Laser manipulation of donor-bound electrons in ultra-pure 28Si:P

Harnessing the quantum nature of donor atoms in silicon may pave the way for a quantum revolution in the modern digital information era. The idea to combine the exceptional spin coherence properties of donor electron spins in silicon with the prospect of exploiting technology prevalent in the semiconductor industry is very appealing. This thesis provides a quantitative limit for the spin coherence times of phosphorus donor-bound electrons in silicon, which is a fundamental parameter for spin-based quantum computation. To this end, the spin-lattice relaxation time in 28Si:P is measured with the highest degree of precision to date for unprecedentedly low temperatures. The measurements yield extremely long spin-lattice relaxation times exceeding twenty hours, which is orders of magnitude larger than originally determined. These long spin-relaxation times confirm the latent potential for devices based on spin manipulation donor electrons in silicon. For very low temperatures and high magnetic fields, the impact of the bosonic phonon distribution on the spin-relaxation time is observed for the very first time and with high accuracy which was predicted by theory more than 60 years ago. Furthermore, a new method of measuring the bandgap using donor electrons based on optical spectroscopy of the D0X transition is presented. This new method can be used to locally detect the lattice temperature via the Si bandgap with exceptional accuracy and excellent temporal resolution. With the help of this method, measurements of the bandgap temperature dependence are performed with 7e-10 relative precision. Although the precise measurements verify the theoretical T^4 limit of the bandgap energy shift with high certainty, a discrepancy of the absolute shift questions the existing theory of electron-phonon coupling in semi- conductors in the low temperature limit. Additional time-resolved experiments facilitate the use of this new method as a precise local thermometer to be used in 28Si:P based device

Interferometric experiments towards advanced gravitational wave detectors

In 1905, Einstein postulated that the speed of light is not only finite, but that its speed in vacuum is a universal limit that no process can exceed. The Theory of General Relativity later extended this concept to include gravitational interactions, and Eddington's timely measurements of stellar positions during a solar eclipse in 1919 confirmed that gravity's effect on spacetime is both real and entirely physical -- not merely a mathematical curiosity. With the death of Newton's notions of universal time and instantaneous gravity came the idea of gravitational waves as distortions in space-time that propagate the gravitational interaction at the speed of light. These gravitational waves are emitted from any object undergoing a non-axi-symmetric acceleration of mass, but -- due to the exceptionally weak coupling between gravitational waves and matter -- are expected to induce displacements of the order of 10^-18 m in kilometre-scale detectors: the extraordinary diminutiveness of this effect has thus far precluded any direct detection of the phenomenon. Numerous gravitational wave detectors have been built since the 1960s, in the form of both interferometric detectors and resonant mass devices. Interferometric detectors currently represent the most promising form of detector, due to their relatively wide-band response to gravitational wave signals and promising levels of sensitivity. In recent years a worldwide network of these interferometric detectors (LIGO, GEO600, Virgo and TAMA300) have begun to approach (or indeed reach) their design sensitivities. Although these detectors have started to provide upper limit results for gravitational wave emission that are of astrophysical significance, there have as yet been no direct detections. As such, work is underway to upgrade and improve these detectors. However, increasing the signal sensitivity necessarily leads to an increase in their sensitivity to their limiting noise sources. Two critical noise limits that must be characterised, understood, and hopefully reduced for the benefit of future detectors, are thermal noise (from mirror substrates, reflective coatings and suspension systems) and photon noise -- associated with the intrinsic shot noise of light and the noise due to light's radiation pressure. Two interferometric experiments designed to help inform on these phenomena were constructed at the University of Glasgow's Institute for Gravitational Research. The first experiment compared the relative displacement noise spectra of two specially constructed optical cavities, to extract the thermal noise spectrum of a single test mirror. In future experiments, this optic could be changed and the thermal noise spectrum for any suitable combination of mirror substrate and reflective coating evaluated. The second experiment involved the investigation of suitable control schemes for a three-mirror coupled optical cavity. As the resonant light power in interferometers increases in future devices (in order to decrease the photon shot noise) the need to de-couple the control schemes that govern the respective cavities so that they can be controlled independently, becomes more important. As a three-mirror cavity effectively represents a simple coupled system, it provides a suitable test-bed for characterising suitable control schemes for more advanced interferometers. Together, these experiments may provide information useful to the design of future gravitational wave interferometers

