Efficient preparation of spin-squeezed states with Grover's algorithm

arXiv:2611.07766v1 Announce Type: new Abstract: We propose a scheme for preparing spin-squeezed states in an ensemble of $N$ spin-$1/2$ particles based on Grover's algorithm. With only a few oracles, the scheme can exactly prepare superpositions of a few neighboring Dicke states with the Wineland squeezing parameter scaling as $N^{-1}$. The scheme requires only global rotations and Dicke-selective phase shifts, thus avoiding the need to engineer a dedicated many-body Hamiltonian for the squeezing dynamics. We further discuss the feasibility of realizing the scheme in cavity QED systems, with the phase-matched Grover iterations realized by single-photon reflection from a dispersively coupled cavity.