arXiv:0904.0496 · New Journal of Physics

Spin squeezing in a generalized one-axis twisting model

Guangri Jin, Yong‐Chun Liu, Wu‐Ming Liu

Published Jul 29, 2009• 135 citations

Abstract

We investigate the dependence of spin squeezing on the polar angle of the initial coherent spin state |θ 0 , ϕ 0 ⟩ in a generalized one-axis twisting model, where the detuning δ is taken into account. We show explicitly that regardless of δ and ϕ 0 , previous results of the ideal one-axis twisting are recovered as long as θ 0 =π/2. For a small departure of θ 0 from π/2, however, the achievable variance ( V − ) min ∼ N 2/3 , which is larger than the ideal case N 1/3 . We also find that the maximal squeezing time t min scales as N −5/6 . Analytic expressions of ( V − ) min and t min are presented and they agree with numerical simulations.

DOI: 10.1088/1367-2630/11/7/073049

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arXiv:0904.0496 · New Journal of Physics

Spin squeezing in a generalized one-axis twisting model

Guangri Jin, Yong‐Chun Liu, Wu‐Ming Liu

Published Jul 29, 2009• 135 citations

arXiv HTML PDF

Abstract

DOI: 10.1088/1367-2630/11/7/073049

Related papers

Quantum Fisher information and spin squeezing in one-axis twisting model

Wei Zhong, Jing Liu, Jian Ma +1 more

We investigate the dependence of the average parameter estimation precision (APEP), which is defined by the quantum Fisher information, on the polar angle of the initial coherent spin state |θ 0 , φ 0 〉 in a one-axis twisting model. Jin et al. [ New J. Phys. 11 (2009) 073049 ] found that the spin squeezing sensitively depends on the polar angle θ 0 of the initial coherent spin state. We show explicitly that the APEP is robust to the initial polar angle θ 0 in the vicinity of π/2 and a near-Heisenberg limit ∝ 2/ N in quantum single-parameter estimation may still be achieved for states created with the nonlinear evolution of the nonideal coherent spin states θ 0 ∼ π/2. Based on this model, we also consider the effects of the collective dephasing on spin squeezing and the APEP.We investigate the dependence of the average parameter estimation precision (APEP), which is defined by the quantum Fisher information, on the polar angle of the initial coherent spin state |θ 0 , φ 0 〉 in a one-axis twisting model. Jin et al. [ New J. Phys. 11 (2009) 073049 ] found that the spin squeezing sensitively depends on the polar angle θ 0 of the initial coherent spin state. We show explicitly that the APEP is robust to the initial polar angle θ 0 in the vicinity of π/2 and a near-Heisenberg limit ∝ 2/ N in quantum single-parameter estimation may still be achieved for states created with the nonlinear evolution of the nonideal coherent spin states θ 0 ∼ π/2. Based on this model, we also consider the effects of the collective dephasing on spin squeezing and the APEP.

arXiv:1309.4842Chinese Physics BMay 30, 201415 citations

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We investigate the dependence of the average parameter estimation precision (APEP), which is defined by the quantum Fisher information, on the polar angle of the initial coherent spin state |θ0, φ0〉 in a one-axis twisting model. Jin et al. [New J. Phys. 11 (2009) 073049] found that the spin squeezing sensitively depends on the polar angle θ0 of the initial coherent spin state. We show explicitly that the APEP is robust to the initial polar angle θ0 in the vicinity of π/2 and a near-Heisenberg limit ∝ 2/N in quantum single-parameter estimation may still be achieved for states created with the nonlinear evolution of the nonideal coherent spin states θ0 ∼ π/2. Based on this model, we also consider the effects of the collective dephasing on spin squeezing and the APEP.We investigate the dependence of the average parameter estimation precision (APEP), which is defined by the quantum Fisher information, on the polar angle of the initial coherent spin state |θ0, φ0〉 in a one-axis twisting model. Jin et al. [New J. Phys. 11 (2009) 073049] found that the spin squeezing sensitively depends on the polar angle θ0 of the initial coherent spin state. We show explicitly that the APEP is robust to the initial polar angle θ0 in the vicinity of π/2 and a near-Heisenberg limit ∝ 2/N in quantum single-parameter estimation may still be achieved for states created with the nonlinear evolution of the nonideal coherent spin states θ0 ∼ π/2. Based on this model, we also consider the effects of the collective dephasing on spin squeezing and the APEP.

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arXiv:1504.01984Physical Review ASep 15, 201521 citations

Heisenberg-limit spin squeezing with the spin Bogoliubov Hamiltonian

Jun Zhang, Sheng Chang, Wenxian Zhang

It is well established that the optimal spin squeezing under a one-axis-twisting Hamiltonian follows a scaling law of ${J}^{\ensuremath{-}2/3}$ 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 ${J}^{\ensuremath{-}1}$. 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 excellent spin squeezing, which approaches 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.It is well established that the optimal spin squeezing under a one-axis-twisting Hamiltonian follows a scaling law of ${J}^{\ensuremath{-}2/3}$ 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 ${J}^{\ensuremath{-}1}$. 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 excellent spin squeezing, which approaches 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.

Physical Review ASep 5, 20240 citations

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Jun Zhang, Sheng Chang, Wenxian Zhang

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.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.

arXiv:2409.02402Sep 4, 20240 citations

|\theta_{0}, \phi_0\rangle

with the polar angle

\theta_0=\pi/2

. If the dephasing rate

\gamma\ll S^{-1/3}

, where

S

is total atomic spin, we find that the smallest value of squeezing parameter (i.e., the strongest squeezing) obeys the same scaling with the ideal one-axis twisting case, namely

\xi^2\propto S^{-2/3}

. While for a moderate dephasing, the achievable squeezing obeys the power rule

S^{-2/5}

, which is slightly worse than the ideal case. When the dephasing rate

\gamma>S^{1/2}

, we show that the squeezing is weak and neglectable.

It is well established that the optimal spin squeezing under a one-axis-twisting Hamiltonian follows a scaling law of ${J}^{\ensuremath{-}2/3}$ 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 ${J}^{\ensuremath{-}1}$. 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 excellent spin squeezing, which approaches 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.

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.