Transformation of spin in quantum reference frames
In physical experiments, reference frames are standardly modeled through a specific choice of coordinates used to describe the physical systems, but they themselves are not considered as such. However, any reference frame is a physical system that ultimately behaves according to quantum mechanics. W...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2021-11-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.3.043138 |
| _version_ | 1797210892525371392 |
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| author | Marion Mikusch Luis C. Barbado Časlav Brukner |
| author_facet | Marion Mikusch Luis C. Barbado Časlav Brukner |
| author_sort | Marion Mikusch |
| collection | DOAJ |
| description | In physical experiments, reference frames are standardly modeled through a specific choice of coordinates used to describe the physical systems, but they themselves are not considered as such. However, any reference frame is a physical system that ultimately behaves according to quantum mechanics. We develop a framework for rotational (i.e., spin) quantum reference frames, with respect to which quantum systems with spin degrees of freedom are described. We give an explicit model for such frames as systems composed of three spin coherent states of angular momentum j and introduce the transformations between them by upgrading the Euler angles occurring in classical SO(3) spin transformations to quantum mechanical operators acting on the states of the reference frames. To ensure that an arbitrary rotation can be applied on the spin we take the limit of infinitely large j, in which case the angle operator possesses a continuous spectrum. We prove that rotationally invariant Hamiltonians (such as that of the Heisenberg model) are invariant under a larger group of quantum reference frame transformations. Our result is a development of the quantum reference frame formalism for a non-Abelian group. |
| first_indexed | 2024-04-24T10:17:49Z |
| format | Article |
| id | doaj.art-ddb0a0a1aa6f4a6e8739cd52962a84fd |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:17:49Z |
| publishDate | 2021-11-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-ddb0a0a1aa6f4a6e8739cd52962a84fd2024-04-12T17:15:57ZengAmerican Physical SocietyPhysical Review Research2643-15642021-11-013404313810.1103/PhysRevResearch.3.043138Transformation of spin in quantum reference framesMarion MikuschLuis C. BarbadoČaslav BruknerIn physical experiments, reference frames are standardly modeled through a specific choice of coordinates used to describe the physical systems, but they themselves are not considered as such. However, any reference frame is a physical system that ultimately behaves according to quantum mechanics. We develop a framework for rotational (i.e., spin) quantum reference frames, with respect to which quantum systems with spin degrees of freedom are described. We give an explicit model for such frames as systems composed of three spin coherent states of angular momentum j and introduce the transformations between them by upgrading the Euler angles occurring in classical SO(3) spin transformations to quantum mechanical operators acting on the states of the reference frames. To ensure that an arbitrary rotation can be applied on the spin we take the limit of infinitely large j, in which case the angle operator possesses a continuous spectrum. We prove that rotationally invariant Hamiltonians (such as that of the Heisenberg model) are invariant under a larger group of quantum reference frame transformations. Our result is a development of the quantum reference frame formalism for a non-Abelian group.http://doi.org/10.1103/PhysRevResearch.3.043138 |
| spellingShingle | Marion Mikusch Luis C. Barbado Časlav Brukner Transformation of spin in quantum reference frames Physical Review Research |
| title | Transformation of spin in quantum reference frames |
| title_full | Transformation of spin in quantum reference frames |
| title_fullStr | Transformation of spin in quantum reference frames |
| title_full_unstemmed | Transformation of spin in quantum reference frames |
| title_short | Transformation of spin in quantum reference frames |
| title_sort | transformation of spin in quantum reference frames |
| url | http://doi.org/10.1103/PhysRevResearch.3.043138 |
| work_keys_str_mv | AT marionmikusch transformationofspininquantumreferenceframes AT luiscbarbado transformationofspininquantumreferenceframes AT caslavbrukner transformationofspininquantumreferenceframes |