In this thesis, quantum states of single spin systems in solid state are investigated for potential applications in quantum information processing. The studied system is the nitrogen-vacancy defect in diamond, which can be thought of as a molecule trapped inside the diamond crystal. An issue for high-fidelity state preparation is the intitialization of the system. The photo-induced charge state dynamics of the nitrogen-vacancy defect is determined, and methods for charge state initialization are beeing developed. The electron spin state of single nitrogen-vacancy defects can be read out optically. Here, we focus on nearby nuclear spins coupled to the electron spin. We investigate the quantum evolution of a single nuclear spin, measurement of non-orthogonal quantum states and improved magnetic field sensing. Based on three nuclear spins, a small quantum register is realized. We prepare and measure the GHZ and the W state in this register, and implement an algorithm for quantum error correction.
In this thesis, quantum states of single spin systems in solid state are investigated for potential applications in quantum information processing. The studied system is the nitrogen-vacancy defect in diamond, which can be thought of as a molecule trapped inside the diamond crystal. An issue for high-fidelity state preparation is the intitialization of the system. The photo-induced charge state dynamics of the nitrogen-vacancy defect is determined, and methods for charge state initialization are beeing developed. The electron spin state of single nitrogen-vacancy defects can be read out optically. Here, we focus on nearby nuclear spins coupled to the electron spin. We investigate the quantum evolution of a single nuclear spin, measurement of non-orthogonal quantum states and improved magnetic field sensing. Based on three nuclear spins, a small quantum register is realized. We prepare and measure the GHZ and the W state in this register, and implement an algorithm for quantum error correction.
A functioning qubit must be able to be initialized and measured. The fidelity of these operations is essential for all quantum applications, including quantum sensing, communication, and computation. The diamond nitrogen-vacancy (NV) center is a point defect in the lattice with an optical interface to a coherent ground-state spin, which makes the NV center one of the few spin qubits operable at room temperature. While the NV center spin state can be initialized and read out optically, the fidelity of these operations are far from perfect due to the charge and orbital dynamics. In typical conditions, the NV center is in the proper charge state 75% of the time, and measuring the spin state results in a non-zero signal only 1% of the time. These inefficient mechanisms make many measurements practically intractable. This thesis focuses on improving the preparation and measurement fidelities of NV centers through precise all-optical control of the charge, orbital, and spin dynamics. I first discuss an improved spin readout mechanism which relies on spin-to-charge conversion (SCC) and discuss the potential for single-shot spin readout. Following, I present how charge readout and SCC can be implemented in ensembles of NV centers within nanodiamonds and demonstrate that it provides improvements for spin-relaxometry studies. Finally, I develop a method for initializing a single NV center's charge state with real-time control and show that this capability improves spin readout performance for sensing. To conclude, I discuss how these improved initialization and readout capabilities can be applied to detecting and controlling coupled nuclear spins in the diamond lattice and consider other applications of real-time control.
