Bahrova O. Electromechanical phenomena in normal and superconducting nanostructures based on a movable quantum dot

This dissertation is devoted to the study of new fundamental phenomena arising from electromechanical coupling in mesoscopic systems based on a movable quantum dot. Using the density matrix approximation, the transport properties of a single-molecule transistor arising from a non-equilibrium coherent vibronic subsystem are described. The results of analytical and numerical calculations of the current-voltage characteristics (I-V) are presented and analyzed. The correspondence between the I-Vs obtained under the assumption that the vibronic subsystem is in a coherent (non-equilibrium) state and the Frank-Condon steps for vibronic systems in equilibrium is established. It is shown that, in contrast to the Frank-Condon theory, in the case of coherent vibrons, the steps on the current-voltage characteristics are irregular. Moreover, for the coherent state of the vibrons, the saturation current occurs at much lower values of bias voltages. The latter fact can be decisive in experiments requiring operation in the mode of polaron blockade removal, i.e., maximum currents. The entanglement that arises between electronic and mechanical degrees of freedom in a superconducting nanoelectromechanical device is also obtained and analyzed. It is shown that the initial pure state evolves to a state represented by the entanglement between two qubit states and two coherent states of the mechanical resonator. A specific protocol of manipulation of the bias voltage is proposed, which leads to the formation of entanglement between two states of the charge qubit and two states of the "Schrödinger cat" (superposition of two coherent states), starting from the pure state. Due to its simplicity, the considered protocol can be effectively implemented in experiments with encoding quantum information from the electronic states of the qubit to the coherent states (in particular, the so-called "cat states") of a nanomechanical resonator. Also, the quantum dynamics of a hybrid nanoelectromechanical system based on a carbon nanotube arising from the superconducting proximity effect is investigated. For such a system, the regions of instability are found and the phenomenon of self-saturation arising from the delocalization of Cooper pairs is obtained. Using the density matrix approximation, the effect of ground-state cooling of nanomechanical vibrations for this nanoelectromechanical system, where the electromechanical coupling is of quantum nature, arising from the proximity effect, is obtained.