Dissipative topological superconductors in number-conserving systems

We discuss the dissipative preparation of p-wave superconductors in number-conserving one-dimensional fermionic systems. We focus on two setups: the first one entails a single wire coupled to a bath, whereas in the second one the environment is connected to a two-leg ladder. Both settings lead to stationary states which feature the bulk properties of a p-wave superconductor, identified in this number-conserving setting through the long-distance behavior of the proper p-wave correlations. The two schemes differ in the fact that the steady state of the single wire is not characterized by topological order, whereas the two-leg ladder hosts Majorana zero modes, which are decoupled from damping and exponentially localized at the edges. Our analytical results are complemented by a numerical study based both on an exact representation of the density matrix and on a matrix-product-density-operator one. With these tools we characterize the steady-state properties of the protocols, their asymptotic decay rate, and their robustness.