Protocols for dynamically probing topological edge states and dimerization with fermionic atoms in optical potentials

Behavior of topological states has been observed in ultra-cold atomic systems. However, imposing a confining harmonic potential distorts the energy spectrum and prevents the detection of topological boundary states. We propose protocols to resolve the detection of edge-states arising in a dimerized lattice using ultra-cold fermions. Atoms confined in ring lattice, whose boundary conditions are transformed from periodic to open using an off resonant laser sheet, generate topological boundary states. A particle injected onto the edge site of a dimerized structure in a topological configuration can sustain a finite density as the system evolves in time. Alternatively, depleting an initially filled lattice away from the boundary reveals prominent occupied edge states. Signatures of dimerization in the presence of onsite interactions can be found using certain correlations as the boundary conditions transform from periodic to open. These correlations reveal a memory effect of the initial state which can distinguish topological structures or different insulating phases.