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 $H\left(\lambda \right)=\lambda S_z^2-S_x,$ 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.

• Received 31 October 2002

DOI:https://doi.org/10.1103/PhysRevA.68.013807