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  • self-oscillation... coupled oscillators
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  • The quantum statistics of a laser result in noise when measurements of the beam are made. This noise sets a classical limit beyond which a laser cannot be used with increasing sensitivity. This quantum noise limit is imposed on many of the uses of lasers currently, especially in power limited devices such as optical communications. The statistics of the laser photon field can be modified to produce a non-classical state resulting in lower noise than the quantum noise limit when detected appropriately. This state, called a squeezed state, has been measured previously from a cavity enhanced optical parametric oscillator (OPO) only at frequency sidebands within the linewidth of the cavity. ¶ This thesis reports measurements of squeezing at microwave frequency sidebands on an optical beam produced by an optical parametric oscillator. This is the first reported measurement of squeezing at frequency sidebands at higher longitudinal modes of the cavity from an OPO. Noise reduction below the quantum noise limit is measured at sideband frequencies of 5 MHz, 1.7 GHz, 3.4 GHz and 5.1 GHz, corresponding to the zeroth, first, second and third longitudinal modes from the squeezed beam. These results are the highest frequency sideband measurements of squeezing to date. In addition to measuring squeezing at different longitudinal modes for the fundamental Gaussian spatial mode, non-classical noise reduction is measured at the same frequencies for a squeezed higher order spatial mode, TEM10. ¶ A single mode theoretical model of the OPO is presented, based on the work of ref. [1]. Computer simulations of the squeezing predicted by this model are developed and compared to the experimental results, showing excellent agreement between the different longitudinal modes for each of the two spatial modes measured.
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  • Devices that harness the surprising properties of quantum systems at scale hold the possibility of revolutionary advances in information technology. Algorithms for quantum computers can take advantage of quantum parallelism to solve problems that are intractable with classical hardware, including prime factorization and simulating chemical processes. A quantum communication network that carries qubits instead of bits can leverage the irreversibility of projective measurement to guarantee secure communication. Because quantum states are fragile, building such devices requires exquisite control over many isolated quantum systems. One of the most critical capabilities is the interaction of stationary and flying qubits. In this thesis we consider how to engineer atom-light interactions as an interface for networked quantum systems. Quantum atom-light couplers require the efficient and reversible interaction of atomic and optical qubits, but the natural interaction of atoms and photons is weak. It is this very lack of interaction between light and its environment that makes light such an excellent carrier of quantum information. There are three promising strategies for stronger coherent atom-light interactions. First, the light field may be confined to a cavity so that it interacts with the atom over a longer time. Second, the light field may be focussed to a small spot with high aperture optics and matched to the natural atomic radiation pattern. Third, we may pass the light field through an ensemble of many atoms and store the qubit in a distributed state. In practice, atom-light couplers employ some combination of all three strategies. We will focus our research on the second two approaches: first by coupling one and two trapped ions with high aperture optics, and then operating a quantum optical memory with an ensemble of approximately 10 billion neutral atoms. Atoms that have been ionized and trapped in a common electromagnetic potential are an advanced few-qubit computation platform. Qubit states are associated with an electronic excitation at each atom, controlled coherently with lasers, and made to interact in two (or many) qubit gates by mutual Coulomb repulsion. One path to quantum advantage with ion-trap quantum processors is to scale small qubit registers by distributing entanglement with photonic interconnects. We consider the feasible efficiency of free-space atom-light couplers for atomic dipole transitions, and derive the atomic image by common free-space couplers. We couple a trapped-ion register with high-aperture lenses and operate a single trapped ion as a photon source. We model the dynamic character of the source and show spin-orbit coupling in the single-photon spatial mode. Although the total collection efficiency is only approximately 0.01, the source has exceptional photon-number purity A = (1.9 +/- 0:2) * 10^-3 such that the higher-order quantum nature of the field persists even after most of the field has been discarded. We derive an efficient quantum non-Gaussian witness and surpass it, the first such demonstration for a trapped-atom single-photon source. We entangle two trapped atoms by single-photon detection, and observe an interference pattern in the spatial mode of the bipartite state. Constructive interference between the entangled components enhances the emission probability by up to 29%, an example of collective enhancement by a two-atom ensemble. The efficiency of free-space atom-light couplers