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T. van der Sar
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Topology in engineered quantum systems
Device design and artificial material implementation
Topological quantum matter offers robust, protected quantum states that could benefit quantum technologies. However, most work has focused on idealized systems rather than controllable platforms suitable for quantum information applications. This thesis investigates how topological features can be engineered in artificial quantum systems and what advantages they actually provide.
I study four questions through theoretical analysis and proposed experimental implementations: Can topological edge states stabilize quantum entanglement? How can topological phase transitions be controlled and measured? What are the practical limitations of topological protection in finite systems? How do topological quantum walks relate to quantum algorithms?
The results show that topological edge states do stabilize entangled Bell states against parameter fluctuations compared to trivial states. Real-time tuning of SSH arrays enables tracking of topological phase transitions and mid-gap state evolution. However, conventional topological invariants can mislead in finite systems, to which I propose a criterion bridging experimentally measurable quantities with real-space topology. Finally, discrete-time quantum walks on topological systems exhibit localization phenomena reminiscent of quantum search algorithms.
This work demonstrates that simple topological models can be implemented in realistic quantum hardware, revealing both the potential and limitations of topological protection in finite, noisy systems. The results inform future applications in quantum simulation and algorithm design while providing practical guidance for engineering topological features in quantum technologies.
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I study four questions through theoretical analysis and proposed experimental implementations: Can topological edge states stabilize quantum entanglement? How can topological phase transitions be controlled and measured? What are the practical limitations of topological protection in finite systems? How do topological quantum walks relate to quantum algorithms?
The results show that topological edge states do stabilize entangled Bell states against parameter fluctuations compared to trivial states. Real-time tuning of SSH arrays enables tracking of topological phase transitions and mid-gap state evolution. However, conventional topological invariants can mislead in finite systems, to which I propose a criterion bridging experimentally measurable quantities with real-space topology. Finally, discrete-time quantum walks on topological systems exhibit localization phenomena reminiscent of quantum search algorithms.
This work demonstrates that simple topological models can be implemented in realistic quantum hardware, revealing both the potential and limitations of topological protection in finite, noisy systems. The results inform future applications in quantum simulation and algorithm design while providing practical guidance for engineering topological features in quantum technologies.
...
Topological quantum matter offers robust, protected quantum states that could benefit quantum technologies. However, most work has focused on idealized systems rather than controllable platforms suitable for quantum information applications. This thesis investigates how topological features can be engineered in artificial quantum systems and what advantages they actually provide.
I study four questions through theoretical analysis and proposed experimental implementations: Can topological edge states stabilize quantum entanglement? How can topological phase transitions be controlled and measured? What are the practical limitations of topological protection in finite systems? How do topological quantum walks relate to quantum algorithms?
The results show that topological edge states do stabilize entangled Bell states against parameter fluctuations compared to trivial states. Real-time tuning of SSH arrays enables tracking of topological phase transitions and mid-gap state evolution. However, conventional topological invariants can mislead in finite systems, to which I propose a criterion bridging experimentally measurable quantities with real-space topology. Finally, discrete-time quantum walks on topological systems exhibit localization phenomena reminiscent of quantum search algorithms.
This work demonstrates that simple topological models can be implemented in realistic quantum hardware, revealing both the potential and limitations of topological protection in finite, noisy systems. The results inform future applications in quantum simulation and algorithm design while providing practical guidance for engineering topological features in quantum technologies.
I study four questions through theoretical analysis and proposed experimental implementations: Can topological edge states stabilize quantum entanglement? How can topological phase transitions be controlled and measured? What are the practical limitations of topological protection in finite systems? How do topological quantum walks relate to quantum algorithms?
The results show that topological edge states do stabilize entangled Bell states against parameter fluctuations compared to trivial states. Real-time tuning of SSH arrays enables tracking of topological phase transitions and mid-gap state evolution. However, conventional topological invariants can mislead in finite systems, to which I propose a criterion bridging experimentally measurable quantities with real-space topology. Finally, discrete-time quantum walks on topological systems exhibit localization phenomena reminiscent of quantum search algorithms.
This work demonstrates that simple topological models can be implemented in realistic quantum hardware, revealing both the potential and limitations of topological protection in finite, noisy systems. The results inform future applications in quantum simulation and algorithm design while providing practical guidance for engineering topological features in quantum technologies.
