Spin squeezing in open Heisenberg spin chains

Spin squeezing protocols successfully generate entangled many-body quantum states, the key pillars of the second quantum revolution. In our recent work Phys. Rev. Lett. 129, 090403 (2022) we showed that spin squeezing described by the one-axis twisting model can be generated in the Heisenberg spin-1/2 chain with periodic boundary conditions when accompanied by a position-dependent spin-flip coupling induced by a single laser field. In this work, we show analytically that the change in boundary conditions from the periodic to the open ones significantly modifies spin squeezing dynamics. A broad family of twisting models can be simulated by the system in the weak-coupling regime, including one- and two-axis twisting under specific conditions, providing the Heisenberg level of squeezing and acceleration of the dynamics. Our analytical findings are confirmed by full numerical simulations.