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The Stokes and the anti-Stokes Raman spectra from the high energy carbon–carbon stretching modes in graphene and diamond are studied, with a focus on their intensity dependence on the excitation laser power. For diamond, the experiment was performed on a 50 μm slice of chemical vapour deposition grown single crystal using a 785 nm laser, in both the continuous wave (CW) and pulsed mode-locked (ML—130 fs pulses) excitation regimes. For graphene, the experiments were performed on suspended samples, including single layer, bilayer with AB-staking, twisted bi-layer and a sample with 4–6 layers, using λ = 532 and 633 nm CW lasers. The Stokes and anti-Stokes intensities vary largely from sample to sample, and the anti-Stokes/Stokes intensity ratio shows different excitation laser power behaviours. These differences can be explained on the basis of laser heating or correlated Stokes–anti-Stokes scattering phenomena.

Twisted-bilayer graphene (tBLG) exhibits van Hove singularities in the density of states that can be tuned by changing the twisting angle θ. A θ-defined tBLG has been produced and characterized with optical reflectivity and resonance Raman scattering. The θ-engineered optical response is shown to be consistent with persistent saddle-point excitons. Separate resonances with Stokes and anti-Stokes Raman scattering components can be achieved due to the sharpness of the two-dimensional saddle-point excitons, similar to what has been previously observed for one-dimensional carbon nanotubes. The excitation power dependence for the Stokes and anti-Stokes emissions indicate that the two processes are correlated and that they share the same phonon., Nano Letters, 14 (10), ISSN:1530-6984, ISSN:1530-6992

As computing requirements and data volumes continue to increase, the need for faster, more efficient memories has become a driving force in many research areas. One proposed alternative to current ferromagnetic (FM) storage technology is antiferromagnetic (AFM) memories, which promise faster, more energy-efficient switching and higher bit densities. Developing such technologies requires progress on two fronts. On the one hand, we must understand and harness the AFM magnetic textures central to the proposed memory devices. At the same time, we require technologies capable of addressing these typically hard-to-access systems. In this thesis, we use magnetometry based on the nitrogen vacancy (NV) center in diamond to address both sides of this problem. NV magnetometry, in particular scanning magnetometry, can be employed in a variety of environmental conditions, providing access to a wide range of materials and phenomena. Furthermore, the high magnetic field sensitivity and spatial resolution achievable with this technique enable us to address the nanoscale magnetic textures of interest. However, sensitivity and resolution are limited by our ability to collect the NV center photoluminescence (PL) and by how close we can bring the NV to the magnetic field source, respectively. Here, we aim to improve on the state-of-the-art scanning NV magnetometry probe with a novel design based on a truncated parabolic pillar. The parabolic nature of the pillar leads to excellent directional emission of the PL, allowing us to demonstrate median PL rates of 2.1 MHz and collection efficiencies of 57%. As such, we realize improved sensitivities compared to the state-of-the art scanning probes while simultaneously achieving nanoscale resolution through the truncated end facet of the pillar. We then use these improved scanning probes to study the magnetic properties of a magnetoelectric AFM: chromia. Due to its room-temperature AFM ordering and the ability to switch the magnetic order with electric fields, this material is a popular candidate for spintronics applications. In our study, we demonstrate control over the magnetic orientation of a bulk chromia (Cr$_2$O$_3$) crystal and employ its magnetoelectric properties to nucleate domain walls (DWs). Using NV magnetometry, we characterize the surface magnetization of Cr$_2$O$_3$ and investigate the DW structure. We furthermore demonstrate an interaction between the DW and patterned surface topography, allowing us to develop a model of the DW mechanics. In particular, we observe a Snell's law-like behavior of the DW in the presence of topographical steps and pinning of the DW to the edges of these steps. We use this pinning, together with local heating of the Cr$_2$O$_3$ crystal, to exert control over the motion of the DW. These results bring us one step closer to achieving AFM-based memories. Having shown the ability to generate, control, and move DWs in an AFM crystal, we have laid the groundwork for a DW-based memory. Moreover, by improving the understanding of antiferromagnetic DW mechanics, we highlight material properties of Cr$_2$O$_3$ that may benefit and guide future material research.

