Final Activity Report Summary - NONLINEAR TRANSPORT (Nonlinear transport and tunneling in low dimensional lattices)
General theoretical approaches for boundary driven nonlinear transport and tunnelling processes have been developed and their applications to various realistic nonlinear physical systems have been pointed out.
Particularly, we have predicted the conditions for the realisation of macroscopic tunnelling effects in optical waveguide arrays, Josephson junction parallel arrays and Bose-Einstein condensates in optical lattices. We discovered that our theoretical findings can lead to technological advances in the creation of novel all optical switching and amplifying devices and, moreover, similar devices are proposed for mesoscopic systems (long Josephson junctions and quantum Hall bilayers) for the amplification of ultra weak signals. In our publications on these topics we discuss how to estimate physical parameters and how to choose appropriate sample geometries. All this will find applications in spintronics and quantum computing.
Besides that, we discovered the coexistence of Josephson oscillations and a novel self trapping regime in the same system. Based on this discovery, we have proposed to examine the same effect in the case of Bose-Einstein condensates in engineered optical lattices (since both waveguide arrays and Bose-Einstein condensates are described by the nonlinear Schroedinger equation). Moreover, the fellow together with the colleagues from Tbilisi State University started the studies of various exotic phenomena related with beam splitting dependence upon the spectral width. It appears that the stochasticity of the injected beam greatly affects its propagation behaviour.
These studies serve as a basis of the ongoing collaboration and establishment of the competitive research team in Georgia.
Particularly, we have predicted the conditions for the realisation of macroscopic tunnelling effects in optical waveguide arrays, Josephson junction parallel arrays and Bose-Einstein condensates in optical lattices. We discovered that our theoretical findings can lead to technological advances in the creation of novel all optical switching and amplifying devices and, moreover, similar devices are proposed for mesoscopic systems (long Josephson junctions and quantum Hall bilayers) for the amplification of ultra weak signals. In our publications on these topics we discuss how to estimate physical parameters and how to choose appropriate sample geometries. All this will find applications in spintronics and quantum computing.
Besides that, we discovered the coexistence of Josephson oscillations and a novel self trapping regime in the same system. Based on this discovery, we have proposed to examine the same effect in the case of Bose-Einstein condensates in engineered optical lattices (since both waveguide arrays and Bose-Einstein condensates are described by the nonlinear Schroedinger equation). Moreover, the fellow together with the colleagues from Tbilisi State University started the studies of various exotic phenomena related with beam splitting dependence upon the spectral width. It appears that the stochasticity of the injected beam greatly affects its propagation behaviour.
These studies serve as a basis of the ongoing collaboration and establishment of the competitive research team in Georgia.