Singularity of the time-energy uncertainty in adiabatic perturbation and cycloids on a Bloch sphere
<p dir="ltr">Adiabatic perturbation is shown to be singular from the exact solution of a spin-1/2 particle in a uniformly rotating magnetic field. Due to a non-adiabatic effect, its quantum trajectory on a Bloch sphere is a cycloid traced by a circle rolling along an adiabatic path....
محفوظ في:
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| مؤلفون آخرون: | , , |
| منشور في: |
2016
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| الموضوعات: | |
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| _version_ | 1864513556413677568 |
|---|---|
| author | Sangchul Oh (10980923) |
| author2 | Xuedong Hu (15399955) Franco Nori (1511329) Sabre Kais (1409968) |
| author2_role | author author author |
| author_facet | Sangchul Oh (10980923) Xuedong Hu (15399955) Franco Nori (1511329) Sabre Kais (1409968) |
| author_role | author |
| dc.creator.none.fl_str_mv | Sangchul Oh (10980923) Xuedong Hu (15399955) Franco Nori (1511329) Sabre Kais (1409968) |
| dc.date.none.fl_str_mv | 2016-02-26T03:00:00Z |
| dc.identifier.none.fl_str_mv | 10.1038/srep20824 |
| dc.relation.none.fl_str_mv | https://figshare.com/articles/journal_contribution/Singularity_of_the_time-energy_uncertainty_in_adiabatic_perturbation_and_cycloids_on_a_Bloch_sphere/27101677 |
| dc.rights.none.fl_str_mv | CC BY 4.0 info:eu-repo/semantics/openAccess |
| dc.subject.none.fl_str_mv | Physical sciences Condensed matter physics Adiabatic perturbation Spin-1/2 particle Bloch sphere Non-adiabatic effects Aharonov-Anandan geometric phase Berry phase Quantum trajectory Transitionless driving |
| dc.title.none.fl_str_mv | Singularity of the time-energy uncertainty in adiabatic perturbation and cycloids on a Bloch sphere |
| dc.type.none.fl_str_mv | Text Journal contribution info:eu-repo/semantics/publishedVersion text contribution to journal |
| description | <p dir="ltr">Adiabatic perturbation is shown to be singular from the exact solution of a spin-1/2 particle in a uniformly rotating magnetic field. Due to a non-adiabatic effect, its quantum trajectory on a Bloch sphere is a cycloid traced by a circle rolling along an adiabatic path. As the magnetic field rotates more and more slowly, the time-energy uncertainty, proportional to the length of the quantum trajectory, calculated by the exact solution is entirely different from the one obtained by the adiabatic path traced by the instantaneous eigenstate. However, the non-adiabatic Aharonov- Anandan geometric phase, measured by the area enclosed by the exact path, approaches smoothly the adiabatic Berry phase, proportional to the area enclosed by the adiabatic path. The singular limit of the time-energy uncertainty and the regular limit of the geometric phase are associated with the arc length and arc area of the cycloid on a Bloch sphere, respectively. Prolate and curtate cycloids are also traced by different initial states outside and inside of the rolling circle, respectively. The axis trajectory of the rolling circle, parallel to the adiabatic path, is shown to be an example of transitionless driving. The non-adiabatic resonance is visualized by the number of cycloid arcs.</p><h2>Other Information</h2><p dir="ltr">Published in: Scientific Reports<br>License: <a href="https://creativecommons.org/licenses/by/4.0" target="_blank">https://creativecommons.org/licenses/by/4.0</a><br>See article on publisher's website: <a href="https://dx.doi.org/10.1038/srep20824" target="_blank">https://dx.doi.org/10.1038/srep20824</a></p> |
| eu_rights_str_mv | openAccess |
| id | Manara2_723fac7278dfa8d5b3af575e6f62a068 |
| identifier_str_mv | 10.1038/srep20824 |
| network_acronym_str | Manara2 |
| network_name_str | Manara2 |
| oai_identifier_str | oai:figshare.com:article/27101677 |
| publishDate | 2016 |