In recent years, tunable Fabry-Perot microcavities have emerged as a compelling platform for enhancing the flux of coherent photons from single colour centres in solid-state hosts. A prominent example of one such colour centre is the nitrogen-vacancy (NV) centre in diamond. The NV centre has a highly coherent, optically addressable electron spin. Furthermore, the NV centre is a source of single photons. Advances in the creation of entangled spin-photon pairs allow for establishing remote spin-spin entanglement – a key building block in a quantum network. However, the scalability past a few network nodes is limited by modest entanglement rates, in turn limited by the detection efficiency of coherent photons. Limiting factors include the long radiative lifetime and the small branching ratio of “useful” photons into the zero-phonon line (ZPL). However, neither the radiative lifetime nor the branching ratio are rigid features of the NV centre – the flux of ZPL photons can be greatly accelerated in a resonant microcavity. This thesis reports on the realisation of a high-quality tunable Fabry-Perot microcavity embedded with a diamond membrane. However, the diamond alters the cavity performance, rendering the cavity sensitive to surface related losses. Despite operating in a geometry where the standing wave inside the cavity possesses an anti-node at the diamond surface, quality ($\mathcal{Q}$) factors exceeding $100\,000$ were realised. The benefit of this geometry is the strong confinement of the vacuum electric-field to the diamond – the current cavity design allows for the realisation of Purcell factors exceeding 300, thus increasing the fraction of photons emitted into the ZPL from $3\,\%$ to $89\,\%$. The versatile design of the microcavity was demonstrated further by enhancing the Raman transition from the single crystalline diamond. Compared to free-space measurements under likewise identical conditions, a 59-fold intensity enhancement was demonstrated. This enhancement factor encompasses the Purcell effect and the improved detection efficiency provided by the cavity. The Raman transition couples to all cavity modes, allowing for in situ optimising and benchmarking the cavity performance. Additionally, it facilitates coupling to the external single-mode detection optics. Further enhancement of the Raman intensity can be achieved by establishing a double resonant condition, with both the pump laser and the Raman transition being resonant. Resonant recirculation of the pump laser increases the power density inside the cavity, providing a platform with prospects of realising a Raman laser with sub-mW threshold pump power. Exploiting a small thickness gradient in the diamond enabled continuous tuning of the double resonance condition across a spectral window of $\sim1\,\textrm{THz}$. The tuning range is only limited by the travel range of the piezo – with an adequate travel range, continuous tuning is, at least in principle, possible across the entire reflective stopband.

