Tuning the resonance properties of 2D carbon nanotube networks towards a mechanical resonator

The capabilities of the mechanical resonator-based nanosensors in detecting ultra-small mass or force shifts have driven a continuing exploration of the palette of nanomaterials for such application purposes. Based on large-scale molecular dynamics simulations, we have assessed the applicability of a new class of carbon nanomaterials for nanoresonator usage, i.e. the single-wall carbon nanotube (SWNT) network. It is found that SWNT networks inherit excellent mechanical properties from the constituent SWNTs, possessing a high natural frequency. However, although a high quality factor is suggested from the simulation results, it is hard to obtain an unambiguous Q-factor due to the existence of vibration modes in addition to the dominant mode. The nonlinearities resulting from these extra vibration modes are found to exist uniformly under various testing conditions including different initial actuations and temperatures. Further testing shows that these modes can be effectively suppressed through the introduction of axial strain, leading to an extremely high quality factor in the order of 109 estimated from the SWNT network with 2% tensile strain. Additional studies indicate that the carbon rings connecting the SWNTs can also be used to alter the vibrational properties of the resulting network. This study suggests that the SWNT network can be a good candidate for applications as nanoresonators.

Quantum squeezing of motion in a mechanical resonator

Quantum mechanics places limits on the minimum energy of a harmonic oscillator via the ever-present "zero-point" fluctuations of the quantum ground state. Through squeezing, however, it is possible to decrease the noise of a single motional quadrature below the zero-point level as long as noise is added to the orthogonal quadrature. While squeezing below the quantum noise level was achieved decades ago with light, quantum squeezing of the motion of a mechanical resonator is a more difficult prospect due to the large thermal occupations of megahertz-frequency mechanical devices even at typical dilution refrigerator temperatures of ~ 10 mK.

Kronwald, Marquardt, and Clerk (2013) propose a method of squeezing a single quadrature of mechanical motion below the level of its zero-point fluctuations, even when the mechanics starts out with a large thermal occupation. The scheme operates under the framework of cavity optomechanics, where an optical or microwave cavity is coupled to the mechanics in order to control and read out the mechanical state. In the proposal, two pump tones are applied to the cavity, each detuned from the cavity resonance by the mechanical frequency. The pump tones establish and couple the mechanics to a squeezed reservoir, producing arbitrarily-large, steady-state squeezing of the mechanical motion. In this dissertation, I describe two experiments related to the implementation of this proposal in an electromechanical system. I also expand on the theory presented in Kronwald et. al. to include the effects of squeezing in the presence of classical microwave noise, and without assumptions of perfect alignment of the pump frequencies.

In the first experiment, we produce a squeezed thermal state using the method of Kronwald et. al.. We perform back-action evading measurements of the mechanical squeezed state in order to probe the noise in both quadratures of the mechanics. Using this method, we detect single-quadrature fluctuations at the level of 1.09 +/- 0.06 times the quantum zero-point motion.

In the second experiment, we measure the spectral noise of the microwave cavity in the presence of the squeezing tones and fit a full model to the spectrum in order to deduce a quadrature variance of 0.80 +/- 0.03 times the zero-point level. These measurements provide the first evidence of quantum squeezing of motion in a mechanical resonator.

Tunable mechanical resonator with aluminum nitride piezoelectric

The electromechanical response of piezoelectrically-actuated AlN micromachined bridge resonators has been characterized using laser interferometry and electrical admittance measurements. We compare the response of microbridges with different dimensions and buckling (induced by the initial residual stress of the layers). The resonance frequencies are in good agreement with numerical simulations of the electromechanical behavior of the structures. We show that it is possible to perform a rough tuning of the resonance frequencies by allowing a determined amount of builtin stress in the microbridge during its fabrication. Once the resonator is made, a DC bias added to the AC excitation signal allows to fine-tune the frequency. Our microbridges yield a tuning factor of around 88 Hz/V for a 500 ?m-long microbridge.

Nonlinearity and nonclassicality in a nanomechanical resonator

We address quantitatively the relationship between the nonlinearity of a mechanical resonator and the nonclassicality of its ground state. In particular, we analyze the nonclassical properties of the nonlinear Duffing oscillator (being driven or not) as a paradigmatic example of a nonlinear nanomechanical resonator. We first discuss how to quantify the nonlinearity of this system and then show that the nonclassicality of the ground state, as measured by the volume occupied by the negative part of the Wigner function, monotonically increases with the nonlinearity in all the working regimes addressed in our study. Our results show quantitatively that nonlinearity is a resource to create nonclassical states in mechanical systems.

