We plan to investigate the resonant electron tunneling through a trapped degenerate atomic Bose or Fermi systems. Electronic conductivity in the unitary limit and current-voltage characteristics of an optoelectronic device called as tunneling optical trap is estimated. We explore the coherent effects due to the gauge symmetry breaking of atomic or molecular condensates from the point of view of non-demolition quantum measurements. The models of coherent electronic conductivity of a BEC via virtual transitions of electrons between Fermi seas of electrodes will be presented. The Fano factor of current noise and heat effects is calculated for electronic transport within the resonance window. The role of atomic collisions and half-collisions affecting the BEC resistance is clarified. Echoes phenomena on bound-free transition in a BEC will be studied. Entropy of entanglement of electrons tunneling through a BEC will be calculated. The 3D micro-spheres for the low threshold lasers and supporting the high Q-whispering-gallery modes (WGM) will be prepared and their properties demonstrated. The 2D-lattice of WGM would allow the atomic and photonic entanglement addressed by the optoelectronic devices. Electronic transport via resonant tunneling in dipolar BEC of indirect excitons in electrostatic trap will be investigated. Paradigms of quantum control is developed for combined system of "excitonic BEC +electron" in nanostructures. The coherent population trapping for atoms in quantized light field, optical lattices of cold atoms and coherent control of their states will be investigated.