In modern-day research, magnetometry provides valuable information for a wide range of studies. Among all the different forms of magnetometers, the nitrogenvacancy (NV) lattice defect in diamond has emerged as a powerful magnetic field sensor thanks to the combination of sensitivity, spatial resolution and versatile capabilities. High-fidelity microwave control and optical readout of the NV spin over a wide range of conditions has enabled applications in condensed matter physics, chemistry, biology, geoscience and many more. In particular, its capability of visualizing magnetic phenomena with high spatial resolution has proven to be a powerful tool in both fundamental physics and applied sciences. Advances in NV magnetometry in the past decade have led to numerous breakthroughs, especially in revealing the nanoscale physics of condensed matter systems. However, the free-space optics generally used for optical interrogation of the NV spins are challenging to realize in cryogenic, intra-cellular, or other hard-to-reach environments. As such, realizing robust all-fiber-based NV probes with efficient optical readout could enable new measurements in low-temperature (quantum) or biological systems...
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In modern-day research, magnetometry provides valuable information for a wide range of studies. Among all the different forms of magnetometers, the nitrogenvacancy (NV) lattice defect in diamond has emerged as a powerful magnetic field sensor thanks to the combination of sensitivity, spatial resolution and versatile capabilities. High-fidelity microwave control and optical readout of the NV spin over a wide range of conditions has enabled applications in condensed matter physics, chemistry, biology, geoscience and many more. In particular, its capability of visualizing magnetic phenomena with high spatial resolution has proven to be a powerful tool in both fundamental physics and applied sciences. Advances in NV magnetometry in the past decade have led to numerous breakthroughs, especially in revealing the nanoscale physics of condensed matter systems. However, the free-space optics generally used for optical interrogation of the NV spins are challenging to realize in cryogenic, intra-cellular, or other hard-to-reach environments. As such, realizing robust all-fiber-based NV probes with efficient optical readout could enable new measurements in low-temperature (quantum) or biological systems...
In working towards a quantum internet, nodes based on nitrogen-vacancy (NV) centres in diamond have shown great potential. A key challenge in scaling these networks is the low entanglement generation rate due to low coherent photon emission (≈ 3%) and limited collection efficiency (≈ 15% using state-of-the-art solid immersion lens setups). Both can be improved by integrating NV centres in an optical cavity. In this thesis NV centres coupled to an open Fabry-Pérot microcavity are investigated. The NV centres are integrated into the cavity by bonding a μm-thin diamond sample to one of the mirrors.
The goal of this thesis is to move towards the realisation of an efficient spin photon interface of NV centres in an open microcavity. To this end, short optical pulses for eventual spinphoton entanglement creation and microwave electronics for spin control are implemented.
A cavity is formed and characterised. A finesse of 3.3×103 is found, along with a quality factor of (3.14 ± 0.03)×105 and a mode volume of 83 𝜆3. From this, a theoretical outcoupled coherent photon fraction of 14% is determined. NV centres are found in the cavity, and their coupling strength is determined using off-resonant lifetime measurements. From this, the actual outcoupled coherent photon fraction is determined to be (12 ± 1) %. Which represents a more than 25 times improvement over NV centres in solid immersion lenses.
The electron spin resonance (ESR) of an NV centre is measured and a magnetic field strength aligned with its spin axis of (36 ± 1) G is found. A lifetime measurement of an NV centre using pulsed resonant excitation is shown. The last two measurements can be extended to achieve coherent control and resonant readout of the NV spin. Paving the way towards a more efficient spin-photon interface. ...
The goal of this thesis is to move towards the realisation of an efficient spin photon interface of NV centres in an open microcavity. To this end, short optical pulses for eventual spinphoton entanglement creation and microwave electronics for spin control are implemented.
A cavity is formed and characterised. A finesse of 3.3×103 is found, along with a quality factor of (3.14 ± 0.03)×105 and a mode volume of 83 𝜆3. From this, a theoretical outcoupled coherent photon fraction of 14% is determined. NV centres are found in the cavity, and their coupling strength is determined using off-resonant lifetime measurements. From this, the actual outcoupled coherent photon fraction is determined to be (12 ± 1) %. Which represents a more than 25 times improvement over NV centres in solid immersion lenses.
The electron spin resonance (ESR) of an NV centre is measured and a magnetic field strength aligned with its spin axis of (36 ± 1) G is found. A lifetime measurement of an NV centre using pulsed resonant excitation is shown. The last two measurements can be extended to achieve coherent control and resonant readout of the NV spin. Paving the way towards a more efficient spin-photon interface. ...
In working towards a quantum internet, nodes based on nitrogen-vacancy (NV) centres in diamond have shown great potential. A key challenge in scaling these networks is the low entanglement generation rate due to low coherent photon emission (≈ 3%) and limited collection efficiency (≈ 15% using state-of-the-art solid immersion lens setups). Both can be improved by integrating NV centres in an optical cavity. In this thesis NV centres coupled to an open Fabry-Pérot microcavity are investigated. The NV centres are integrated into the cavity by bonding a μm-thin diamond sample to one of the mirrors.
