Heisenberg-limit spin squeezing with spin Bogoliubov Hamiltonian
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916381591601152 |
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| author | Zhang, Jun Chang, Sheng Zhang, Wenxian |
| author_facet | Zhang, Jun Chang, Sheng Zhang, Wenxian |
| contents | It is well established that the optimal spin squeezing under a one-axis-twisting Hamiltonian follows a scaling law of $J^{-2/3}$ for $J$ interacting atoms after a quench dynamics. Here we prove analytically and numerically that the spin squeezing of the ground state of the one-axis-twisting Hamiltonian actually reaches the Heisenberg limit $J^{-1}$. By constructing a bilinear Bogoliubov Hamiltonian with the raising and lowering spin operators, we exactly diagonalize the spin Bogoliubov Hamiltonian, which includes the one-axis twisting Hamiltonian as a limiting case. The ground state of the spin Bogoliubov Hamiltonian exhibits wonderful spin squeezing, which approaches to the Heisenberg limit in the case of the one-axis twisting Hamiltonian. It is possible to realize experimentally the spin squeezed ground state of the one-axis-twisting Hamiltonian in dipolar spinor condensates, ultracold atoms in optical lattices, spins in a cavity, or alkali atoms in a vapor cell. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_02402 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Heisenberg-limit spin squeezing with spin Bogoliubov Hamiltonian Zhang, Jun Chang, Sheng Zhang, Wenxian Quantum Gases Optics Quantum Physics It is well established that the optimal spin squeezing under a one-axis-twisting Hamiltonian follows a scaling law of $J^{-2/3}$ for $J$ interacting atoms after a quench dynamics. Here we prove analytically and numerically that the spin squeezing of the ground state of the one-axis-twisting Hamiltonian actually reaches the Heisenberg limit $J^{-1}$. By constructing a bilinear Bogoliubov Hamiltonian with the raising and lowering spin operators, we exactly diagonalize the spin Bogoliubov Hamiltonian, which includes the one-axis twisting Hamiltonian as a limiting case. The ground state of the spin Bogoliubov Hamiltonian exhibits wonderful spin squeezing, which approaches to the Heisenberg limit in the case of the one-axis twisting Hamiltonian. It is possible to realize experimentally the spin squeezed ground state of the one-axis-twisting Hamiltonian in dipolar spinor condensates, ultracold atoms in optical lattices, spins in a cavity, or alkali atoms in a vapor cell. |
| title | Heisenberg-limit spin squeezing with spin Bogoliubov Hamiltonian |
| topic | Quantum Gases Optics Quantum Physics |
| url | https://arxiv.org/abs/2409.02402 |