is limited by our capability to engineer high-precision, high-aperture optics. We fabricate ultra-precise hemispheric mirrors with numerical aperture 0.996 by single point diamond turning. The mirrors are amongst the smoothest hemispheric surfaces ever manufactured with root-mean-square (RMS) errors consistently below 25 nm. The smoothest of our mirrors has a RMS error of 14 nm and peak-to-valley error of 88 nm. A mirror with this surface is capable of suppressing or enhancing the spontaneous emission of an atom into free space by 96% in a proposed quantum electrodynamics experiment. We show how these mirrors, with a simple modification, can shape the spatial mode of a trapped atom by similar vacuum-mode engineering. We derive a near-hemispheric mirror coupling scheme that should be 72% efficient with mirrors as precise as ours. We design an ion trap for use with such high-aperture optics. With careful conditioning and control, ensembles of many atoms can be made to store and release photonic qubits on demand. Such optical quantum memories leverage the collective interaction of a light field with many billions of atoms to achieve storage and recall efficiencies approaching unity. We show how stationary light fields for photonic phase gates can be generated in optically deep ensembles, an effect which has since been observed. We implement the gradient echo memory (GEM) scheme in an ultra-high optical depth cold-atom ensemble. The performance of a practical quantum memory is contingent on the chosen qubit encoding. We extend the GEM protocol to allow the simultaneous storage of frequency separated signals and demonstrate that this `dual-rail' memory is suitable for high-fidelity frequency qubits. Dual-rail signals are recalled with 35% efficiency, 82% interference fringe visibility and 6 degrees of phase stability. We describe how the fidelity of the scheme is limited by frequency-dependent polarization rotation and how this may be addressed in an improved configuration. Finally, we demonstrate single-rail storage by GEM with 87% efficiency and 1 ms memory lifetime. Our memory surpasses the no-cloning limit for up to 600 us of storage, out-performing an optical fibre delay line by a factor of six. This is the first quantum memory to beat this important benchmark.
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  • A rich low-frequency wave phenomenology has been observed in plasmas generated on the H-1 heliac. A significant proportion of these fluctuations show Alfvenic characteristics. The strongly shaped magnetic geometry of H-1 presents a major obstacle to theoretical modelling of macroscopic wave physics, even under the simplifying assumptions of ideal MHD. An additional obstacle has been the dearth of literature on low-frequency Alfvenic oscillations in fusion plasmas in general, and stellarator plasmas in particular, until quite recently. A recent surge of interest in the low-frequency Alfvenic oscillations as well as the low equilibrium uncertainty of H-1 makes a physical theory of the dominant H-1 oscillations desirable. Apart from intrinsic scientific interest, the underlying driver of Alfven wave activity studies in the broader context of the physics of magnetically confined plasmas is the potential role such wave activity may have in achieving good plasma confinement. Interactions of Alfven waves with energetic particles can lead to reduced energetic ion confinement with consequent heating losses and vessel damage. MHD spectroscopy offers the prospect of using wave behaviour as a proxy for determining underlying plasma parameters and conversely, there is scope for active control of plasma parameters through excitation of Alfven waves. In this thesis, the three-dimensional, compressible ideal spectrum for H-1 is presented, based on numerical simulations with the CAS3D three-dimensional ideal MHD linear eigenmode solver. A significant mirror term in combination with a variety of strong field-strength modulations within a cross-section induces coupling of eigenmode Fourier harmonics in both toroidal and poloidal directions. It is shown that the conditions for convergence of the code in Fourier space are quite stringent for H-1 configurations, in the sense that shear Alfven frequencies dip sharply near the core unless the component of fluid motion along the field lines has a Fourier basis including at least two toroidal sidebands, even for high frequency modes with negligible acoustic interaction. The first two HAE gaps and the TAE gap are identified. A significant beta-induced gap is found, bounded above by the geodesic acoustic frequency, which is found to lie at around 30-40 kHz. Consequently, H-l fluctuations, which typically lie below 40 kHz, can be considered sub-GAM modes. Based on analytic estimates, it is proposed that H-1 fluctuations may include sub-GAM beta-induced Alfvenic eigenmodes reproducing a characteristic "whale tail" sloping in configuration space due to temperature gradients. Low frequency CAS3D spectra and quasi-discrete modes are presented. To provide context for the new results presented, a from-first-principles review of the ideal theory relevant to H-1 plasmas is given starting with a definition of the plasma state. A summary of the assumptions underlying ideal MHD and its reliability in a fusion plasma wave analysis context is given and linear ideal wave physics in three dimensional toroidal geometry is reviewed. Limitations of ideal-MHD in the sub-GAM frequency range are discussed.