| repository.mail.fl_str_mv | |
| repository.name.fl_str_mv | |
| repository_id_str | |
| rights_invalid_str_mv | CC BY 4.0 |
| spelling | Singularity of the time-energy uncertainty in adiabatic perturbation and cycloids on a Bloch sphereSangchul Oh (10980923)Xuedong Hu (15399955)Franco Nori (1511329)Sabre Kais (1409968)Physical sciencesCondensed matter physicsAdiabatic perturbationSpin-1/2 particleBloch sphereNon-adiabatic effectsAharonov-Anandan geometric phaseBerry phaseQuantum trajectoryTransitionless driving<p dir="ltr">Adiabatic perturbation is shown to be singular from the exact solution of a spin-1/2 particle in a uniformly rotating magnetic field. Due to a non-adiabatic effect, its quantum trajectory on a Bloch sphere is a cycloid traced by a circle rolling along an adiabatic path. As the magnetic field rotates more and more slowly, the time-energy uncertainty, proportional to the length of the quantum trajectory, calculated by the exact solution is entirely different from the one obtained by the adiabatic path traced by the instantaneous eigenstate. However, the non-adiabatic Aharonov- Anandan geometric phase, measured by the area enclosed by the exact path, approaches smoothly the adiabatic Berry phase, proportional to the area enclosed by the adiabatic path. The singular limit of the time-energy uncertainty and the regular limit of the geometric phase are associated with the arc length and arc area of the cycloid on a Bloch sphere, respectively. Prolate and curtate cycloids are also traced by different initial states outside and inside of the rolling circle, respectively. The axis trajectory of the rolling circle, parallel to the adiabatic path, is shown to be an example of transitionless driving. The non-adiabatic resonance is visualized by the number of cycloid arcs.</p><h2>Other Information</h2><p dir="ltr">Published in: Scientific Reports<br>License: <a href="https://creativecommons.org/licenses/by/4.0" target="_blank">https://creativecommons.org/licenses/by/4.0</a><br>See article on publisher's website: <a href="https://dx.doi.org/10.1038/srep20824" target="_blank">https://dx.doi.org/10.1038/srep20824</a></p>2016-02-26T03:00:00ZTextJournal contributioninfo:eu-repo/semantics/publishedVersiontextcontribution to journal10.1038/srep20824https://figshare.com/articles/journal_contribution/Singularity_of_the_time-energy_uncertainty_in_adiabatic_perturbation_and_cycloids_on_a_Bloch_sphere/27101677CC BY 4.0info:eu-repo/semantics/openAccessoai:figshare.com:article/271016772016-02-26T03:00:00Z |
| spellingShingle | Singularity of the time-energy uncertainty in adiabatic perturbation and cycloids on a Bloch sphere Sangchul Oh (10980923) Physical sciences Condensed matter physics Adiabatic perturbation Spin-1/2 particle Bloch sphere Non-adiabatic effects Aharonov-Anandan geometric phase Berry phase Quantum trajectory Transitionless driving |
| status_str | publishedVersion |
| title | Singularity of the time-energy uncertainty in adiabatic perturbation and cycloids on a Bloch sphere |
| title_full | Singularity of the time-energy uncertainty in adiabatic perturbation and cycloids on a Bloch sphere |
| title_fullStr | Singularity of the time-energy uncertainty in adiabatic perturbation and cycloids on a Bloch sphere |
| title_full_unstemmed | Singularity of the time-energy uncertainty in adiabatic perturbation and cycloids on a Bloch sphere |
| title_short | Singularity of the time-energy uncertainty in adiabatic perturbation and cycloids on a Bloch sphere |
| title_sort | Singularity of the time-energy uncertainty in adiabatic perturbation and cycloids on a Bloch sphere |
| topic | Physical sciences Condensed matter physics Adiabatic perturbation Spin-1/2 particle Bloch sphere Non-adiabatic effects Aharonov-Anandan geometric phase Berry phase Quantum trajectory Transitionless driving |