Cryogenic silicon Fabry-Perot resonator with Al0.92Ga0.08As/GaAs mirror coatings

The sensitivity and stability of today's most precise optical interferometers, like gravitational wave detectors and ultra-stable lasers, are fundamentally limited by thermodynamically induced length fluctuations of high-reflectivity mirror coatings. Among them, Brownian thermal noise related to internal friction is the dominant contribution and can be reduced by using coating materials with lower mechanical loss. Owing to their low mechanical losses, AlGaAs/GaAs crystalline mirror coatings are expected to reduce this limit set by conventional dielectric coatings as demonstrated from a room temperature measurement. However, due to the high noise contributions from other resonator constituents in previous study, accurate characterization of the noise of crystalline coatings has yet been possible. In this work, the first detailed study on the spatial and temporal noise properties of crystalline coatings at an unprecedented level of precision is presented. This was achieved by using these novel coatings in a cryogenic silicon Fabry-Perot resonator operating at a temperature of 124 K and at a wavelength of 1.5 µm. To observe the expected low fractional frequency instability of mod σ_y=1x10^-17 imposed significant challenges in suppressing technical noise contributions. With methods and experimental setups described in this work, technical noise contributions were suppressed to a level well below the predicted coating noise. Nevertheless, the measured frequency was significantly higher than the predicted thermal and the total technical noise, which indicates the existence of excess noise in crystalline coatings. To disentangle the different excess noise sources, a sophisticated interrogation scheme, which investigates spatiotemporal correlations between different cavity eigenmodes by stabilizing two independent lasers simultaneously on the resonator, was developed. With this interrogation scheme, noise mechanisms related to the large birefringence mode splitting in these coatings were discovered. Upon a step change of optical power, anticorrelated frequency transient responses between the two birefringence-induced polarization eigenmodes of the silicon resonator were measured. The frequency noise induced by power fluctuations from this photo-birefringent effect was reduced to a neglectable level by active stabilization of optical power. However, anticorrelated spontaneous frequency fluctuations between the two polarization eigenmodes were still observed, indicating intrinsic birefringence fluctuations. To cancel this dominant excess noise - birefringent noise - in the crystalline coating, a dual-frequency locking technique was developed to stabilize the laser to the average of both polarization eigenmodes. With this technique, the expected low Brownian thermal noise was verified, but at the same time, this revealed another novel global excess noise with a correlation length larger than the mode diameter of 1 mm. This excess noise currently limits the frequency stability of the new cryogenic silicon resonator at a level comparable to dielectric coatings. Due to its large correlation length, increasing the beam size will only marginally reduce the noise level. In future ultra-sensitive interferometers using similar coatings based on semiconductor materials, these novel noise contributions discovered in this thesis must be carefully considered

Experimental investigations into diffractive optics and optomechanical systems for future gravitational wave detectors

