Optimally squeezed spin states

TL;DR

This paper identifies the optimal spin-squeezed states for enhanced Ramsey spectroscopy sensitivity, showing they are eigenstates of a specific Hamiltonian and become equivalent to quadrature squeezed states as particle number grows.

Contribution

It proves that optimal spin-squeezed states are eigenstates of a particular Hamiltonian and establishes their asymptotic equivalence to quadrature squeezed states for large N.

Findings

Optimal states maximize signal-to-noise ratio in Ramsey spectroscopy.

States are eigenstates of the Hamiltonian H(λ)=λS_z^2 - S_x.

Large N states become equivalent to quadrature squeezed states.

Abstract

We consider optimally spin-squeezed states that maximize the sensitivity of the Ramsey spectroscopy, and for which the signal to noise ratio scales as the number of particles $N$. Using the variational principle we prove that these states are eigensolutions of the Hamiltonian $ H(\lambda)=\lambda S_z^2-S_x, $ and that, for large $N$, the states become equivalent to the quadrature squeezed states of the harmonic oscillator. We present numerical results that illustrate the validity of the equivalence.