Majorana representation of adiabatic and superadiabatic processes in three-level systems
We show that stimulated Raman adiabatic passage (STIRAP) and its superadiabatic version (saSTIRAP) have a natural geometric two-star representation on the Majorana sphere. In the case of STIRAP, we find that the evolution is confined to a vertical plane. A faster evolution can be achieved in the saS...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2020-10-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.2.043079 |
| _version_ | 1797211172900962304 |
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| author | Shruti Dogra Antti Vepsäläinen G. S. Paraoanu |
| author_facet | Shruti Dogra Antti Vepsäläinen G. S. Paraoanu |
| author_sort | Shruti Dogra |
| collection | DOAJ |
| description | We show that stimulated Raman adiabatic passage (STIRAP) and its superadiabatic version (saSTIRAP) have a natural geometric two-star representation on the Majorana sphere. In the case of STIRAP, we find that the evolution is confined to a vertical plane. A faster evolution can be achieved in the saSTIRAP protocol, which employs a counterdiabatic Hamiltonian to nullify the nonadiabatic excitations. We derive this Hamiltonian in the Majorana picture, and we observe how, under realistic experimental parameters, the counterdiabatic term corrects the trajectory of the Majorana stars toward the dark state. We also introduce a spin-1 average vector and present its evolution during the two processes, demonstrating that it provides a measure of nonadiabaticity. We show that the Majorana representation can be used as a sensitive tool for the detection of process errors due to ac Stark shifts and nonadiabatic transitions. Finally, we provide an extension of these results to mixed states and processes with decoherence. |
| first_indexed | 2024-04-24T10:22:16Z |
| format | Article |
| id | doaj.art-0b739cea89ca441f9b91ba3af650749d |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:22:16Z |
| publishDate | 2020-10-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-0b739cea89ca441f9b91ba3af650749d2024-04-12T17:02:28ZengAmerican Physical SocietyPhysical Review Research2643-15642020-10-012404307910.1103/PhysRevResearch.2.043079Majorana representation of adiabatic and superadiabatic processes in three-level systemsShruti DograAntti VepsäläinenG. S. ParaoanuWe show that stimulated Raman adiabatic passage (STIRAP) and its superadiabatic version (saSTIRAP) have a natural geometric two-star representation on the Majorana sphere. In the case of STIRAP, we find that the evolution is confined to a vertical plane. A faster evolution can be achieved in the saSTIRAP protocol, which employs a counterdiabatic Hamiltonian to nullify the nonadiabatic excitations. We derive this Hamiltonian in the Majorana picture, and we observe how, under realistic experimental parameters, the counterdiabatic term corrects the trajectory of the Majorana stars toward the dark state. We also introduce a spin-1 average vector and present its evolution during the two processes, demonstrating that it provides a measure of nonadiabaticity. We show that the Majorana representation can be used as a sensitive tool for the detection of process errors due to ac Stark shifts and nonadiabatic transitions. Finally, we provide an extension of these results to mixed states and processes with decoherence.http://doi.org/10.1103/PhysRevResearch.2.043079 |
| spellingShingle | Shruti Dogra Antti Vepsäläinen G. S. Paraoanu Majorana representation of adiabatic and superadiabatic processes in three-level systems Physical Review Research |
| title | Majorana representation of adiabatic and superadiabatic processes in three-level systems |
| title_full | Majorana representation of adiabatic and superadiabatic processes in three-level systems |
| title_fullStr | Majorana representation of adiabatic and superadiabatic processes in three-level systems |
| title_full_unstemmed | Majorana representation of adiabatic and superadiabatic processes in three-level systems |
| title_short | Majorana representation of adiabatic and superadiabatic processes in three-level systems |
| title_sort | majorana representation of adiabatic and superadiabatic processes in three level systems |
| url | http://doi.org/10.1103/PhysRevResearch.2.043079 |
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