We propose an approach for an optical qubit rotation in the negatively charged nitrogen vacancy (NV) center in diamond. The qubit is encoded in the ground degenerate states at a relatively low-temperature limit. The basic idea of the rotation procedure is the non-Abelian geometric phase in an adiabatic passage, which is produced by the non-adiabatic transition between the two degenerate dark states. The feasibility is based on the success of modeling the NV center as an excited-doublet four-level atom. By applying two pump and two Stokes laser pulses, we found that the behavior of the adiabatic passage depends crucially on the applied intensity of each applied laser field and the detunings between the laser frequencies and their corresponding atomic transition. Particularly, a non-adiabatic transition appears when the applied pump and Stokes laser pulses are off resonance with their corresponding atomic transition.
We propose an approach for an optical qubit rotation in the negatively charged nitrogen vacancy (NV) center in diamond. The qubit is encoded in the ground degenerate states at a relatively low-temperature limit. The basic idea of the rotation procedure is the non-Abelian geometric phase in an adiabatic passage, which is produced by the non-adiabatic transition between the two degenerate dark states. The feasibility is based on the success of modeling the NV center as an excited-doublet four-level atom. By applying two pump and two Stokes laser pulses, we found that the behavior of the adiabatic passage depends crucially on the applied intensity of each applied laser field and the detunings between the laser frequencies and their corresponding atomic transition. Particularly, a non-adiabatic transition appears when the applied pump and Stokes laser pulses are off resonance with their corresponding atomic transition.
We describe an all-optical scheme for spin manipulation in the ground-state triplet of the negatively charged nitrogen-vacancy (NV) center in diamond. Virtual optical excitation from the 3A2 ground state into the 3E excited state allows for spin rotations by virtue of the spin-spin interaction in the two-fold orbitally degenerate excited state. We derive an effective Hamiltonian for optically induced spin-flip transitions within the ground state spin triplet due to off-resonant optical pumping. Furthermore, we investigate the spin qubit formed by the Zeeman sublevels with spin projection mS=0 and ${m}_{S}=\ensuremath{-}1$ along the NV axis around the ground state level anticrossing with regard to full optical control of the electron spin.
The nitrogen-vacancy (NV) center in diamond has garnered great interest over the past decade as its electronic spin shows promise as a quantum bit (qubit) and nanoscale sensor. Consisting of a substitutional nitrogen adjacent to a vacant site within the carbon lattice of diamond, this defect exhibits millisecond-long spin coherence times extending beyond room temperature, spin-dependent optical addressability, coupling to intrinsic and nearby nuclear spins, and it can be controlled and manipulated through electrical, magnetic, and optical means. In particular, at cryogenic temperatures (T < 25 K), the NV center's excited state becomes sharp and optically resolvable, providing a solid-state quantum optical testbed. In this thesis, I describe several experiments that explore this quantum optical interface to facilitate the development of a photonic network of single spins linked and controlled by light. We begin by exploring how electric fields tune the orbital levels within the NV center through the DC Stark effect, finding a surprising photo-induced field that aids in the ability to tune multiple NV centers' optical transitions to degeneracy. We then develop techniques to fully control the spin state of the NV center by coupling through a lambda system, an energy configuration consisting of two lower levels coupled to one of higher energy. When a lambda system is optically driven, the spin becomes trapped in a dark state, or the eigenstate of the system that is not coupled to the light fields through destructive interference, forming the basis for the various types of control demonstrated. We demonstrate arbitrary-basis initialization and readout of the spin state through coherent population trapping, as well as the ability to rotate about any arbitrary basis through stimulated Raman transitions. Combining these techniques, we measure the NV center's spin coherence through a completely optical measurement. We then extend these lambda system techniques to adiabatically move the dark state in trajectories around the Bloch sphere. Such trajectories accumulate a quantum mechanical phase that depends only on the geometry of the path enclosed, not on the energetics or time of the interaction. We characterize the interaction, measure this phase, known as Berry phase, and explore the limits of its control and resilience to noise. Finally, we demonstrate another all-optical control technique that uses strong ultrafast pulses of light to transfer the spin between the ground and excited states, deriving spin manipulation from the excited state dynamics. This technique also provides time-resolved spectroscopy of the excited state and its various decay and decoherence mechanisms. These experiments advance the progress toward the development of photonic networks coupling and controlling defects through light-matter interactions.
