Driven-dissipative creation of a topologically ordered state (AKLT state)

Dissipation of a quantum system coupled to an environment often destroys a quantum state of interest, but if carefully engineered, it can be used as a tool to prepare interesting quantum states. We propose an experimentally viable method to dissipatively create the AKLT (Affleck-Lieb-Kennedy-Tasaki) state which exhibits symmetry protected topological order. We analyze a system of lattice bosons, which are constrained to move in a one dimensional tilted optical lattice and couple them to a bosonic superfluid bath. We use a coherent raman beam to drive rabi oscillations of atoms between the lowest two motional bands of nearest neighbor sites. Under the driven-disipative process, the AKLT state emerges as the only steady state. We use exact diagonalization and DMRG methods to calculate the time scale for state preparation and find that the state preparation time scales qudratically with the system size.