This work investigates the applicability of the nitrogen-vacancy (NV) defect center in diamond for quantum computation and metrology purposes. The NV center is a molecule like defect in the diamond lattice which is optically active and possesses an electron spin in its ground state. The spin can be used as a quantum bit and as a field sensor. The NV center has three major properties enabling individual control of single defects. Its optical properties depend on the spin state, the spin can be polarized optically and the spin state has an exceptionally long lifetime. Single NV centers can be controlled by optical and microwave radiation. Generally, the research on individually controllable quantum systems is not only motivated by quantum computation and communication. With the ongoing miniaturization nowadays electronic and electro-optic devices will soon reach the limit of single quantum building blocks. While in these applications the full complexity of single quantum systems might not be needed, small sensors based on single atoms or molecules might very well take advantage of the susceptibility of quantum coherences to environmental conditions. Major challenges for all approaches towards single quantum system control are the individual addressing, the measurement of the quantum state and the protection of quantum coherence from environmental noise. Today, there is a variety of systems (including the NV center) that allow control on the single quantum level. These are for example single photons, single ions and atoms in traps, single spins in semiconductors or single molecules in solid state systems. Rather mesoscopic examples are superconducting devices, nanomechanical oscillators or surface plasmon polaritons. Regarding the NV center it has been shown that the magnetic moment of its electron spin allows individual sensing and coupling to other surrounding electron and nuclear spins. Especially single nuclear spins were shown to be exceptional quantum memories. In this work small quantum registers of up to 5 spins have been used to test major requirements for a feasible quantum processor. Therefore, mainly artificially created high purity diamond samples with controlled spin and impurity concentration were used. The NV centers were either grown in or created via ion implantation techniques in a controlled fashion. As a first requirement for quantum computation entanglement among up to three spins has been generated and was verified by quantum state tomography. This proves the access of the full Hilbert space. Especially, entanglement among nuclear spins was very long-living. In further experiments this processor was used for first quantum algorithms like super-dense coding and the Deutsch algorithm. In addition, this work demonstrates new methods to initialize nuclear spin qubits into a desired quantum state. This is particularly important as improper initialization inhibits quantum computation. One of these methods is related to dynamic nuclear spin polarization and the other to measurement based state preparation. Nuclear spins in the diamond lattice originate mainly from the C-13 isotope. By artificially altering its content the influence on the NV center spin was investigated. The coherence times of the NV center were increasing inversely with the nuclear spin density. Even increasing nuclear spin density to offer more nuclear spin qubits to an operational quantum register was possible. As an alternative route of scaling up the quantum register pairs of closely spaced NV centers were investigated. For the first time two qubit gates among two NV centers mediated by magnetic dipolar coupling have been realized. Furthermore the sensing ability was demonstrated by measuring the relative distance of the two centers (10 nm) with sub-nm precision. Eventually, this work contains new insight into the electronically excited state of the NV center which allowed a more advanced control of the electron and nuclear spins. A comparably high magnetic field was used to decouple electron and nuclear spins. Finally, this allowed quantum nondemolition measurements on single nuclear spins which manifests in the observation of quantum jumps. The new insight was used to drastically improve the performance of quantum state readout. Summarizing, it was shown that single NV centers and proximal nuclear spins form versatile small quantum registers which can be interconnected with neighboring such NV quantum registers. Although the number of qubits used in this work is still small the experimental results propose a way of how to proceed when building a quantum computer. Regarding quantum metrology, however, the use of such a small register which can sense fields and store and process the results would already outperform a single NV electron spin by orders of magnitude.
Digital information based on the laws of quantum mechanics promisses powerful new ways of computation and communication. However, quantum information is very fragile; inevitable errors continuously build up and eventually all information is lost. Therefore, realistic large-scale quantum information processing requires the protection of quantum bits (qubits) against errors. In this thesis we present the experimental implementation of quantum error correction protocols based on spins in diamond. In such protocols, a quantum state is protected against errors by encoding in multiple qubits. Errors can be detected and corrected by measurement of correlations, so-called stabilizer-measurements, on these qubits.The experimental work presented in this thesis employs multiple spins in diamond as qubits to explore and implement error correction protocols. The nitrogen-vacancy (NV) centre in diamond is a lattice defect consisting of a nitrogen atom (N) and a