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(λ)=λ
S
2
z
−
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.