Emerging quantum technologies, such as quantum information processing and quantum metrology, require quantum systems that provide reliable toolsets for initialization, readout, and coherent manipulation as well as long coherence times. The coherence of these systems, however, is usually limited by uncontrolled interactions with the surrounding environment. In particular, innovations building on solid-state spin systems like the Nitrogen-Vacancy (NV) center in diamond ordinarily involve the use of magnetic field-sensitive states. In this case, ambient magnetic field fluctuations constitute a serious impediment that shortens the coherence time considerably. Thus, the protection of individual quantum systems from environmental perturbations constitutes a fundamentally important but also a challenging task for the further development of quantum appliances. In this thesis, we address this challenge by extending the widely used approach of dynamical decoupling to protect a quantum system from decoherence. Specifically, we study three-level dressed states that emerge under continuous, `closed-contour' interaction driving. To implement and investigate these dressed states, we exploit well-established methods for coherent microwave and strain manipulation of the NV center spin in a hybrid spin-mechanical system. Our results reveal that this novel continuous decoupling mechanism can overcome external magnetic fluctuations in a robust way. We demonstrate experimentally that the dressed states we created are long-lived and find coherence times nearly two orders of magnitude longer than the inhomogeneous dephasing time of the NV spin, even for moderate driving strengths. To realize direct and efficient access to the coherence-protected dressed states under closed-contour driving, we further demonstrate the use of state transfer protocols for their initialization and readout. In addition to an adiabatic approach, we apply recently developed protocols based on `shortcuts to adiabaticity' to accomplish the initialization process, which ultimately accelerates the transfer speed by a factor of $2.6$ compared to the fastest adiabatic protocol with similar fidelity. Moreover, we show bidirectionality of the accelerated state transfer, which allows us to directly read out the dressed state population and to quantify the transfer fidelity of $\approx$$\,99\,\%$. By employing the methods to prepare and read out the dressed states, we lay the foundation to meet the remaining key requirement for quantum systems -- coherent quantum control. We present direct, coherent manipulation of the dressed states in their own manifold and exploit this for extensive characterization of the dressed states' properties. Thus, our results constitute an elementary step to establish the dressed states as a powerful resource in prospective quantum sensing applications. Harnessing quantum systems like the dressed states as nanoscale sensors of external fields requires the detailed characterization of the local internal environment. In the final part of this thesis, we report on the determination of intrinsic effective fields of individual NV center spins. We study single NVs in high purity diamond and find that local strain dominates over local electric fields. In addition, we experimentally demonstrate and theoretically describe a new technique for performing single spin-based polarization analysis of microwave fields in a tunable, linear basis.

The liquefaction of helium and the dilution refrigerator have enabled cooling down objects to 4K and even mK temperatures. Fascinating effects, such as superconductivity and strongly correlated electron systems (SCES) emerge at these temperatures and can be studied in appropriate cryogenics experiments. A powerful tool to study magnetic phenomena in such systems is a point lattice defect in diamond, the nitrogen-vacancy (NV) center. The NV center contains an electron spin that offers exceptional properties in terms of coherence time and optical addressability, and can thereby be employed for high-performance magnetic field sensing. Due to its atom-like size, the NV center can be used for nanoscale magnetometry, particularly in a scanning probe configuration where a single NV is located in a tip. This allows for nanometric spatial resolution combined with sensitivities of approximately 1 µT/Hz^0.5. In this work, we pave the way towards NV magnetometry at mK temperature by implementing NV magnetometry in a dilution refrigerator, so far at 4 K, and by conducting transport experiments on a SCES at mK temperature. At first, two phenomena in the type-II superconductor YBCO are examined at 4K in a liquid helium bath cryostat. On the one hand, the Meissner effect is measured over a thin YBCO disk by directly imaging the penetration of magnetic fields into the superconductor. On the other hand, stray magnetic fields emerging from vortices in the same superconductor are imaged with approximately 30nm resolution. In both cases, we benchmark our findings against existing theoretical models and use this analysis to extract quantitative values for the London penetration depth. Additionally, we examine out-of-plane (OOP)-oriented NV centers with respect to the scanning plane, which offer benefits such as improved sensitivity and data interpretability. OOP-oriented NV centers in our fabricated scanning probes are uniquely identified and used for nanoscale magnetic imaging for the first time. The oxide interface LAO/STO, which hosts a two-dimensional electron gas that exhibits SCES physics, is examined in the dilution refrigerator. Transport measurements show signs of superconductivity and laser illumination is found to significantly increase the conductance. In terms of NV magnetometry in a dilution refrigerator at 4 K, current imaging reveals an inhomogeneous current ow through the interface. In contrast to previous findings, no magnetic signatures are found. Lastly, longitudinal T1 relaxation is studied in a high-density NV ensemble. Relaxation rates at mK are found to be lower than at 4 K, on the order of 1 Hz. However, they are still much higher than in previous findings, possibly explainable by spin diffusion out of the laser focus. At mK temperature, a shift of the thermal spin population is observed, corresponding to the Boltzmann distribution. Overall, in this thesis we can present meaningful results in several areas, some of which have already been published. In the future, we will use the increased sensitivity of OOP-oriented NV magnetometers and explore magnetism and superconductivity in various exotic materials at mK temperatures.

