Heisenberg-limit spin squeezing with spin Bogoliubov Hamiltonian

Jun Zhang; Sheng Chang; Wenxian Zhang

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arXiv · 2409.02402

Heisenberg-limit spin squeezing with spin Bogoliubov Hamiltonian

Jun Zhang·Sheng Chang·Wenxian Zhang

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Abstract

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.

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Jun Zhang, Sheng Chang, Wenxian Zhang. 2024-09-04. Heisenberg-limit spin squeezing with spin Bogoliubov Hamiltonian. https://arxiv.org/abs/2409.02402

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