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  • The presence and migration of fluids in Earth’s upper crust is a topic of broad interest in geophysics, with applications ranging from imaging earthquake fault zones, through hydrocarbon and geothermal reservoir exploration, to the monitoring of sequestered supercritical carbon dioxide. The mechanical response of a fluid-saturated rock to an applied oscillatory stress depends on the scale of stress-induced pore-fluid flow within solid matrix, and hence is time (or frequency) dependent. Uncertainty, therefore, arises in applying ultrasonic measurements on elastic moduli/velocities of rocks at MHz frequencies, as the most commonly used technique in laboratory, to field data mainly acquired at frequencies of tens of Hz to a few kHz. A precise interpretation of the field data requires characterization of such frequency dependence or dispersion of seismic-wave velocities related to fluid flow, over the entire range of frequencies from mHz to MHz. Broadband mechanical measurements were performed on a suite of synthetic media made either by sintering soda-lime-silica glass beads or from glass rods of similar composition with artificially controlled microstructures involving both equant pores and cracks. The goal was an improved understanding of the origin of wave-induced fluid flow and the influence of microstructure on fluid-flow related dispersion. Various fluid-flow regimes are accessed either by using pore fluids with contrasting viscosity or exciting fluid-saturated rocks at different oscillating frequencies. Synthetic samples, therefore, were measured under dry, argon- and water-saturated conditions in sequence, with a combined use of three techniques, namely, forced oscillation at mHz-Hz frequencies, resonant bar at kHz frequency, and ultrasonic wave transmission at MHz frequency, to cover a wide frequency range. Complementary measurements on permeability were also conducted on these synthetic glass samples with either argon or water. Pressure dependent crack closure has been inferred for the cracked samples from the measured pressure dependence of the elastic and hydraulic properties. The microstructure of each cracked sample has been inferred from the measured pressure-dependent modulus deficit relative to the uncracked medium through a micromechanical model. A water-saturated glass-rod specimen tested at mHz frequencies has a systematically higher shear modulus than its dry counterpart – evidence of the saturated isolated regime at seismic frequencies. Accordingly, the application of the Gassmann equation for the saturated isobaric regime, usually considered suitable for seismic frequencies, is inappropriate in this case. With argon and water saturation, a dispersion of shear modulus as high as ~ 10% has been observed over the frequency range from mHz to MHz on the cracked samples, and various fluid flow regimes have been assigned based on the change in modulus due to fluid saturation and estimated characteristic frequencies. The observed dispersion indicates that conventional ultrasonic lab measurements of wavespeeds on cracked and fluid-saturated rocks cannot be directly applied in the interpretation of field data. Water with much greater viscosity than argon lowers the frequency for the squirt-flow transition on a cracked glass-rod specimen. The fluid-saturated samples with various equant porosities respond differently to the applied stress at the same frequency, indicating the influence of microstructure on the fluid-flow related dispersion.
