The work presented in this thesis revolves around quantum enhanced magnetic field sensing. The core of the study is the nitrogen-vacancy (NV) center, a point defect in the diamond lattice with atomic like properties and magnetic field susceptibility. The central task was to develop control schemes and protocols to enhance the lifetime and the coherences of the NV center with the overall goal of enhancing the capabilities of this sensor in the field of magnetometry. In order to realize complex protocols, a sophisticated software control of the measurement setup is required. A general software framework, termed Qudi, was designed and developed from scratch to improve drastically the measurement abilities and to facilitate the transfer of knowledge between the measurement protocols and the underlying physical idea. The transparent character of the core code, fully open to the scientific community, is serving as rigorous framework to reduce the complexity of the setup configuration by a fundamental separation of tasks. As a consequence, the general idea of this framework is not limited to experiments with color centers in diamond, but can find application in any laboratory environment. The measurement of magnetic fields in the high-frequency GHz regimes is challenging. In this thesis, a continuous dynamical decoupling protocol is developed and implemented, which extends the capabilities of the NV sensor to probe GHz signals with a narrow bandwidth. Moreover, the protocol protects the system from noise, attributed to the drive, and from external magnetic noise thereby prolonging the coherence time and reaching the lifetime limitation of the quantum states. We measured a coherence time of 1.43 ms at room temperature in a diamond crystal with a natural abundance of 13C atoms, resulting in a smallest detectable magnetic field strength of 4 nT at 1.6 GHz. Creating a protected qubit from a three-level system requires multiple drive fields addressing different transition frequencies. Continuous dynamical decoupling can protect the system from external magnetic noise, but typically introduces large drive noise to the system. The combination of on-resonant and off-resonant driving fields serves an approach to circumvent the challenges associated with drive noise. While on-resonant drive maintains a large energy gap in order to protect the sensor from external magnetic noise, the off-resonant drive creates AC-Stark shifted energy levels, thereby significantly reducing the amount of drive noise on the three-level system. We experimentally demonstrate an improvement in coherence time, which is only limited by the second order contributions of the magnetic field noise while suppressing entirely the drive noise contributions. Further improvement can be achieved by a mere increase of the drive field as its noise is efficiently decoupled from the sensor.
The work presented in this thesis revolves around quantum enhanced magnetic field sensing. The core of the study is the nitrogen-vacancy (NV) center, a point defect in the diamond lattice with atomic like properties and magnetic field susceptibility. The central task was to develop control schemes and protocols to enhance the lifetime and the coherences of the NV center with the overall goal of enhancing the capabilities of this sensor in the field of magnetometry. In order to realize complex protocols, a sophisticated software control of the measurement setup is required. A general software framework, termed Qudi, was designed and developed from scratch to improve drastically the measurement abilities and to facilitate the transfer of knowledge between the measurement protocols and the underlying physical idea. The transparent character of the core code, fully open to the scientific community, is serving as rigorous framework to reduce the complexity of the setup configuration by a fundamental separation of tasks. As a consequence, the general idea of this framework is not limited to experiments with color centers in diamond, but can find application in any laboratory environment. The measurement of magnetic fields in the high-frequency GHz regimes is challenging. In this thesis, a continuous dynamical decoupling protocol is developed and implemented, which extends the capabilities of the NV sensor to probe GHz signals with a narrow bandwidth. Moreover, the protocol protects the system from noise, attributed to the drive, and from external magnetic noise thereby prolonging the coherence time and reaching the lifetime limitation of the quantum states. We measured a coherence time of 1.43 ms at room temperature in a diamond crystal with a natural abundance of 13C atoms, resulting in a smallest detectable magnetic field strength of 4 nT at 1.6 GHz. Creating a protected qubit from a three-level system requires multiple drive fields addressing different transition frequencies. Continuous dynamical decoupling can protect the system from external magnetic noise, but typically introduces large drive noise to the system. The combination of on-resonant and off-resonant driving fields serves an approach to circumvent the challenges associated with drive noise. While on-resonant drive maintains a large energy gap in order to protect the sensor from external magnetic noise, the off-resonant drive creates AC-Stark shifted energy levels, thereby significantly reducing the amount of drive noise on the three-level system. We experimentally demonstrate an improvement in coherence time, which is only limited by the second order contributions of the magnetic field noise while suppressing entirely the drive noise contributions. Further improvement can be achieved by a mere increase of the drive field as its noise is efficiently decoupled from the sensor.