In 1916 Einstein published his General Theory of Relativity, from which the existence of gravitational waves was predicted. Gravitational waves are considered to be ripples or fluctuations in the curvature of space-time, propagating isotropically from their source at the speed of light. However, due to the weak nature of gravity, observing this phenomenon presents a great challenge to the scientific community. Small deviations in the apparent positions of stellar objects were measured by Eddington during a solar eclipse in 1919, which confirmed the curvature of space-time and its effect on light, and there have since been many astronomical observations of gravitational lenses. In 1993 Hulse and Taylor were awarded the Nobel Prize in Physics for their observations of a pulsar in a binary system, providing strong evidence for energy loss by emission of gravitational waves. However, the quest for a direct detection of gravitational waves is ongoing through the development of ever more sensitive technology. The development of laser interferometry, based on Michelson topologies, pro- vides the most encouraging route to observing gravitational radiation. There is currently a global network of first generation interferometric gravitational wave detectors in operation, including GEO600 (UK/Germany), Virgo (Italy/France) and TAMA (Japan) as well as several second generation detectors under construction such as Advanced LIGO (USA) and LIGO-Australia (Australia). In the coming years GEO600 will also undergo a series of small sequential upgrades to GEO-HF, while Virgo aims to become an order of magnitude more sensitive across the entire frequency band, as Advanced Virgo. The Institute for Gravitational Research (IGR) at the University of Glasgow has for many years been in strong collaboration with the Albert Einstein Institute in Hanover and Golm, the University of Hanover, the University of Cardiff and the University of Birmingham. The Glasgow group have been involved with developments on GEO600 since its initial construction in 1995, from which a lot of technology has been subsequently adopted for use in other large baseline detectors. There is a 10m prototype interferometer housed in the JIF laboratory at Glasgow, which is utilised for testing new technology and optical configurations of interest to this and the wider collaboration. The research contained in this thesis has been carried out on the Glasgow prototype to investigate novel technology of potential importance to future generations of gravitational wave detectors. In Chapter 1 the history of gravitational radiation is discussed, along with a summary of Einstein’s General Theory of Relativity to reveal the nature of gravitational radiation production. From this analysis several potential sources of astronomical origin are detailed for which the design of ground based detectors are optimised. Various interferometric solutions for detecting gravitational waves are described in Chapter 2, beginning with the most fundamental Michelson topology and thereupon key enhancements, such as Fabry-Perot cavities, power recycling and signal recycling are outlined. The Pound-Drever-Hall scheme used to sense and control the relative distances between each optical component is detailed, including modifications to this technique for controlling significantly more complex systems with many optical elements. The most important attribute in the overall design of an interferometric gravitational wave detector is the total noise limit to the sensitivity, which is comprised of both technical noise and fundamental noise. A summary is provided of the seismic, thermal, and laser noise contributing to technical noise as well as the fundamental quantum noise, consisting of photon shot noise and radiation pressure noise. From this discussion, the author introduces the current global network, and proposed future generations of ground-based detectors intended to open a new field of gravitational wave astronomy. In all proposed upgrades and future detectors the input power must be increased to improve detector sensitivity. Two experiments were designed, con- structed and completed at the Glasgow prototype interferometer related to separate issues of concern for high power regimes. In the first experiment, one of the arms of the Glasgow prototype was commissioned as an all-reflective optical cavity, whereby the partially transmissive input mirror was replaced with a three-port diffraction grating mounted on the bottom stage of a triple pendulum. This investigation was designed to characterise the performance of the grating compared to the conventional input mirror of a Fabry-Perot cavity, whilst revealing issues related to the dynamics of suspended grating input couplers on the control signals. The realisation of grating devices for use in interferometric systems would open a pathway to mitigating the otherwise limiting thermal noise associated to the mirror coatings. The other arm of the Glasgow prototype was chosen to investigate the modified dynamic behaviour of suspended cavity mirrors when signifiant radiation pressure forces are incident. The experiment involved replacing one of the suspended cavity mirrors with a light-weight counterpart designed specifically to increase the overall sensitivity to radiation pressure. By probing the system response for different cavity detunings, it was possible to observe and char- acterise the opto-mechanical resonance, commonly termed an optical spring, which induces optical rigidity at lower frequencies and enhanced sensitivity around the resonant feature. Although optical rigidity suppresses the system response, which is otherwise undesired within gravitational wave detectors, it does however enable systems, which under the right conditions can be self-locking, i.e. the mirror control turned off. Furthermore, the enhanced detector sensitivity at the optical spring frequency can be optimised for different frequencies of interest, and could potentially be used to beat the limit imposed by the Heisenberg Uncertainty Principle for independent cavity mirrors. Together, these experiments may provide information useful to the design of future interferometric gravitational wave detectors

A Solid-State Phase Camera for Advanced Gravitational Wave Detectors

I present a novel way of wavefront sensing using a commercially available, continuouswavetime-of- ight camera with QVGA-resolution. This CMOS phase camera is capable of sensing externally modulated light sources with frequencies up to 100 MHz. The high-spatial-resolution of the sensor, combined with our integrated control electronics, allows the camera to image power modulation index as low as -62 dBc/second/pixel. The phase camera is applicable to problems where alignment and mode-mismatch sensing is needed and suited for diagnostic and control applications in gravitationalwave detectors. Specically, I explore the use of the phase camera in sensing the beat signals due to thermal distortions from point-like heat absorbers on the test masses in the Advanced LIGO detectors. The camera is capable of sensing optical path distortions greater than about two nanometers in the Advanced LIGO input mirrors, limited by the phase resolution. In homodyne readout, the performance can reach up to 0.1 nm, limited by the modulation amplitude sensitivity

Locking the Advanced LIGO Gravitational Wave Detector: with a focus on the Arm Length Stabilization Technique

