Localized and extended states in finite-sized mosaic Wannier-Stark lattices

Sammanfattning: Anderson localization occurs when an otherwise conductive solid becomes insulatingdue to a sufficiently large degree of disorder in the medium. The electron band energy(as a function of disorder) at which this transition between extended and localizedelectron states occur is called the mobility edge (ME) and is energy-dependent only in3-dimensional systems. In lower dimensional systems, energy-independent ME (allstates localized or all extended) has been demonstrated by replacing disorder withquasi-periodic potential. However, recent theoretical findings indicate that neitherdisorder nor quasi-periodic potential is necessary for a material to exhibit electronlocalization and existence of energy-dependent pseudo ME at finite system size.In this thesis work, we use light in coupled silicon nitride waveguides to simulatesingle-particle transport of a solid-state medium and investigate the coexistence ofdelocalized and localized states in disorder-free photonic lattices of finite systemsize. This was achieved by implementing a simulated linearly increasing electricpotential on even-numbered sites by varying the refractive index of the wave guide(ch. 3). Through our experimental setup, we successfully achieved a coexistence oflocalized and delocalized states, where the degree of localization varies depending onthe strength of the applied electric field.The findings have implications for the field of quantum technology, whereunderstanding and controlling quantum states is crucial. The ability to achievelocalization in the absence of disorder opens new possibilities for designing andengineering photonic devices for quantum information processing tasks.