  The interplay between antiferromagnetic interaction and hole motion is
capable of inducing intriguing conducting topological Haldane phases described
by a finite non-local string order parameter. Here we show that these states of
matter are captured by the one dimensional $t-J_z$ model which can be
experimentally realized with dressed Rydberg atoms trapped onto a one
dimensional optical lattice. In the sector with vanishing total magnetization
exact Bethe ansatz calculations associated to bosonization technique allow to
predict that both metallic and superconducting topological Haldane states can
be achieved. With the addition of an appropriate magnetic field the system
enters in a domain wall structure with finite total magnetization. In this
regime conducting topological Haldane states are confined in domains separated
by regions where fully polarized Luttinger liquid occurs. A procedure to
dynamically stabilize such Haldane topological phases starting from a confined
Ising state is also described