The Advanced LIGO gravitational wave detectors have recently achieved a new milestone. The two detector network is now operational and is being tuned for sensitivity. Currently, the state of the art detectors are the most sensitive ground-based interferometers to date and are closer than ever to the reality of a gravitational wave detection. For many years, there has been a worldwide effort to directly detect gravitational waves, a phenomena that was predicted in Einstein's theory of general relativity. A direct detection would further validate Einstein's theory, but more importantly would provide a novel approach to studying the universe and the elusive physics of gravity beyond Einstein's theory. However, none of this would be possible without the success of the arm length stabilization scheme. This recently demonstrated technique, which will be the focus of this thesis, is a critical step required to get the LIGO interferometers operational. This scheme is unique to the advanced generations of detectors and is extremely valuable for such a complex instrument. As part of my research, I characterized, modeled, and helped design this important technique. I was also a part of a small team that brought the LIGO Hanford interferometer to its operational point for the first time. For astrophysical reasons, the goal of Advanced LIGO's design is to measure a gravitational strain as small as 4x10⁻²⁴/rtHz, requiring a length resolution of approximately 10⁻¹⁹ m. This high sensitivity demands multiple optical cavities to enhance the response of the interferometer. The interferometer is a Michelson interferometer geometry consisting of two 4km arm cavities, whose differential length is measured by the phase change of a resonating infrared laser at the gravitational wave readout port. The Michelson interferometer is enhanced by Fabry-Perot arm cavities, a power recycling cavity, and a signal extraction cavity. The Fabry-Perot arm cavities effectively increase the arm lengths by two orders of magnitude. Meanwhile, the power recycling cavity is used to enhance the circulating power within the interferometer, and the signal extraction cavity is used to enhance the optical response at the gravitational-wave readout. Besides the increased design sensitivity of Advanced LIGO, a crucial requirement for a gravitational wave detection will be a high duty cycle. As an example, a worldwide Advanced LIGO network of five detectors, each with an 80% up-time, would only produce about 30% network up-time. A deterministic, robust, and fast sequence to transition the interferometer from an uncontrolled to a controlled state is mandatory. Advanced LIGO has five longitudinal degrees of freedom which must be controlled in order for the interferometer to be operational. However, all degrees of freedom are strongly coupled making this a traditionally challenging process. The state of the arm cavities can completely alter the state of the dual-recycled Michelson interferometer. Active feedback control is required to operate these instruments and keep the cavities locked on resonance. The optical response is highly non-linear until a good operating point is reached. The linear operating range is between 0.01% and 1% of a fringe for each degree of freedom. The resonance lock has to be achieved in all five degrees of freedom simultaneously, making the acquisition difficult. Furthermore, the cavity linewidth seen by the laser is only ~1Hz which is four orders of magnitude smaller than the linewdith of the free running laser. To mitigate several of these critical problems, a new arm length stabilization technique was introduced to the lock sequence. The arm length stabilization technique utilizes two additional green lasers that are brought into resonance in each arm cavity. This effectively decouples the arm cavities from the rest of the interferometer. While the main infrared beam is kept off resonance from the arm cavity, a modulation technique utilizing third harmonics locks the central dual-recycled Michelson interferometer. In the final step, both arm cavities are slowly tuned onto resonance, nominal sensors are used, and full lock is achieved. To ensure a high duty cycle for Advanced LIGO and confirm repeatability of the locking sequence, a detailed study and characterization of the arm length stabilization technique was conducted. A model of the scheme and a noise budget was developed. The model was beneficial while designing and implementing the scheme for the first time at the Advanced LIGO observatories. Meanwhile, the noise budget was critical to determine if this scheme would be viable in the lock process. Ultimately, the advent of the arm length stabilization to the lock process has been successful, a decisive milestone for future prospect of collecting meaningful astrophysical data. The technique has been implemented at both detectors and proven reliable and robust. Given the complexity of the interferometers, the success of this scheme to bring the detectors operational was a large accomplishment for the collaboration. With the technique's repeatable performance, efforts can be focused on tuning the interferometers sensitivity and achieving a first direct detection. This thesis begins with an introduction on the theory of general relativity and gravitational waves. Common astrophysical sources are described in Chapter 2. Chapter 3 begins with a description of the installed instrument. A discussion on the detector design sensitivity, limiting noise sources, and estimated detection rates is also given. At the end of Chapter 3, the complications of lock acquisition are highlighted. The arm length stabilization system was introduced to Advanced LIGO as a partial way to solve the difficulties of locking. Chapter 4 discusses the motivation for the use of this scheme and explains the methodology. A detailed discussion on the arm length stabilization model is given, along with the noise budget in Chapters 5 and 6 respectively. The full lock sequence is described in Chapter 7. The thesis concludes with the current status of the interferometers

Homodyne detection for laser-interferometric gravitational wave detectors

Gravitational waves are ripples of space-time predicted by Einstein\u27s theory of General Relativity. The Laser Interferometer Gravitational-wave Observatory (LIGO), part of a global network of gravitational wave detectors, seeks to detect these waves and study their sources. The LIGO detectors were upgraded in 2008 with the dual goals of increasing the sensitivity (and likelihood of detection) and proving techniques for Advanced LIGO, a major upgrade currently underway. As part of this upgrade, the signal extraction technique was changed from a heterodyne scheme to a form of homodyne detection called DC readout. The DC readout system includes a new optical filter cavity, the output mode cleaner, which removes unwanted optical fields at the interferometer output port. This work describes the implementation and characterization of the new DC readout system and output mode cleaner, including the achieved sensitivity, noise couplings, and servo control systems

