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

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

Spin squeezing in a generalized one-axis twisting model

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

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.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.

arXiv:0904.0496New Journal of PhysicsJul 29, 2009135 citations

Spin squeezing of one-axis twisting model in the presence of phase dephasing

Chen-Gang Ji, Yong‐Chun Liu, Guangri Jin

We present a detailed analysis of spin squeezing of the one-axis twisting model with a many-body phase dephasing, which is induced by external field fluctuation in a two-mode Bose-Einstein condensates. Even in the presence of the dephasing, our analytical results show that the optimal initial state corresponds to a coherent spin state $|\theta_{0}, \phi_0\rangle$ 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.We present a detailed analysis of spin squeezing of the one-axis twisting model with a many-body phase dephasing, which is induced by external field fluctuation in a two-mode Bose-Einstein condensates. Even in the presence of the dephasing, our analytical results show that the optimal initial state corresponds to a coherent spin state $|\theta_{0}, \phi_0\rangle$ 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.

arXiv:1312.3743Quantum Information and ComputationMar 1, 20134 citations

Quantum Fisher information and spin squeezing of the non-Hermitian one-axis twisting model and the effect of dephasing

Tie-Jun Hou

A detailed analysis of the quantum Fisher information (QFI) and spin squeezing (SS) of the non-Hermitian one-axis twisting model is conducted. The results show that the non-Hermitian model achieves significant entanglement in many-body systems, which is quite different from the Hermitian case, and achieves more SS than the optimal value of the Hermitian counterpart. Furthermore, we investigate the effect of dephasing, which is induced by external field fluctuations, and find out to what extent it weakens QFI and SS of the non-Hermitian one-axis twisting model.A detailed analysis of the quantum Fisher information (QFI) and spin squeezing (SS) of the non-Hermitian one-axis twisting model is conducted. The results show that the non-Hermitian model achieves significant entanglement in many-body systems, which is quite different from the Hermitian case, and achieves more SS than the optimal value of the Hermitian counterpart. Furthermore, we investigate the effect of dephasing, which is induced by external field fluctuations, and find out to what extent it weakens QFI and SS of the non-Hermitian one-axis twisting model.

Physical Review AJan 13, 20177 citations

Dephasing-assisted parameter estimation in the presence of dynamical decoupling

Qing-Shou Tan, Yixiao Huang, Le‐Man Kuang +1 more

We study the dephasing-assisted parameter estimation precision (PEP) enhancement in an atom interferometer with dynamical decoupling (DD) pulses. Through calculating the spin squeezing (SS) and the quantum Fisher information, we find that dephasing noise can improve PEP by inducing SS, and the DD pulses can maximize the improvement. It is indicated that when using the DD pulse the dephasing-induced SS can reach the limit of ``one-axis twisting'' model ${\ensuremath{\xi}}^{2}\ensuremath{\simeq}{N}^{\ensuremath{-}2/3}$ with ${\ensuremath{\xi}}^{2}$ being the SS parameter and $N$ the number of atoms. In particular, we find that the DD pulses can amplify the dephasing-induced quantum Fisher information by a factor of $\ensuremath{\simeq}N/2$ compared with the noise-free case, which means that under the control of DD pulses, the dephasing noise can enhance the precision of parameter estimation to the scale of $\sqrt{2}/N$ , the same scale of the Heisenberg limit ( $1/N$ ).We study the dephasing-assisted parameter estimation precision (PEP) enhancement in an atom interferometer with dynamical decoupling (DD) pulses. Through calculating the spin squeezing (SS) and the quantum Fisher information, we find that dephasing noise can improve PEP by inducing SS, and the DD pulses can maximize the improvement. It is indicated that when using the DD pulse the dephasing-induced SS can reach the limit of ``one-axis twisting'' model ${\ensuremath{\xi}}^{2}\ensuremath{\simeq}{N}^{\ensuremath{-}2/3}$ with ${\ensuremath{\xi}}^{2}$ being the SS parameter and $N$ the number of atoms. In particular, we find that the DD pulses can amplify the dephasing-induced quantum Fisher information by a factor of $\ensuremath{\simeq}N/2$ compared with the noise-free case, which means that under the control of DD pulses, the dephasing noise can enhance the precision of parameter estimation to the scale of $\sqrt{2}/N$, the same scale of the Heisenberg limit ($1/N$).

arXiv:1306.0642Physical Review AJun 4, 201424 citations

Super-Heisenberg scaling of the quantum Fisher information using spin-motion states

Venelin P. Pavlov, Peter Ivanov

We propose a spin-motion state for high-precision quantum metrology with super-Heisenberg scaling of the parameter estimation uncertainty using a trapped ion system. Such a highly entangled state can be created using the Tavis-Cummings Hamiltonian which describes the interaction between a collective spin system and a single vibrational mode. Our method relies on an adiabatic evolution in which the initial motional squeezing is adiabatically transferred into collective spin squeezing. In the weak squeezing regime, we show that the adiabatic evolution creates a spin-squeezed state, which reduces the quantum projective noise to a sub-shot noise limit. For strong bosonic squeezing we find that the quantum Fisher information follows a super-Heisenberg scaling law $\propto N^{5/2}$ in terms of the number of ions $N$ . Furthermore, we discuss the spin squeezing parameter which quantifies the phase sensitivity enhancement in Ramsey spectroscopic measurements and show that it also exhibits a super-Heisenberg scaling with $N$ . Our work enables the development of high-precision quantum metrology based on entangled spin-boson states that lead to faster scaling of the parameter estimation uncertainty with the number of spins.We propose a spin-motion state for high-precision quantum metrology with super-Heisenberg scaling of the parameter estimation uncertainty using a trapped ion system. Such a highly entangled state can be created using the Tavis-Cummings Hamiltonian which describes the interaction between a collective spin system and a single vibrational mode. Our method relies on an adiabatic evolution in which the initial motional squeezing is adiabatically transferred into collective spin squeezing. In the weak squeezing regime, we show that the adiabatic evolution creates a spin-squeezed state, which reduces the quantum projective noise to a sub-shot noise limit. For strong bosonic squeezing we find that the quantum Fisher information follows a super-Heisenberg scaling law $\propto N^{5/2}$ in terms of the number of ions $N$. Furthermore, we discuss the spin squeezing parameter which quantifies the phase sensitivity enhancement in Ramsey spectroscopic measurements and show that it also exhibits a super-Heisenberg scaling with $N$. Our work enables the development of high-precision quantum metrology based on entangled spin-boson states that lead to faster scaling of the parameter estimation uncertainty with the number of spins.

arXiv:2411.10117Nov 15, 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.

N

the number of atoms. In particular, we find that the DD pulses can amplify the dephasing-induced quantum Fisher information by a factor of $\ensuremath{\simeq}N/2$ compared with the noise-free case, which means that under the control of DD pulses, the dephasing noise can enhance the precision of parameter estimation to the scale of

\sqrt{2}/N

, the same scale of the Heisenberg limit (

1/N

\propto N^{5/2}

in terms of the number of ions

N

. Furthermore, we discuss the spin squeezing parameter which quantifies the phase sensitivity enhancement in Ramsey spectroscopic measurements and show that it also exhibits a super-Heisenberg scaling with

N

. Our work enables the development of high-precision quantum metrology based on entangled spin-boson states that lead to faster scaling of the parameter estimation uncertainty with the number of spins.