The development of quantum information in the last decades has opened new horizons in science and technology.It turns out that quantum physics, apart from playing a fundamental role in the structure of matter, also opens new opportunities for computation and communication, if one can harness the quantum superposition and entanglement.This started a new scientific challenge to find the platform that can offer two well isolated discrete levels (a qubit), that are a standard building block for many quantum devices, like bits are those for a classical computer.In this thesis we focus on one such platform, the negatively charged nitrogen-vacancy (NV -) center in diamond.It uses the triplet states of two fermionic spin-1/2 particles (holes) to encode the information.In order to build a working device, be it a quantum computer or a communication hardware, one needs to have a very good control over the quantum system.Usually, the NV -centers are controlled with the microwave magnetic field of an antenna, that is placed in the vicinity of the NV -.One of the issues we address in this thesis is whether we can replace the magnetic field with electric field or strain to control the system.We derive the corresponding coupling Hamiltonian and discuss the schemes to measure its parameters.Another approach we are investigating to simplify the control of an NV -based device is replacing the antenna magnetic field with spin-waves, that couple to the NV -centers.We show that for a magnetic material with low damping, the spin waves can propagate over very long distances with no dissipation and can provide the control of NV -centers even if the microwave antenna is far away and can not reach the center.We develop the theoretical formalism that allows to calculate the coupling enhancement, offered with this approach with respect to a pure antenna driving.Another essential ingredient of a quantum device is the ability to generate state superpositions and entanglement between different qubits.This is done by means of quantum gates, that must be performed with extremely high fidelity in order for the system to work.We investigate the possibility to perform geometric quantum gates, that are tolerant to certain types of errors, on the spin of NV -centers in diamond.We are interested in both adiabatic and non-adiabatic geometric quantum computation.Inspired by a recent observation of Berry phase with NV -centers, we develop an effective Hamiltonian description of adiabatic geometric gates, alternative to conventional Berry connection approach.For non-adiabatic geometric gates, we analyze the fidelities and error channels, when the gates are performed optically through the orbital excited state of the NV -centers.We also develop a scheme to apply all-microwave universal non-adiabatic geometric gates on small registers of coupled NV -and nuclear spins.Finally, we develop an entanglement protocol, that generates a universal two-qubit gate on two NV -centers, coupled to a common mode of a high Q cavity.We show that it is possible to implement this gate fast and at a fidelity, that is high enough to apply error-correction protocols.
The holonomic approach to controlling (nitrogen-vacancy) NV-center qubits provides an elegant way of theoretically devising universal quantum gates that operate on qubits via calculable microwave pulses. There is, however, a lack of simulated results from the theory of holonomic control of quantum registers with more than two qubits describing the transition between the dark states. Considering this, we have been experimenting with the IBM Quantum Experience technology to determine the capabilities of simulating holonomic control of NV-centers for three qubits describing an eight-level system that produces a non-Abelian geometric phase. The tunability of the geometric phase via the detuning frequency is demonstrated through the high fidelity (~85%) of three-qubit off-resonant holonomic gates over the on-resonant ones. The transition between the dark states shows the alignment of the gate's dark state with the qubit's initial state hence decoherence of the multi-qubit system is well-controlled through a π/3 rotation.
A non-Abelian geometric method is proposed for rotating of heavy hole spins in a singly positive charged quantum dot in Voigt geometry. The key ingredient is the delay-dependent non-Abelian geometric phase, which is produced by the nonadiabatic transition between the two degenerate dark states. We demonstrate, by controlling the pump, the Stokes and the driving fields, that the rotations about y and z axes with arbitrary angles can be realized with high fidelity. Fast initialization and heavy hole-spin-state readout are also possible.
Geometric phases encode the holonomy acquired under cyclic control of a quantum Hamiltonian: for nondegenerate eigenstates the effect is Abelian (a scalar phase), while in degenerate manifolds the Wilczek-Zee generalization yields a matrix-valued holonomy that can mix states and depends on path ordering. We present an overview of measuring Abelian and non-Abelian geometric phases in nitrogen-vacancy (NV) centers in diamond and propose a non-rotating measurement protocol enabled by the intrinsic14Nhyperfine manifold. As a first step, we propose to measure the Abelian Berry phase on a single hyperfine-resolved two-level transition using microwaveengineered closed loops with dynamical-phase cancellation by loop reversal. We then propose a non-Abelian protocol that engineers a two-dimensional degenerate dark subspace in an NV-14Nmanifold via RF dressing and three phase-coherent microwave couplings (a tripod Hamiltonian). Two closed control loops implemented by winding independent microwave phases generate non-commuting SU(2) holonomies, which can be verified using final-only population readout and minimal tomography. We also present timing trade-off curves, full unitary Schrödinger evolution of the four-level tripod, and projected dark-subspace diagnostics that quantify both leakage and non-commuting holonomy.