Near-optimal two-mode spin squeezing via feedback

We propose a feedback scheme for the production of two-mode spin squeezing. We determine a general expression for the optimal feedback, which is also applicable to the case of single-mode spin squeezing. The two-mode spin squeezed states obtained via this feedback are optimal for $j=1/2\mathrm{}$ and are very close to optimal for $j>\mathrm{}1/2.\mathrm{}$ In addition, the master equation suggests a Hamiltonian that would produce two-mode spin squeezing without feedback, and is analogous to the two-axis countertwisting Hamiltonian in the single-mode case.