vacancy (V) on two adjacent diamond lattice sites. This defect effectively results in an electronic spin that can be addressed as a qubit. The spin state can be manipulated by microwave fields and optically read out. At liquid helium temperatures (cryogenic temperature, ~4 K = -269 C), the NV electron spin provides high-fidelity single-shot readout and long coherence times.The NV centre is surrounded by naturally available (1.1% abundance) nuclear C13 spins. As the number of spins that are close enough to the NV centre to be strongly coupled is limited, we employ the weakly coupled nuclear spins in the spin bath of the NV centre. Using dynamical decoupling techniques these nuclear spins can be detected via the NV electron spin through the hyperfine interaction. The nuclear spins are long-lived and robust against optical excitation of the NV electron spin, which can make these spins a robust quantum register for quantum error correction.In Ch. 4 we demonstrate universal control over multiple of such weakly coupled nuclear C13 spins in the environment of the NV centre at ambient temperatures. We demonstrate initialization, control and read-out of individual nuclear spins. Finally, we implement a quantum error correction protocol by encoding a quantum state in the NV electron spin and two nuclear spins. Errors are detected by un-encoding the quantum state back to the electron spin and correction via a double controlled operation.For universal fault-tolerant quantum computations it is essential that the quantum information remains encoded at all times. In Ch. 5 we present multiple rounds of quantum error correction and active feedback on a continuously encoded qubit at cryogenic temperatures. A quantum state is protected by encoding in three weakly coupled spins. Errors are detected via high-fidelity non-demolition readout of the NV electron spin and actively corrected using fast classical electronics. We demonstrate that an actively error-corrected qubit is robust against phase flip errors and show that a superposition state can live longer than the best physical qubit in the encoding.The presented methods and results can be extended to a range of future experiments. In Ch. 6 we propose the implementation of five-qubit quantum error correction, the smallest code to correct for general single-qubit errors on the physical qubits in the encoding, by extending the experimental methods as developed in Chs. 4&5. Besides the exploration and development of larger error correction protocols and fault-tolerant quantum computing, the presented quantum register based in spins in diamond can be employed as a quantum node and combined with recent advances in the realization of quantum entanglement over large distances to form quantum networks. These networks can be used to study both fundamental questions as well as future applications in quantum information technology.
This thesis describes a series of experiments on the control of the optical properties of the nitrogen-vacancy (NV) center in diamond, and on control of the electron and nuclear spin states associated with the NV center. The NV center is a fluorescing atomic defect center in diamond, consisting of a substitutional nitrogen atom adjacent to a vacancy in the diamond carbon lattice. The electron spin of the NV center can be initialized and read out optically, and coherently manipulated with high fidelity even at room temperature. This unique combination of properties has attracted much attention to the NV center in recent years for application in quantum information technologies. The experiments in this work focus on exploiting the intrinsic hybrid nature of the NV center. The NV center forms a hybrid spin register, as its electron spin is always coupled to the nuclear spin of its own nitrogen nucleus, and can furthermore be coupled to additional nuclear carbon-13 spins in the diamond. In addition, the electronic spin state can be mapped onto the state of a photon, in principle allowing long range transmission of quantum information and measurement-based entanglement of distant NV center registers. The long-term goal is to achieve a large scale quantum network where the different constituents each perform the task they are most well suited for: the stable nuclear spins store the quantum information, photons transfer quantum information over long distances, and the fast electron spin interfaces between spin and photon states. For measurement-based entanglement of distant NV centers it is of primary importance to maximize the emission and detection of coherent photons emitted by the NV center. Spontaneous emission can be controlled and enhanced by coupling an emitter to a photonic cavity. Chapters 3, 4, and 5 of this thesis describe experiments aimed at maximizing the coherent photon emission rate of an NV center by coupling the NV center to a photonic crystal cavity. One of the main challenges is to position a single NV center into the nanometer-sized cavity mode. Chapter 3 describes the development of a nanopositioning technique, which allows diamond nanocrystals ~50 nm in size containing single NV centers to be placed at arbitrary locations on a chip, with nanometer precision. By using a sharp etched tungsten tip, individual nanocrystals can be picked up, moved and placed under real-time imaging with an electron microscope. We explicitly demonstrate that the unique optical and spin properties of the NV center are conserved by the nanopositioning process. In chapter 4, we apply the nanopositioning technique to couple single NV centers contained in a diamond nanocrystals to gallium phosphide photonic crystal cavities. These cavities resonate in the visible with high quality factors, and are designed to have the lowest energy mode coincide with the