Three-Boson Spectrum in the Presence of 1D Spin-Orbit Coupling: Efimov’s Generalized Radial Scaling Law
Spin-orbit-coupled cold-atom systems, governed by Hamiltonians that contain quadratic kinetic energy terms typical for a particle’s motion in the usual Schrödinger equation and linear kinetic energy terms typical for a particle’s motion in the usual Dirac equation, have attracted a great deal of att...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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American Physical Society
2018-06-01
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| Series: | Physical Review X |
| Online Access: | http://doi.org/10.1103/PhysRevX.8.021057 |
| _version_ | 1818717127649001472 |
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| author | Q. Guan D. Blume |
| author_facet | Q. Guan D. Blume |
| author_sort | Q. Guan |
| collection | DOAJ |
| description | Spin-orbit-coupled cold-atom systems, governed by Hamiltonians that contain quadratic kinetic energy terms typical for a particle’s motion in the usual Schrödinger equation and linear kinetic energy terms typical for a particle’s motion in the usual Dirac equation, have attracted a great deal of attention recently since they provide an alternative route for realizing fractional quantum Hall physics, topological insulators, and spintronics physics. The present work focuses on the three-boson system in the presence of 1D spin-orbit coupling, which is most relevant to ongoing cold-atom experiments. In the absence of spin-orbit-coupling terms, the three-boson system exhibits the Efimov effect: the entire energy spectrum is uniquely determined by the s-wave scattering length and a single three-body parameter; i.e., using one of the energy levels as input, the other energy levels can be obtained via Efimov’s radial scaling law, which is intimately tied to a discrete scaling symmetry. It is demonstrated that the discrete scaling symmetry persists in the presence of 1D spin-orbit coupling, implying the validity of a generalized radial scaling law in five-dimensional space. The dependence of the energy levels on the scattering length, spin-orbit-coupling parameters, and center-of-mass momentum is discussed. It is conjectured that three-body systems with other types of spin-orbit-coupling terms are also governed by generalized radial scaling laws, provided the system exhibits the Efimov effect in the absence of spin-orbit coupling. |
| first_indexed | 2024-12-17T19:30:13Z |
| format | Article |
| id | doaj.art-4c3bdddf39e0492a9861a8e3af7a92eb |
| institution | Directory Open Access Journal |
| issn | 2160-3308 |
| language | English |
| last_indexed | 2024-12-17T19:30:13Z |
| publishDate | 2018-06-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review X |
| spelling | doaj.art-4c3bdddf39e0492a9861a8e3af7a92eb2022-12-21T21:35:16ZengAmerican Physical SocietyPhysical Review X2160-33082018-06-018202105710.1103/PhysRevX.8.021057Three-Boson Spectrum in the Presence of 1D Spin-Orbit Coupling: Efimov’s Generalized Radial Scaling LawQ. GuanD. BlumeSpin-orbit-coupled cold-atom systems, governed by Hamiltonians that contain quadratic kinetic energy terms typical for a particle’s motion in the usual Schrödinger equation and linear kinetic energy terms typical for a particle’s motion in the usual Dirac equation, have attracted a great deal of attention recently since they provide an alternative route for realizing fractional quantum Hall physics, topological insulators, and spintronics physics. The present work focuses on the three-boson system in the presence of 1D spin-orbit coupling, which is most relevant to ongoing cold-atom experiments. In the absence of spin-orbit-coupling terms, the three-boson system exhibits the Efimov effect: the entire energy spectrum is uniquely determined by the s-wave scattering length and a single three-body parameter; i.e., using one of the energy levels as input, the other energy levels can be obtained via Efimov’s radial scaling law, which is intimately tied to a discrete scaling symmetry. It is demonstrated that the discrete scaling symmetry persists in the presence of 1D spin-orbit coupling, implying the validity of a generalized radial scaling law in five-dimensional space. The dependence of the energy levels on the scattering length, spin-orbit-coupling parameters, and center-of-mass momentum is discussed. It is conjectured that three-body systems with other types of spin-orbit-coupling terms are also governed by generalized radial scaling laws, provided the system exhibits the Efimov effect in the absence of spin-orbit coupling.http://doi.org/10.1103/PhysRevX.8.021057 |
| spellingShingle | Q. Guan D. Blume Three-Boson Spectrum in the Presence of 1D Spin-Orbit Coupling: Efimov’s Generalized Radial Scaling Law Physical Review X |
| title | Three-Boson Spectrum in the Presence of 1D Spin-Orbit Coupling: Efimov’s Generalized Radial Scaling Law |
| title_full | Three-Boson Spectrum in the Presence of 1D Spin-Orbit Coupling: Efimov’s Generalized Radial Scaling Law |
| title_fullStr | Three-Boson Spectrum in the Presence of 1D Spin-Orbit Coupling: Efimov’s Generalized Radial Scaling Law |
| title_full_unstemmed | Three-Boson Spectrum in the Presence of 1D Spin-Orbit Coupling: Efimov’s Generalized Radial Scaling Law |
| title_short | Three-Boson Spectrum in the Presence of 1D Spin-Orbit Coupling: Efimov’s Generalized Radial Scaling Law |
| title_sort | three boson spectrum in the presence of 1d spin orbit coupling efimov s generalized radial scaling law |
| url | http://doi.org/10.1103/PhysRevX.8.021057 |
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