This thesis investigates the theoretical foundations, material properties, and experimental realization of quantum sensors based on the Nitrogen-Vacancy (NV) centers in diamond, a solid-state system that combines quantum coherence with room-temperature operability. The first chapter introduces the principles of quantum sensing, outlining the fundamental definitions, operating protocols, and physical processes underlying the quantum measurement paradigm. Emphasis is placed on the quantum sensing Hamiltonian and the distinction between various classes of quantum sensors. The second chapter focuses on diamond as a host material and on the NV center as a quantum defect. The electronic structure, optical transitions, and spin properties of the NV center are analyzed in detail. Several techniques of NV-based magnetometry are presented, including continuouswave and pulsed optically detected magnetic resonance (ODMR). The discussion also addresses coherence times (T1, T2, and T∗2 ) and methods of diamond synthesis together with NV-center generation through irradiation and annealing. Chapter three develops the physical theory describing the NV center. The Hamiltonian formalism includes spin-spin, hyperfine, and quadrupolar interactions, as well as couplings to external magnetic fields. The chapter further introduces the Bloch sphere representation, magnetic resonance phenomena, and models of lightmatter interaction, ranging from the semiclassical to the fully quantum Rabi framework. A seven-level rate-equation model is proposed to capture the spin dynamics and optical cycling processes of the NV center. The fourth chapter reports the experimental results. After describing materials and methods, several ODMR-based vector magnetometry experiments are presented, highlighting different spectral regimes and the dependence of resonance features on the external magnetic field geometry. Additional studies demonstrate temperature sensing and microwave-free magnetometry techniques for mapping magnetic field distributions. Sensitivity analysis and calibration procedures are also discussed.
In recent years, the field of quantum sensing has garnered increasing attention due to its potential to revolutionize various scientific and technological domains. Among the different quantum sensors, the nitrogen-vacancy (NV) color center in diamond stands out for its ease of use, ability to be read out and initialized with a laser, and long coherence times even at room temperature. Over the past years, numerous quantum control sequences have been developed to successfully deploy NV sensors in diverse situations, such as measuring nearby spin clusters, classical AC signals, and static magnetic fields. However, the NV center faces limitations when coupling to high frequency signals. More specifically, as the frequency of the target signal increases, stronger driving fields over NVs are needed, ultimately reaching the limits of current experimental capabilities. In this thesis, we propose several protocols to address this high-frequency problem in different scenarios.
In modern-day quantum metrology, quantum sensors are widely employed to detect weak magnetic fields or nanoscale signals. Quantum devices, exploiting quantum coherence, are inevitably connected to physical constants and can achieve accuracy, repeatability, and precision approaching fundamental limits. As a result, these sensors have shown utility in a wide range of research domains spanning both science and technology. A rapidly emerging quantum sensing platform employs atomic-scale defects in crystals. In particular, magnetometry using nitrogen-vacancy (NV) color centers in diamond has garnered increasing interest. NV systems possess a combination of remarkable properties, optical addressability, long coherence times, and biocompatibility. Sensors based on NV centers excel in spatial resolution and magnetic sensitivity. These diamond-based sensors promise comparable combination of high spatial resolution and magnetic sensitivity without cryogenic operation. The above properties of NV magnetometers promise increasingly integrated quantum measurement technology, as a result, they have been extensively developed with various protocols and find use in numerous applications spanning materials characterization, nuclear magnetic resonance (NMR), condensed matter physics, paleomagnetism, neuroscience and living systems biology, and industrial vector magnetometry. In this chapter, NV centers are explored for magnetic sensing in a number of contexts. In general, we introduce novel regimes for magnetic-field probes with NV ensembles. Specifically, NV centers are developed for sensitive magnetometers for applications where microwaves (MWs) are prohibitively invasive and operations need to be carried out under zero ambient magnetic field. The primary goal of our discussion is to improve the utility of these NV center-based magnetometers.
The recent decade has witnessed exciting developments in quantum science and technology. Quantum sensing is a rapidly growing branch, which exploits the fragility of quantum systems to detect small external signals. The extreme control at the single-atom level and the remarkably long coherence time of engineered quantum systems enable unprecedented sensitivity and precision, beating the performance of classical techniques. The nitrogen-vacancy (NV) center in diamond is one of the most promising quantum sensors. Its unique advantages have attracted considerable attention, including a long spin coherence time throughout a broad temperature range, nanoscale resolution limited by the sensor-sample distance, convenient optical control of its spin states and remarkably versatile sensing capabilities. Its properties are well studied under a bias magnetic field oriented along its quantization axis. However, its sensing capabilities in the presence of an off-axis magnetic field are much less explored. My research aims to unlock the full potential of NV quantum sensor by developing new sensing modalities under a magnetic field acting perpendicular to the NV axis, and furthermore, integrating them into a scanning probe microscope. In this dissertation, I will report our progress toward building a scanning NV multimodal quantum imaging platform, which will open up exciting opportunities in measuring nanoscale phenomena. The first chapter provides an introduction to the background of quantum sensing with NV centers, followed by a discussion on its basic properties and established sensing techniques. The second and third chapters are dedicated to two experiments performed under a perpendicular magnetic field where traditional NV magnetometry based on the Zeeman effect fails. In the second chapter, I will introduce a new sensing strategy that uses the entanglement between the electron and nuclear spins to restore the magnetic field sensitivity under this unfavored condition. This allows us to sense small changes in the magnetic field angle relative to the NV axis, and to detect anisotropic magnetic noise in the local environment. In the third chapter, I will present our latest development of scanning NV electrometry, where a single NV at the apex of a diamond scanning probe images external alternating (AC) and direct (DC) electric fields with sub-100 nm resolution. In the last chapter, I will discuss our efforts on four experiments that were left unfinished. I will present the results we have achieved, analyze the challenges that we faced and propose potential solutions to overcome them.