Individual electronic spins can yield close-to-ideal magnetometers to investigate magnetic phenomena on the nanoscale. Spins offer sensitivity to magnetic fields by virtue of the Zeeman effect and can be localized to atomic length scales, which enables nanoscale resolution in imaging. The electronic spin of the Nitrogen-Vacancy (NV) center in diamond has been identified as a particularly fruitful system to implement these concepts, as its additional ability of optical spin initialization and readout renders the NV center a non-invasive and quantitative magnetometer with single-spin sensitivity and nanoscale spatial resolution. Nitrogen-Vacancy based magnetometry has been widely exploited exclusively under ambient conditions. Advancing the frontiers of nanoscience at low temperature, however, hinges on the availability of novel sensors for nanoscale imaging such as the Nitrogen-Vacancy center. To fill this gap, in this thesis we developed and employed an NV-based scanning magnetometer at cryogenic temperatures. We present the implementation of an atomic force microscope, which is functionalized with a single NV center, situated in a liquid helium bath cryostat, and interfaced with a confocal microscope for optical initialization and readout of the NV's electronic spin. We demonstrate DC magnetic field sensitivities better than uT/sqrt(Hz) and an unprecedented spatial resolution of 30 nm. Moreover, we introduce powerful post-processing techniques and employ them on the recorded quantitative magnetic stray field maps. This allows for the retrieval of important material parameters by recovering the underlying planar current distribution or spin texture. To demonstrate the performance of our cryogenic magnetometer, we focused on nanoscale studies of magnetic phenomena in superconductors. We were able to image stray fields of individual vortices with highest spatial resolution and perform nanoscale studies of the Meissner effect in superconductor nanostructures. Both of these measurements enabled the unambiguous determination of the London penetration depth, allowed for the inspection of nanoscale defects inhibiting superconductivity and for benchmarking competing, microscopic models for supercurrent flow. In a second experiment, the application of the cryogenic scanning setup to recently discovered two-dimensional magnets in van der Waals heterostructures led to one of the key results of this thesis. We quantitatively determined the magnetization of a monolayer CrI3 and demonstrated that the magnetic coupling between individual layers in a multi-layer stack CrI3 is intimately connected to the material structure, and that structural modifications can induce a relaxation to the magnetic ground state, which has not been observed so far in this material. Our results therefore illustrate the power of NV magnetometry in exploring local magnetic properties of electronic systems with high resolution, and the great potential for future nanoscale explorations of a large range of complex, condensed matter systems at cryogenic temperatures.

Moore's Law demands for innovation not only to solve the question of how to store even more information on even smaller areas but also in how to access this information. Both problems make point defects in solid-state systems very interesting. Color centers in diamond are one of these atom-like systems. Their electronic spins can be used as a versatile sensor or quantum storage. These sensors live up to their full potential when combined with a scanning technique as atomic force microscopy (AFM). The precise control of the position combined with an atom-sized light source or sensor opens up various possibilities. The main struggles encountered by the field so far are the difficulty of retaining the crystal quality of bulk diamond and simultaneously have a sharp tip to get the best topological feedback possible. In our work, we present three different avenues to tackle this. We conduct a study of the cause of decoherence in plasma etched nanostructures and test different treatments to reduce the effect. We test a novel method to stabilize an alternative color center believed to be less sensitive to electric field noise. Furthermore, we explore a new approach combining top-down fabrication and bottom-up overgrowth to get sharp tips with good crystal quality. The combination of the individual avenues has the potential to bring the sensing and imaging capabilities of color center-based sensing to the next level.

