Heisenberg-limit spin squeezing with spin Bogoliubov Hamiltonian

TL;DR

This paper analytically and numerically demonstrates that the ground state of a spin Bogoliubov Hamiltonian can achieve Heisenberg-limit spin squeezing, surpassing the traditional $J^{-2/3}$ scaling of one-axis-twisting dynamics.

Contribution

It introduces an exactly diagonalizable spin Bogoliubov Hamiltonian that reveals ground state spin squeezing reaching the Heisenberg limit, with potential experimental realizations.

Findings

Ground state exhibits spin squeezing approaching the Heisenberg limit J^{-1}.

Exact diagonalization of the spin Bogoliubov Hamiltonian including one-axis-twisting as a limit.

Experimental platforms include dipolar spinor condensates and ultracold atoms.

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.