Quantum metrology enhanced by the $XY$ spin interaction in a generalized Tavis-Cummings model
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866911831686119424 |
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| author | Su, Yuguo Lu, Wangjun Shi, Hai-Long |
| author_facet | Su, Yuguo Lu, Wangjun Shi, Hai-Long |
| contents | Quantum metrology is recognized for its capability to offer high-precision estimation by utilizing quantum resources, such as quantum entanglement. Here, we propose a generalized Tavis-Cummings model by introducing the $XY$ spin interaction to explore the impact of the many-body effect on estimation precision, quantified by the quantum Fisher information (QFI). By deriving the effective description of our model, we establish a closed relationship between the QFI and the spin fluctuation induced by the $XY$ spin interaction. Based on this exact relation, we emphasize the indispensable role of the spin anisotropy in achieving the Heisenberg-scaling precision for estimating a weak magnetic field. Furthermore, we observe that the estimation precision can be enhanced by increasing the strength of the spin anisotropy. We also reveal a clear scaling transition of the QFI in the Tavis-Cummings model with the reduced Ising interaction. Our results contribute to the enrichment of metrology theory by considering many-body effects, and they also present an alternative approach to improving the estimation precision by harnessing the power provided by many-body quantum phases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_16166 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Quantum metrology enhanced by the $XY$ spin interaction in a generalized Tavis-Cummings model Su, Yuguo Lu, Wangjun Shi, Hai-Long Quantum Physics Quantum metrology is recognized for its capability to offer high-precision estimation by utilizing quantum resources, such as quantum entanglement. Here, we propose a generalized Tavis-Cummings model by introducing the $XY$ spin interaction to explore the impact of the many-body effect on estimation precision, quantified by the quantum Fisher information (QFI). By deriving the effective description of our model, we establish a closed relationship between the QFI and the spin fluctuation induced by the $XY$ spin interaction. Based on this exact relation, we emphasize the indispensable role of the spin anisotropy in achieving the Heisenberg-scaling precision for estimating a weak magnetic field. Furthermore, we observe that the estimation precision can be enhanced by increasing the strength of the spin anisotropy. We also reveal a clear scaling transition of the QFI in the Tavis-Cummings model with the reduced Ising interaction. Our results contribute to the enrichment of metrology theory by considering many-body effects, and they also present an alternative approach to improving the estimation precision by harnessing the power provided by many-body quantum phases. |
| title | Quantum metrology enhanced by the $XY$ spin interaction in a generalized Tavis-Cummings model |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2307.16166 |