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  • Both space and laboratory plasmas can be associated with static magnetic field, and the field geometry varies from uniform to non-uniform. This thesis investigates the impact of magnetic geometry on wave modes in cylindrical plasmas. The cylindrical configuration is chosen so as to explore this impact in a tractable but experimentally realisable configuration. Three magnetic geometries are considered: uniform, focused and rippled. For a uniform magnetic field, wave oscillations in a plasma cylinder with axial flow and azimuthal rotation are modelled through a two-fluid flowing plasma model. The model provides a qualitatively consistent description of the plasma configuration on a Radio Frequency (RF) generated linear magnetised plasma (WOMBAT, Waves On Magnetised Beams And Turbulence [Boswell and Porteous, Appl. Phys. Lett. 50, 1130 (1987)]), and yields agreement between measured and predicted dependences of the wave oscillation frequency with axial field strength. The radial profile of the density perturbation predicted by this model is consistent with the data. Parameter scans show that the dispersion curve is sensitive to the axial field strength and the electron temperature, and the dependence of the oscillation frequency with electron temperature matches the experiment. These results consolidate earlier claims that the density and floating potential oscillations are a resistive drift mode, driven! by the density gradient. This, to our knowledge, is the first detailed physics modelling of plasma flows in the diffusion region away from the RF source. For a focused magnetic field, wave propagations in a pinched plasma (MAGPIE, MAGnetised Plasma Interaction Experiment [Blackwell et al., Plasma Sources Sci. Technol. 21, 055033 (2012)]) are modelled through an ElectroMagnetic Solver (EMS) based on Maxwell's equations and a cold plasma dielectric tensor. [Chen et. al., Phys. Plasmas 13, 123507 (2006)] The solver produces axial and radial profiles of wave magnitude and phase that are consistent with measurements, for an enhancement factor of 9.5 to the electron-ion Coulomb collision frequency and a 12% reduction in the antenna radius. It is found that helicon waves have weaker attenuation away from the antenna in a focused field compared to a uniform field. This may be consistent with observations of increased ionisation efficiency and plasma production in a non-uniform field. The relationship between plasma density, static magnetic field strength and axial wavelength agrees well with a simple theory developed previously. More! over, the wave amplitude is lowered and the power deposited into the core plasma decreases as the enhancement factor to the electron-ion Coulomb collision frequency increases, possibly due to the stronger edge heating for higher collision frequencies. For a rippled magnetic field, the spectra of radially localised helicon (RLH) waves [Breizman and Arefiev, Phys. Rev. Lett. 84, 3863 (2000)] and shear Alfvén waves (SAW) in a cold plasma cylinder are investigated. A gap-mode analysis of the RLH waves is first derived and then generalised to ion cyclotron range of frequencies for SAW. The EMS is employed to model the spectral gap and gap eigenmode. For both the RLH waves and SAW, it is demonstrated that the computed gap frequency and gap width agree well with the theoretical analysis, and a discrete eigenmode is formed inside the gap by introducing a defect to the system's periodicity. The axial wavelength of the gap eigenmode is close to twice the system's periodicity, which is consistent with Bragg's law, and the decay length agrees well with the analytical estimate. Experimental realisation of a gap eigenmode on a linear plasma device such as the LArge Plasma Device (LAPD) [Gekelman et al., Rev. Sci. Instrum. 62, 2875 (1991)] may be possible by introducing a symmetry-breaking defect to the system's periodicity. Such basic science studies could provide the possibility to accelerate the science of gap mode formation and mode drive in toroidal fusion plasmas, where gap modes are introduced by symmetry-breaking due to toroidicity, plasma ellipticity and higher order shaping effects. These studies suggest suppressing drift waves in a uniformly magnetised plasma by increasing the field strength, enhancing the efficiency of helicon wave production of plasma by using a focused magnetic field, and forming a gap eigenmode on a linear plasma device by introducing a local defect to the system's periodicity, which is useful for understanding the gap-mode formation and interaction with energetic particles in fusion plasmas.
