טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentGuy Moshel
SubjectInitialization and Tomography of a Non-Rotating Qubit in
Diamond
DepartmentDepartment of Physics
Supervisor Full Professor Gershoni David


Abstract

In this research we studied a non-degenerate, physical-two-level system (a non-rotating qubit) implemented in the ground state of a single nitrogen-vacancy (NV) center in diamond. We succeeded in demonstrating initialization of the qubit state as well as full state tomography of qubit using polarized microwave (MW) fields.

The NV-center is a color center in diamond that consists of a substitutional nitrogen with an adjacent vacancy in the diamond lattice. The ground state is a spin triplet (S=1) with three magnetic sub-levels ms=0,±1 and a large zero-field splitting between the ms=0 and the ms=±1 states. The ground state can be initialized to the ms=0 sub-level by green laser illumination, and it can also be readout by the increase in the red light photoluminescence (PL) when this level is occupied.

We used the ms=±1 states as the two basis states for a non-rotating qubit. For this purpose, we enforced degeneracy on these states by nulling the external magnetic field using a three-coil apparatus located above the diamond sample. We then applied MW currents with frequency tuned to the ms=0 to the ms=±1 transition frequency. The currents were supplied into two orthogonal thin copper wires suspended above the diamond surface. These MW currents with variable amplitudes and relative phase differences produced MW radiation with various polarizations and fast switching times.

Using this apparatus, we were able to demonstrate arbitrary initialization of the qubit states in any coherent superposition. For this effect, we first optically initialized the ms=0 state using green illumination and then, by applying a polarized MW π-pulse, we initialized the ms=±1 qubit in a coherent superposition of its two states, depending on the MW polarization. Right-hand circular (R) MW polarization excites the ms= state and left-hand circular (L) polarization excites the ms=-1 state. Thus, any desired coherent superposition of the qubit can be initialized by the MW pulse polarization.

We also demonstrated full quantum-state-tomography of the qubit by projecting an unknown qubit state onto the ms=0  state using four basis pre-calibrated MW polarizations.  Each basis polarization projects a component of the unknown state onto the ms=0 state, which can then be measured. The four basis polarizations were found by fitting double-quantum-Ramsey measurements with a numerical model of the ground state that we constructed. We achieved fidelities of about 90% for these basis polarization projections.