Environment-assisted quantum transport in two dimensional lattices

Noise is commonly regarded as an adverse effect disrupting communication and coherent transport. However, as has been shown for small light-harvesting protein complexes decoherence can facilitate quantum transport processes, a phenomenon termed environment-assisted quantum transport (ENAQT). We here study numerically and analytically how dephasing noise

improves the efficiency of spin excitation transport in a two dimensional lattice with small homogeneous losses.  In particular we investigate the efficiency and time of excitation transfer from a random initial site to a specific target site and show that for system sizes below a characteristic scale it can be substantially enhanced by adding small dephasing noise. We derive approximate analytic expressions for the efficiency which become rather accurate in the two limits of small (coherent regime) and large noise (Zeno regime) and give a very good overall estimate. They provide a quantitative description of ENAQT in spatially extended systems and allow to derive conditions for its existence.