Hybrid spin-oscillator systems, formed by single spins coupled to mechanical oscillators, have attracted ever-increasing attention over the past few years, triggered largely by the prospect of employing such devices as high-performance nanoscale sensors or transducers in multi-qubit networks. Provided the spin-oscillator coupling is strong and robust, such systems can even serve as test-beds for studying macroscopic objects in the quantum regime. In this thesis we present a novel hybrid spin-oscillator system that consists of a diamond cantilever whose mechanical motion couples to the spin degree of freedom of embedded NV centers through crystal strain. This thesis starts with a characterization of the coupling strength between NV spin and resonator motion. Static cantilever bending experiments reveal spin-strain coupling constants of several GHz per unit of strain, corresponding to a single phonon coupling strength $g_0 \approx$\,Hz. Although we demonstrate that our hybrid system resides deep in the resolved sideband regime, our current experimental conditions prevent bringing the diamond resonator to its motional ground state, since spin decoherence rate and mechanical heating rate exceed $g_0$ by several orders of magnitude. However, cooling the resonator, even to its motional ground state, is possible if cantilever dimensions are reduced to the nanometer scale and corresponding experiments are performed at cryogenic temperatures. While spin-strain coupling is not favorable for such experiments in the quantum regime, it offers many other exciting features. In the second part of this thesis, we report on the implementation of a novel continuous decoupling scheme that protects the NV spin from environmental noise, increasing both Rabi oscillation decay time and inhomogeneous coherence time by two orders of magnitude. The remarkable coherence protection is explained by the robust, drift-free strain-coupling mechanism and the narrow linewidth of the high-quality diamond mechanical oscillators. A major finding of this thesis is the demonstration of coherent spin manipulation with transverse AC strain fields, which is presented in the third part of this thesis. We show that AC strain driving not only addresses a magnetic dipole forbidden transition, but also allows working in the strong driving regime, in which the induced spin rotation frequency exceeds the initial spin splitting. Few systems have reached this regime, despite the appeal of studying dynamics beyond the rotating wave approximation. Additionally, continuous strain driving enhances the NV’s spin coherence time by decoupling it from environmental magnetic noise. In the last part of this thesis, we combine coherent MW and strain spin driving to realize a three-level $\nabla$-system in the NV ground state by coherently addressing all three spin transitions. Our studies of the spin dynamics not only confirm the theoretical prediction that the global phase (i.e.\,the relative phase of the three driving fields) governs the occurring spin dynamics, but also that closed-contour driving shields the NV's spin from environmental noise without applying complicated decoupling schemes. The corresponding decoupling mechanism is well explained by the effect of noise on the $\nabla$-system Hamiltonian. Based on our findings, we believe our closed-contour interaction scheme will have future applications in sensing and quantum information processing, for example as a phase sensor or as a test-bed for state transfer protocols.

Scanning nanomagnetometry based on the electronic spin of the nitrogen vacancy (NV) center in diamond is an emerging sensing technology, which allows for the probing of magnetic fields on the nanoscale. High sensitivity, of a few tens of nT$/\sqrt{\rm{Hz}}$, can be achieved by exploiting the extraordinary properties of this special lattice defect. Incorporating this atomic sized sensor in the apex of all-diamond scanning probes allows controlled proximity of the NV center and a sample to be achieved. The resulting resolution of a few tens of nm in combination with an NV's sensitivity offers unique possibilities for exploring new physical properties or phenomena. In this thesis, we developed and characterized a high performance scanning NV magnetometer and we demonstrate its potential for probing magnetic fields in two applications. We implemented a procedure to fabricate single-crystal, all-diamond scanning probes and developed a highly efficient and robust approach for integrating these devices into our setup. The resulting sensitivities of $\eta_{\rm{DC}}\sim750\,$nT$/\sqrt{\rm{Hz}}$ for DC and $\eta_{\rm{AC}}\sim114\,$nT$/\sqrt{\rm{Hz}}$ for AC-magnetic fields and resolution of $50\pm32\,$nm enabled real space imaging of the stray field of an antiferromagnet and the imaging of microwave magnetic fields with unprecedented spatial resolution. Both applications illustrate the potential of this powerful technique for imaging weak magnetic fields and revealing physical properties that are inaccessible with alternative approaches. Scanning NV magnetometry therefore forms an attractive, new technique, which will have a profound impact on many different research areas ranging from magnetism and advanced material sciences to spintronics and quantum computing.