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  • A small bench top interferometer, built to study modulation interferometry is described. A number of different interferometer configurations are trialed, all using a continuos wave, Nd:YAG laser. The ability of these configurations to operate at the shot noise limit is documented and technical noise sources that detract from this limit are investigated. The frequency and intensity noise properties of the Nd:YAG laser, used throughout this work, are documented. It is shown that the free running laser has considerable frequency noise structure from DC to approximately 100kHz. The effects of this frequency noise on interferometry are documented and means of overcoming these problems discussed. The free running laser is shown to exhibit strong intensity noise structure associated with the resonant relaxation oscillation present in the lasing crystal. The resonant relaxation oscillation is modelled by a noise-driven second order system. This description is used to design an intensity stabilisation servo to suppress the free running laser noise. The performance of the stabilisation system is documented and its ability to suppress laser intensity noise by up to 35dB across a wide bandwidth is demonstrated. A simple scalar theory, to describe modulation interferometry is developed. All necessary non-ideal parameters are included and accurate predictions of practical interferometer sensitivity are made. The theory is used to analyse the performance of all interferometers tested here. Bench top interferometer experiments are performed for direct detection, internal modulation, external modulation and power recycling interferometer configurations. The shot noise sensitivity of each configuration is measured and excellent agreement with theory is achieved. An application for the direct detection interferometer is demonstrated; noninvasive shot noise limited RF electric field measurements. Several circuit boards are mapped using this device and the results presented. Non-stationary shot noise in internal modulation interferometers is investigated. Using a large modulation depth and high fringe visibility interferometer, approximately 4.8dB of noise variation dependent on the demodulation phase is achieved. Non-stationary shot noise is shown to cause excess noise (1.7dB) in the signal quadrature, leading to shot noise limited sensitivity of √ (3/2) worse than direct detection. A complex modulation-demodulation system is then implemented using both the first and third harmonic. The addition of the third harmonic is shown to introduce correlated shot noise that can be used to reduce the excess 1.7dB nonstationary shot noise occurring in the signal quadrature.
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  • Density fluctuations in the LT-4 tokamak plasma are investigated using a Phase Scintillation Interferometer operating at 10.6/Ltm which is sensitive to density fluctuations of δnₑ/nₑ> 10⁻¹⁴. The plasma is imaged across a linear detector array which can be rotated to record projections in any direction, from toroidal to poloidal. The theory of forward scattering from plasmas is developed from the Rytov approximation and aspects of the Fourier diffraction projection theorem relevant to plasma scattering. The result is a clear conceptual picture of diffraction from arbitrary extended refractive media, from which important analytical tools are developed. The Phase Scintillation Interferometer is used to image density perturbations produced by large scale magnetohydro dynamic (MHD) modes in the plasma associated with Mimov oscillations. Structural characteristics are determined, and a comparison between experimental and computed projections of the Dubois model is made which shows that the density fluctuations are consistent with a model of rotating magnetic islands. Island widths and local magnetic field fluctuations are determined and are found to compare well with measured poloidal magnetic field fluctuations. The interferometer is used in conjunction with other diagnostics to investigate minor and major disruptions in LT-4. The time frequency distribution is introduced as an important analytical tool in the characterization of the various regimes of MHD activity. Frequency and amplitude variations of an m = 3 mode during current rise appear correlated with variations in toroidal loop voltage. The mode is also found to persist throughout the whole discharge and to play a part in mode locking which precedes major disruptions. Mode frequencies are found to vary in a regular way with the safety factor q(a). Precursor oscillations before minor and major disruptions are identified. A strong m — 1 type of internal relaxation is found to follow rapid growth and locking of an m = 2 mode during minor disruptions. The interferometer is also applied to the measurement of fine scale density fluctuations in the LT-4 tokamak during periods of low level MHD activity. Line integral measurements indicate an edge fluctuation level of about 10% and broad band spectra typical of strong turbulence. Anisotropy in the spectrum of fluctuations perpendicular to the magnetic field is observed. This observation runs counter to reported measurements of isotropic fluctuations made on other tokamaks using small angle scattering techniques. Very long correlation lengths along the field lines are observed, which are consistent with nearly all models of turbulence in tokamak plasmas. The images are numerically filtered so as to isolate and display counter-propagating structures in the turbulent flow.
