Nanomechanical manipulation and readout of spins and the creation of arbitrary quantum phonon states

Hybrid nanomechanical systems are promising candidates for quantum computation and quantum information. This thesis studies coupled systems of single electron spins and mechanical motions based on the spin-phonon coupling in suspended carbon nanotubes (CNTs). CNTs are appropriate for nanomechanical resonators from both mechanical and electrical points of view. As mechanical resonators, CNTs have particular physical properties such as low mass, high resonance frequency and large quality factors. Electron spins have long coherence times due to the low density of nuclear spins in CNTs. The extra degree of freedom of valley and strong curvatureinduced spin-orbit coupling make CNTs very interesting for the field of spin-based quantum computation. Using spin-phonon coupling, one can mechanically manipulate or read out the qubit, and vice versa, it is possible to utilize the spin-phonon coupling to create arbitrary phonon Fock states and cool the mechanical resonator. We theoretically study the nanomechanical readout of a single spin in a quantum dot in a CNT. A single electron is trapped in a quantum dot in a suspended CNT. A magnetic field is applied along the axis of the CNT and an AC electrical field can be applied to drive the CNT to vibrate. The degeneracy of spin and valley degrees of freedom are lifted and we can define the two spin states near the avoided crossing in the upper valley as our qubit. The coupling of the qubit and the nano-mechanical motion is caused by inherent curvature-induced spin-orbit coupling and the spatial change of the direction of the nanotube axis. The response of the amplitude of the mechanical motion to different pulsed external drivings of the system with different spins are estimated. The mechanical motion can be detected by the current through a nearby charge sensor. We also solve a master equation with realistic parameters to consider the effects of a thermal bath and the damping of the resonator. In a similar setup with a single-electron quantum dot in a CNT without the nearby charge sensor, we theoretically study a mechanically-induced single electron spin resonance based on the coupling between the spin and the mechanical degree of freedom due to the intrinsic curvature-induced spin-orbit coupling. An off-resonant external electric driving field results in a rotation of the electron spin about the z axis of the Bloch sphere of the qubit. The rotation axis of the spin resonance and the rotation about z axis can be adjusted by varying the external electric field, and hence arbitrary single qubit gates can be obtained. We theoretically analyze two quantum dots with two single electrons on a suspended CNT in a magnetic field. An external AC electric field is applied to drive the vibration of the CNT. An indirect coupling of two distant single electron spins is mediated by spin-phonon coupling. A two-qubit iSWAP gate is obtained by the XY coupling term which is induced from the spin-phonon coupling and the coupling of two distant single electron spins in the Hamiltonian. Maximally entangled states of two spins can be generated with the iSWAP gate and a rotation about the x axis of the Bloch sphere of the qubit by varying the frequency and the strength of the external electric driving field. We propose electrostatically shifting the electron wave function in a quantum dot can turn off the spin-phonon coupling. We propose creating singleand multi-phonon Fock states and arbitrary superpositions of quantum phonon states in a CNT resonator based on spin-phonon coupling. Pulses of different driving are applied on the single-electron quantum dot formed by a voltage potential in the suspended CNT in a magnetic field. The CNT resonator is initialized in the ground state and the spin states can flip by single-electron spin resonance. Quantum information is transferred from the spin qubit state to the mechanical motion by the spin-phonon coupling. Wigner tomography is applied to obtain the phase information of the prepared phonon states.