Majorana fusion in interacting one-dimensional Kitaev chains.

Motivated by experimental progress in one-dimensional quantum wires using tunable local gates, we employ a simple and experimentally feasible time-dependent real-space local density-of-states method to observe the movement and fusion of Majoranas. Using the time-dependent real-space local density-of-states method to study the fusion of Majorana zero modes in the 1D interacting Kitaev model based on the time evolution of many-body states. We study the dynamics and fusion channels of Majoranas using time-dependent potentials, either Wall or Well, focusing on the local density-of-states and charge-density of fermions varying with time. For a Wall, i.e., repulsive strong potential, after fusion of Majoranasthe, electron (or hole) forms at ω= 0, whereas for a Well, i.e., attractive deep potential, electron(or hole) forms at ω∼−V, where V is the Coulomb repulsion. We also provide quantitative time estimates of upper and lower limits on the Majorana movement needed to reduce non-adiabatic effects and avoid poisoning due to decoherence, focusing on forming a full electron (or hole) after the fusion.