Novel cavity-enhanced techniques for metrology

Over the past a few decades, Cavity Enhanced Laser Spectroscopy (CES) has been developed and applied to a broad range of industrial and research fields. It uses the optical cavities to effectively enhance the absorption strength introduced by the presence of intra-cavity gas and provides a powerful tool for gas concentration measurement, pressure detection and other metrology measurements. In this thesis, we will explain a new cavity enhanced spectroscopy technique (named as PIMS) which by manipulating the polarisation state of light when it interacts with a resonant cavity, to probe the optical cavity impedance matching condition. The concept of this PIMS technique was introduced and discussed in multiple conferences and places. This project was initially in collaboration with an industrial partner and the focus is on the proof of concept demonstration. Thus different from purely scientific research, practical concerns, such as easy-to-use and commercial implementability, are the other factors which defined the research direction. Therefore, we aimed at an instrument which is compact in size, immune to laser intensity noise and capable of real time measurement. Incredibly, all of those requirements can be met with the PIMS techniques. More attractively, the PIMS by nature is modulation-free. Depending on the application, it is flexible and can be implemented with no optical modulator, which opens up the opportunities of absorption measurement at different wavelengths and different species. In this thesis, we will not only explain how PIMS works, but also emphasis on the effort and progress we have made throughout the PIMS development. Most of them are not limited to PIMS system, and, more importantly, can be applied to other cavity involved systems. Since gas molecule detections with low absorption strength or low concentration are always challenging, we strived to improve the sensitivity of the PIMS system by eliminating noise sources and improving the readout through post-processing. In this thesis, we explain the process of design and implement a laser frequency stabilisation system and feed-forward correction. Along with improving the readout, we propose a cavity configuration to reduce the beam-pointing error and discuss the scattering induced parasitic etalons present in our system, which is common to all free-space system. We demonstrate two different methods that address this etalon problem both actively and passively. The experimental result shows a reduction in etalon size by a factor of 600 in total, which indicates the efficiency and effectiveness of those two ideas. Combing those effort, we manage to probe the real-time absorption spectrum with the state of art Noise Equivalent Absorption of 3x10^(-13) cm-1 Hz-1/2 using a 1-meter-long equilateral triangle cavity and the cavity finesse of around 2000. This reaches the fundamental shot noise limit and indicates the capability of measuring gas molecules with extremely low concentrations, which fulfils both scientific interests and commercial requirements

Interrogation of fiber Bragg-grating resonators by polarization-spectroscopy laser-frequency locking.

We report on an optically-based technique that provides an efficient way to track static and dynamic strain by locking the frequency of a diode laser to a fiber Bragg-grating Fabry-Pérot cavity. For this purpose, a suitable optical frequency discriminator is generated exploiting the fiber natural birefringence and that resulting from the gratings inscription process. In our scheme, a polarization analyzer detects dispersive-shaped signals centered on the cavity resonances without need for additional optical elements in the resonator or any laser-modulation technique. This method prevents degradation of the resonator quality and maintains the configuration relatively simple, demonstrating static and dynamic mechanical sensing below the picostrain level

Beware of warped surfaces: near-unstable cavities for future gravitational wave detectors

The present thesis focuses on the behaviour of a particular type of Near-Unstable Cavities (NUCs), and their application to the sensitivity enhancement of current and future gravitational wave detectors. Advanced detectors use high power laser beams. A small fraction of the light energy is absorbed by the cavity mirrors and converted into heat. The operation of near-unstable cavities requires high-precision thermal control of the cavity mirrors, and thus a thermal model of the cavity mirror and its surroundings was built and is presented in this thesis. The model aids the development of mitigation strategies of thermal effects on detector sensitivity. Nearunstable cavities have been proposed as an enabling technology for future gravitational wave detectors, as their compact structure and large beam spot can reduce the thermal noise floor of the interferometer. Throughout my Ph.D., I designed and built an experiment to investigate the technical hurdles associated with near-unstable cavities. A near-unstable table-top cavity was built and accurate control achieved through length and alignment control systems. This experiment provides an insight into how far cavity parameters can be pushed towards geometrical instability. The work I carried out will aid the design of future ground-based gravitational wave detectors