The goal of this thesis is to move towards the realisation of an efficient spin photon interface of NV centres in an open microcavity. To this end, short optical pulses for eventual spinphoton entanglement creation and microwave electronics for spin control are implemented.
A cavity is formed and characterised. A finesse of 3.3×103 is found, along with a quality factor of (3.14 ± 0.03)×105 and a mode volume of 83 𝜆3. From this, a theoretical outcoupled coherent photon fraction of 14% is determined. NV centres are found in the cavity, and their coupling strength is determined using off-resonant lifetime measurements. From this, the actual outcoupled coherent photon fraction is determined to be (12 ± 1) %. Which represents a more than 25 times improvement over NV centres in solid immersion lenses.
The electron spin resonance (ESR) of an NV centre is measured and a magnetic field strength aligned with its spin axis of (36 ± 1) G is found. A lifetime measurement of an NV centre using pulsed resonant excitation is shown. The last two measurements can be extended to achieve coherent control and resonant readout of the NV spin. Paving the way towards a more efficient spin-photon interface.
The goal of this thesis is to move towards the realisation of an efficient spin photon interface of NV centres in an open microcavity. To this end, short optical pulses for eventual spinphoton entanglement creation and microwave electronics for spin control are implemented.
A cavity is formed and characterised. A finesse of 3.3×103 is found, along with a quality factor of (3.14 ± 0.03)×105 and a mode volume of 83 𝜆3. From this, a theoretical outcoupled coherent photon fraction of 14% is determined. NV centres are found in the cavity, and their coupling strength is determined using off-resonant lifetime measurements. From this, the actual outcoupled coherent photon fraction is determined to be (12 ± 1) %. Which represents a more than 25 times improvement over NV centres in solid immersion lenses.
The electron spin resonance (ESR) of an NV centre is measured and a magnetic field strength aligned with its spin axis of (36 ± 1) G is found. A lifetime measurement of an NV centre using pulsed resonant excitation is shown. The last two measurements can be extended to achieve coherent control and resonant readout of the NV spin. Paving the way towards a more efficient spin-photon interface.
Superconductors expel magnetic fields, a phenomenon known as the Meissner effect. This effect makes it notoriously difficult to predict the magnetic field around a superconductor. One successful way of calculating these fields is through conformal mappings; coordinate transformations that preserve Maxwell's equations of magnetic fields in free space. These were first described by Norris and later improved by Brandt. In this bachelor thesis, conformal mappings are introduced and applied to 8 situations of magnetic field screening of an increasingly complex nature. We look at the screening of applied magnetic fields and of magnetic fields due to a bias current running through a wire itself. We later compare these results with experimental observations of the Van der Sar lab in Delft and measurements from other papers.
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Superconductors expel magnetic fields, a phenomenon known as the Meissner effect. This effect makes it notoriously difficult to predict the magnetic field around a superconductor. One successful way of calculating these fields is through conformal mappings; coordinate transformations that preserve Maxwell's equations of magnetic fields in free space. These were first described by Norris and later improved by Brandt. In this bachelor thesis, conformal mappings are introduced and applied to 8 situations of magnetic field screening of an increasingly complex nature. We look at the screening of applied magnetic fields and of magnetic fields due to a bias current running through a wire itself. We later compare these results with experimental observations of the Van der Sar lab in Delft and measurements from other papers.
Spin-waves, the propagation of circular preccession of spins, have been offered as a way to replace electric currents as information carriers. The overwhelming advantage being the lack of moving charges and Ohmic losses. In this context, the search for an efficient method of detection of becomes crucial. Nitrogen vacancy centers in diamond offer a highly sensitive and effective solution. These diamond lattice defects have quan- tum and optical features allowing them to be used to quantify the surrounding magnetic field. This project is composed of a theoretical study of spin waves followed by an experimental section where AC magnetometry is tried out as a detection method. First the computations for the dispersion relation of spin waves in a ferro- magnetic material where done. A simplified version assuming homogeneity in one direction is presented and then an expansion considering a wave mode of the first order in the previously constant direction is attempted. An analysis on the efficiency of spin wave generation outlines the conditions on the wavelength and the po- larisation needed to correctly drive spin waves while being able to measure them using NV centers. Then the experimental setup and steps of AC magnetometry are layed out. The results of a measurement are shown and are in alignment with the theoretical predictions, proving this to be a valid method.
