This study investigates spin squeezed states in nuclear magnetic resonance (NMR) quadrupolar systems with spins $I=3/2$ and $I=7/2$ at room temperature, taking into account the effects of relaxation on the dynamics. The origin of spin squeezing is attributed to the interaction between the nuclear quadrupole moment and the electric field gradients in the molecular environment. The formal description of the nonlinear operators responsible for spin squeezing is achieved using the spin angular momentum representation via the one-axis twisting mechanism. This approach provides a framework for quantum control and metrology over the spin squeezing process while accounting for the influence of relaxation phenomena. Non-Cartesian angular momentum operators are proposed, with their variances products catching the quantum effects during the dynamics. An upper bound for the squeezing parameter and the Heisenberg uncertainty at thermal equilibrium are also predicted for any spin quantum number.This study investigates spin squeezed states in nuclear magnetic resonance (NMR) quadrupolar systems with spins $I=3/2$ and $I=7/2$ at room temperature, taking into account the effects of relaxation on the dynamics. The origin of spin squeezing is attributed to the interaction between the nuclear quadrupole moment and the electric field gradients in the molecular environment. The formal description of the nonlinear operators responsible for spin squeezing is achieved using the spin angular momentum representation via the one-axis twisting mechanism. This approach provides a framework for quantum control and metrology over the spin squeezing process while accounting for the influence of relaxation phenomena. Non-Cartesian angular momentum operators are proposed, with their variances products catching the quantum effects during the dynamics. An upper bound for the squeezing parameter and the Heisenberg uncertainty at thermal equilibrium are also predicted for any spin quantum number.

arXiv:2504.06204Physical Review AAug 29, 20253 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

Quantum spin squeezing

Jian Ma, Xiaoguang Wang, C. P. Sun +1 more

arXiv:1011.2978Physics ReportsSep 1, 2011846 citations

Heisenberg-limit spin squeezing with 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 $J^{-2/3}$ 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

The Dynamics of Spin Squeezing under Multiple Bosonic Reservoirs

白磊 BAI Lei, 李军奇 LI Jun-qi, 梁九卿 LIANG Jiu-qing

Acta Sinica Quantum OpticaJan 1, 20180 citations

This study investigates spin squeezed states in nuclear magnetic resonance (NMR) quadrupolar systems with spins

I=3/2

and

I=7/2

at room temperature, taking into account the effects of relaxation on the dynamics. The origin of spin squeezing is attributed to the interaction between the nuclear quadrupole moment and the electric field gradients in the molecular environment. The formal description of the nonlinear operators responsible for spin squeezing is achieved using the spin angular momentum representation via the one-axis twisting mechanism. This approach provides a framework for quantum control and metrology over the spin squeezing process while accounting for the influence of relaxation phenomena. Non-Cartesian angular momentum operators are proposed, with their variances products catching the quantum effects during the dynamics. An upper bound for the squeezing parameter and the Heisenberg uncertainty at thermal equilibrium are also predicted for any spin quantum number.

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.