zero-phonon line of the NV center. Efficient coupling is evidenced by a strong enhancement of NV center emission at the cavity wavelength. The high quality factor of a photonic crystal cavity is a result of careful design and fabrication. The introduction of a nanocrystal may therefore be expected to have a detrimental effect on the optical properties of a cavity. In chapter 5 we investigate the effect of a nanocrystal on the optical properties of photonic crystal cavities. Our simulations and measurements show that the effect of a nanocrystal is in fact only minor, a promising result for future work on cavity-QED systems in the solid state and with diamond defect centers in particular. Understanding and mitigating decoherence is a key challenge for quantum science and technology. The main source of decoherence for solid-state spin systems is the uncontrolled spin bath environment. Chapter 6 describes experiments that exploit quantum control of the NV center and recently developed dynamical decoupling techniques to study the properties of the surrounding bath of spins belonging to single substitutional nitrogen atoms. The coherence properties of a single NV center are affected by changes in the state of the bath spins, allowing a single NV center to be used as a probe to detect bath spin resonances and study the quantum dynamics of the spin bath. We use quantum control of the spin bath to extend the dephasing time of the NV center, important for the application of the NV center in DC magnetometry. In chapter 7 we describe the development and implementation of decoherence protected quantum gates for the hybrid spin register formed by the NV center electron spin that is coupled to the nuclear spin of its own nitrogen atom. Electron and nuclear spins evolve and decohere at vastly different rates, making it challenging to use such a hybrid system as a fully functional quantum register. We create a universal set of two-qubit quantum gates by integrating dynamical decoupling techniques into the gate operation. We demonstrate the power of our gate design by implementing for the first time Grover's quantum search algorithm on a solid-state spin register.
TThis thesis presents works not only to understand the spin degree of freedom present in the nitrogen-vacancy defect in diamond: its internal structure and its relation to its environment, but also to find novel applications of it in metrology. First, a mathematical model is develop to understand how this defect couples to a nuclear spin bath of Carbon 13 which constitutes the main dephasing mechanism in pure natural diamond. Next, we demonstrate the use of this defect to sense external oscillating magnetic fields. The high sensitivity and the small sensing volume achieved when a defect is placed in a nanocrystal of few tents of nanometers in diameter, allows this sensor to detect single electronic spins and even single nuclear spins. This sensitivity, proportional to the signal to noise per readout, can be improve by the help of the environment of this defect. We show that strongly interacting nearby nuclei can enable repetitive readout schemes to improve the signal to noise of the electronic spin signal. We also combine ideas from the microscopy community such as stimulated emission depletion to enable high spatial resolution magnetometry. Finally, we develop a formalism based on group theory to understand the internal structure of defects in solids such as their selection rules and the effect of spin-spin and spin-orbit interactions even when perturbations reduce the symmetry group of the system.
The ability to measure and manipulate the quantum state of a single spin in a solid state system opens up a broad range of powerful applications ranging from nano probes to quantum information processing. Over the past few years, a number of ground breaking experiments have been conducted on paramagnetic nitrogen vacancy defect centers in diamond, including up to 3-qubit entanglement, single-shot-readout of a nuclear spin, selective access of two coupled centers and magnetic, electric and thermographic sensing at the nanoscale with promising properties in some cases exceeding most currently known techniques. Yet, almost all of the experiments conducted so far focus on centers deeply buried in the diamond, which is undesirable especially for sensing applications, but also in terms of scalability and electronic access to the information. In this work we focus on the spin physics of centers only few nanometers below the surface, where the unique properties of the center are strongly influenced by the external environment. We coherently manipulated and detected single spins at ambient temperature by combining optically detected magnetic resonance with single molecule spectroscopy using a confocal microscope. We measured the spin dephasing behavior and the phase relaxation time and examined the primary sources of decoherence. Furthermore, we observed effects of water, atmosphere and paramagnetic molecules on the coherence and readability of spins in nanodiamonds and demonstrated ways to preserve the coherence using external magnetic fields and a number of different dynamic decoupling pulse sequences. In addition, we measured couplings to proximal nuclear spins by continuous wave spectroscopy and to molecules on the surface by double electron electron resonance. Also, we demonstrate execution of the refined Deutsch-Jozsa algorithm on a nitrogen vacancy center in a nanodiamond. Finally, we propose new technological approach for realtime measurements of magnetic fields using a single spin in diamond. In test measurements using external fields and spatially resolved measurements of the field from a magnetic microwire a sensitivity of a few uT / sqrt(Hz) was achieved.