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Spin-waves, the propagation of circular preccession of spins, have been offered as a way to replace electric currents as information carriers. The overwhelming advantage being the lack of moving charges and Ohmic losses. In this context, the search for an efficient method of detection of becomes crucial. Nitrogen vacancy centers in diamond offer a highly sensitive and effective solution. These diamond lattice defects have quan- tum and optical features allowing them to be used to quantify the surrounding magnetic field. This project is composed of a theoretical study of spin waves followed by an experimental section where AC magnetometry is tried out as a detection method. First the computations for the dispersion relation of spin waves in a ferro- magnetic material where done. A simplified version assuming homogeneity in one direction is presented and then an expansion considering a wave mode of the first order in the previously constant direction is attempted. An analysis on the efficiency of spin wave generation outlines the conditions on the wavelength and the po- larisation needed to correctly drive spin waves while being able to measure them using NV centers. Then the experimental setup and steps of AC magnetometry are layed out. The results of a measurement are shown and are in alignment with the theoretical predictions, proving this to be a valid method.
Spin waves are the elementary excitations of magnetic materials. They are interesting because of their rich physics and potential role in low-dissipation information technology. To better understand spin-wave transport and explore new ways to control it, this thesis focuses on developing magnetic-imaging techniques based on the single spin of the nitrogen-vacancy (NV) defect in diamond that detects spin waves via their magnetic stray fields. These fields decay evanescently on the scale of the spin wavelength. By using NV centres embedded in an atomic force microscope probe that provides nanometre NV-sample proximity, we achieve sensitivity to nanoscale spin waves.
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Spin waves are the elementary excitations of magnetic materials. They are interesting because of their rich physics and potential role in low-dissipation information technology. To better understand spin-wave transport and explore new ways to control it, this thesis focuses on developing magnetic-imaging techniques based on the single spin of the nitrogen-vacancy (NV) defect in diamond that detects spin waves via their magnetic stray fields. These fields decay evanescently on the scale of the spin wavelength. By using NV centres embedded in an atomic force microscope probe that provides nanometre NV-sample proximity, we achieve sensitivity to nanoscale spin waves.
Magnons are quanta of spin waves, i.e. modes of collectively precessing spins. Thermally excited magnons in thin magnetic films generate stray fields at the film surface which can be detected using nitrogen-vacancy (NV) centers. NVs are lattice defects in diamond and are able to couple with magnon stray fields. Assuming a thermal occupancy of magnon modes, we study the magnetization dynamics of magnons propagating through thin magnetic insulators using the Landau-Lifshitz-Gilbert equation. We implement a numerical model to predict and understand the response of the NV center to proximal magnons in thin films. We investigate how the NV relaxation rate changes for different NV orientations by extending and generalizing the existing theory on chiral magnetic noise, and simulate an experimental setup for an NV placed just above the surface of a thin magnetic insulator. The simulation includes a static bias field in an arbitrary orientation with respect to the quantization axis of the NV center using the diamond's tetrahedral symmetry. This extended model is in demand due to limitations in present-day measurement techniques to align the bias field with an NV center. We use it to detect magnons that contribute to the relaxation rate of the NV, and determine an NV-to-film distance of 0.28(3) μm, from measured relaxation rates of an NV center placed above an yttrium-iron-garnet film with a thickness of 235(10) nm. Our model is available as an open-source Python module.
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Magnons are quanta of spin waves, i.e. modes of collectively precessing spins. Thermally excited magnons in thin magnetic films generate stray fields at the film surface which can be detected using nitrogen-vacancy (NV) centers. NVs are lattice defects in diamond and are able to couple with magnon stray fields. Assuming a thermal occupancy of magnon modes, we study the magnetization dynamics of magnons propagating through thin magnetic insulators using the Landau-Lifshitz-Gilbert equation. We implement a numerical model to predict and understand the response of the NV center to proximal magnons in thin films. We investigate how the NV relaxation rate changes for different NV orientations by extending and generalizing the existing theory on chiral magnetic noise, and simulate an experimental setup for an NV placed just above the surface of a thin magnetic insulator. The simulation includes a static bias field in an arbitrary orientation with respect to the quantization axis of the NV center using the diamond's tetrahedral symmetry. This extended model is in demand due to limitations in present-day measurement techniques to align the bias field with an NV center. We use it to detect magnons that contribute to the relaxation rate of the NV, and determine an NV-to-film distance of 0.28(3) μm, from measured relaxation rates of an NV center placed above an yttrium-iron-garnet film with a thickness of 235(10) nm. Our model is available as an open-source Python module.