to atomic clocks and atom-scale computing. For the widest class of cycle, $m=2$, we highlight sequence duality where every narrowband $π$-element sequence has a broadband $π$-element counterpart, and vice-versa. Higher cycles ($m>2$) connect to polyhedral models for error-tolerant sequence design, characterized by vertex axes with $m$-fold rotational symmetry. We derive original sequences and outline their applications to spin control and spin decoupling. |
| title | Cyclicity of interaction frame transformations |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2506.20594 |