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  • Thermal noise and optical quantum noise place fundamental limits on the displacement sensitivity of interferometric gravitational wave detectors. Projects such as Advanced LIGO employ a wide range of techniques to reduce thermal noise and use very high optical powers to reduce quantum noise. Thermal noise is Brownian motion caused by the thermal energy in each mode of oscillation. It is fundamentally linked with mechanical loss via the fluctuation-dissipation theorem. The thermal energy of, for example, the fundamental resonance of the suspension of a mirror can be concentrated into the resonant peak by using a very high-Q oscillator. This reduces the spectral density of the fluctuations away from resonance. The shape of the thermal noise spectrum depends on the mechanical loss mechanisms, and can have important implications for interferometer design This thesis presents, to the best of my knowledge, the first off-resonance thermal noise measurement of a high-Q suspension which includes both above-and below-resonance regions. The measurements do not conform to the accepted 'structural' damping model, but rather seem to suit a model with both structural and viscous damping. A number of potentially spurious loss mechanisms were investigated, but none were found to substantially alter the spectral shape of the measured noise. A lower quality factor suspension material was then employed to see if structural damping was dominant, but again a mixed damping model fitted the data better than structural damping. A coating-free mirror was designed and experimentally characterised. Removing the optical coating removes a significant source of mechanical loss from the mirror, potentially improving thermal noise. The combination of high optical powers and high-Q oscillators can lead to strong opto-mechanical interactions. The light inside an optical resonator can act as a complex spring, modifying both rigidity and damping. For a very low-loss mechanical system, a small amount of optical anti-damping can lead to instability. Conversely, it is possible to optically damp, or 'cool', an oscillator by extracting thermal energy. Results are presented showing optical cooling of the fundamental mode of a mirror suspension down to an effective temperature of 70 mK. This cooling is measured by the direct observation of the thermal noise spectrum. The measured traces are in agreement with a prediction of the thermal noise spectrum based on the input laser power, optical configuration, and feedback control system used. Results from the suspended gravitational wave detector prototype, the Caltech 40m interferometer, show how a strong optical spring creates an opto-mechancial resonance which alters the frequency response of the interferometer.
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  • In the last decade, the solid-state rare-earth-ion system has demonstrated increasing appeal for quantum computation. Despite this progress, two hardware limitations prevent a scalable implementation. These current limitations are the inability to miniaturise and the inability to perform single-ion qubit readout. This thesis addresses both these limitations and demonstrates that neither poses a fundamental restriction on increasing the scale of rare-earth-ion quantum computers. The challenge in miniaturising rare-earth-ion quantum hardware arises from the increases in homogeneous and inhomogeneous broadening that accompany micron-scale architectures. The success of miniaturised architectures, such as waveguides, depends on the properties of bulk ions being preserved within microns of the crystal surface. In addition, bulk ion properties must also be preserved in regions of high residual stress resultant from waveguide fabrication. The inhomogeneous and homogeneous properties of near-surface ions and ions in highly stressed environments in Pr3+:Y2SiO5 were studied via white light interferometry combined with micron resolution fluorescence microscopy. It was found that the bulk ion properties could be preserved both near the surface and in highly stressed regions close to micron-scale surface damage. The observation of excess inhomogeneous and homogeneous broadening was found to be consistent with the damage present at the crystal surface. The main outcome of the study was a set of waveguide fabrication guidelines to ensure that the appealing properties of bulk crystals can be maintained in a miniaturised architecture. The current inability to perform single-ion qubit readout is a consequence of the difficulty in isolating a single ion and lack of cyclicity in rare-earth-ion materials. Two techniques are proposed to form a solution: Stark activation and Zeeman enhanced cyclicity. When combined, these techniques offer direct readout for single-ion frequency-based quantum computing. Stark activation is designed to isolate a single rare-earth ion in a macroscopic crystal. The proposal is based on defining the condition for resonant excitation through a spatially varying electric field. A proof-of-principle experiment successfully created a 10 um absorption region within a millimetre thick crystal. In addition, the signal-to-noise ratio of the technique was characterised in experiments probing Pr3+:Y2SiO5 at the single-ion level. Future improvements to the apparatus should allow the nanometre spatial resolution and the noise level to be reduced to allow single-ion optical detection. High cyclicity is essential for high-fidelity optical readout of a single-ion qubit. Zeeman enhanced cyclicity achieves this by manipulating the hyperfine structure of the resonant crystal field levels to induce strong hyperfine selection rules. The technique is shown to be applicable to even the lowest symmetry sites. The simulated level of cyclicity in Pr3+:Y2SiO5 was greater than 99.99% by applying a 10 T field. The investigation of scalability in the rare-earth-ion system marks a movement away from the traditional ensemble-based methods in macroscopic crystals. This study required an understanding of these materials at a single-ion level and the development of high spatial resolution spectroscopic techniques. These advances extend the ability to engineer rare-earth-ion systems for applications including, but not limited to, quantum computing.
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