This dissertation investigates applications of the Nitrogen vacancy in diamond (NV). The NV is a unique quantum system allowing for optical polarization and read out even at ambient conditions. Its electron spin (S=1) has coherence times in the order of milliseconds and is therefore an ideal candidate to investigate the foundations of quantum mechanics as well as exploiting quantum effects in metrology and information processing applications. To utilize the NV for quantum technologies, first the interaction of the NV with its surroundings has to be investigated and controlled. Here dynamical decoupling sequences (CPMG) could be utilized to extend the NV coherence time to a few milliseconds by decoupling the NV from its surrounding spin bath (given by the 13C isotope, natural abundance 1.1%). But not only decoupling sequences can be used to suppress the spin bath interaction, also eigen state tailoring can suppress the bath interaction. As long as strain is the dominant interaction, the NV eigen energies are not susceptible to small magnetic field changes. Therefore the magnetic dipole interaction with the spin bath is suppressed. But the spin bath is not only a nuisance limiting NV coherence times, but also a potential resource for quantum technologies. In order to harness the individual 13C nuclear spins, their interaction with the NV and among themselves has to be investigated. To not be limited by the NV coherence times, a new spectroscopy method, only limited by the NV lifetime, was developed. This can in principle be extended to the second range by using a nuclear spin memory. First advances in quantum technology were demonstrated in the field of metrology, where the Zeeman effect of the NV center allowed for precise nanoscale measurement of magnetic fields. Here this concept was extended to us the Stark effect to detect electric fields. A sensitivity of η=142.6±3.6 V/(cmHz1/2) was demonstrated. This is equivalent to the detection of a single elemental charge at a distance of 150 nm in one second. By using two NVs with a distance of less then 20 nm, a demonstration of nanoscale single fundamental charge detection was feasible. Here one NV was used as a controllable fundamental charge while the other NV was used as sensor NV, detecting the electric field of the fundamental charge. This allowed for the detection of a single electronic charge at ambient conditions. Another keystone of quantum technology is the reliable on demand or heralded creation of entanglement. In this dissertation, the successful entanglement of two electron spins in solid state at ambient conditions is demonstrated. The fundamental interaction used to create an entangled state was dipolar coupling between the two electron spins. In order to be able to harness weaker coupling strengths, an entanglement protocol based on dynamical decoupling was developed. A fidelity of F=0.67±0.04 was demonstrated. By using the intrinsic nuclear spins of the nitrogen it was possible to store the entangled state on the millisecond time scale. However, the theoretical limit for the fidelity given by the polarization and the coherence times is F=0.849. The discrepancy can be explained by pulse errors. These can be avoided by using optimal control yielding a fidelity of F=0.824±0.015. Also optimal control allowed for nuclear spin entanglement by storing the electron spin entanglement on the nitrogen nuclear spins. These experiments are first steps towards a room temperature quantum register, where the electron spins are used as bus to transport information and the nuclear spins act as a memory.
Quantum sensing with solid-state spins has attracted considerable attention following the development of single quantum systems. In particular, sub-picotesla level magnetometry has been demonstrated using negatively-charged nitrogen-vacancy (NV) centers in diamond by increasing the number of spins simultaneously employed for sensing. However, scaling up the number of spins inevitably introduces inhomogeneities in detuning and control field amplitudes across the ensemble system, which degrades the achievable sensitivity. Although several techniques, including pulsed dynamical decoupling and shaped pulses, have been studied to overcome such noises, they are not generally compatible with GHz-range AC magnetometry based on Rabi oscillations. This dissertation presents the development of an experimental platform and the demonstration of robust GHz-range AC magnetometry using a large ensemble of NV centers under inhomogeneous fields. Particular emphasis is placed on the effects of control-field amplitude inhomogeneity. To improve the homogeneity of the control field, barrel-shaped microwave forming systems are experimentally characterized, and their performance is compared with that of planar systems. Then, to mitigate detuning noise as well as control-field amplitude noise, concatenated continuous dynamical decoupling (CCDD) is applied to the inhomogeneous ensemble system, and the resulting dynamics are investigated with several initial states prepared with composite pulses. Finally, the CCDD sequence is applied for GHz-range AC magnetometry and compared with the conventional direct Rabi method. The results demonstrate that the robust dressed states generated by CCDD extend the lower bound of measurable amplitudes in GHz-range AC magnetometry.