Nonlinear state estimation and control for chaos suppression in MEMS resonator

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Nonlinear optics and wavelength translation via cavity-optomechanics

The field of cavity-optomechanics explores the interaction of light with sound in an ever increasing array of devices. This interaction allows the mechanical system to be both sensed and controlled by the optical system, opening up a wide variety of experiments including the cooling of the mechanical resonator to its quantum mechanical ground state and the squeezing of the optical field upon interaction with the mechanical resonator, to name two.

In this work we explore two very different systems with different types of optomechanical coupling. The first system consists of two microdisk optical resonators stacked on top of each other and separated by a very small slot. The interaction of the disks causes their optical resonance frequencies to be extremely sensitive to the gap between the disks. By careful control of the gap between the disks, the optomechanical coupling can be made to be quadratic to first order which is uncommon in optomechanical systems. With this quadratic coupling the light field is now sensitive to the energy of the mechanical resonator and can directly control the potential energy trapping the mechanical motion. This ability to directly control the spring constant without modifying the energy of the mechanical system, unlike in linear optomechanical coupling, is explored.

Next, the bulk of this thesis deals with a high mechanical frequency optomechanical crystal which is used to coherently convert photons between different frequencies. This is accomplished via the engineered linear optomechanical coupling in these devices. Both classical and quantum systems utilize the interaction of light and matter across a wide range of energies. These systems are often not naturally compatible with one another and require a means of converting photons of dissimilar wavelengths to combine and exploit their different strengths. Here we theoretically propose and experimentally demonstrate coherent wavelength conversion of optical photons using photon-phonon translation in a cavity-optomechanical system. For an engineered silicon optomechanical crystal nanocavity supporting a 4 GHz localized phonon mode, optical signals in a 1.5 MHz bandwidth are coherently converted over a 11.2 THz frequency span between one cavity mode at wavelength 1460 nm and a second cavity mode at 1545 nm with a 93% internal (2% external) peak efficiency. The thermal and quantum limiting noise involved in the conversion process is also analyzed and, in terms of an equivalent photon number signal level, are found to correspond to an internal noise level of only 6 and 4 times 10x^-3 quanta, respectively.

We begin by developing the requisite theoretical background to describe the system. A significant amount of time is then spent describing the fabrication of these silicon nanobeams, with an emphasis on understanding the specifics and motivation. The experimental demonstration of wavelength conversion is then described and analyzed. It is determined that the method of getting photons into the cavity and collected from the cavity is a fundamental limiting factor in the overall efficiency. Finally, a new coupling scheme is designed, fabricated, and tested that provides a means of coupling greater than 90% of photons into and out of the cavity, addressing one of the largest obstacles with the initial wavelength conversion experiment.

Nanofabrication for On-Chip Optical Levitation, Atom-Trapping, and Superconducting Quantum Circuits

Researchers have spent decades refining and improving their methods for fabricating smaller, finer-tuned, higher-quality nanoscale optical elements with the goal of making more sensitive and accurate measurements of the world around them using optics. Quantum optics has been a well-established tool of choice in making these increasingly sensitive measurements which have repeatedly pushed the limits on the accuracy of measurement set forth by quantum mechanics. A recent development in quantum optics has been a creative integration of robust, high-quality, and well-established macroscopic experimental systems with highly-engineerable on-chip nanoscale oscillators fabricated in cleanrooms. However, merging large systems with nanoscale oscillators often require them to have extremely high aspect-ratios, which make them extremely delicate and difficult to fabricate with an "experimentally reasonable" repeatability, yield and high quality. In this work we give an overview of our research, which focused on microscopic oscillators which are coupled with macroscopic optical cavities towards the goal of cooling them to their motional ground state in room temperature environments. The quality factor of a mechanical resonator is an important figure of merit for various sensing applications and observing quantum behavior. We demonstrated a technique for pushing the quality factor of a micromechanical resonator beyond conventional material and fabrication limits by using an optical field to stiffen and trap a particular motional mode of a nanoscale oscillator. Optical forces increase the oscillation frequency by storing most of the mechanical energy in a nearly loss-less optical potential, thereby strongly diluting the effects of material dissipation. By placing a 130 nm thick SiO₂ pendulum in an optical standing wave, we achieve an increase in the pendulum center-of-mass frequency from 6.2 to 145 kHz. The corresponding quality factor increases 50-fold from its intrinsic value to a final value of Q_m = 5.8(1.1) x 10⁵, representing more than an order of magnitude improvement over the conventional limits of SiO₂ for a pendulum geometry. Our technique may enable new opportunities for mechanical sensing and facilitate observations of quantum behavior in this class of mechanical systems. We then give a detailed overview of the techniques used to produce high-aspect-ratio nanostructures with applications in a wide range of quantum optics experiments. The ability to fabricate such nanodevices with high precision opens the door to a vast array of experiments which integrate macroscopic optical setups with lithographically engineered nanodevices. Coupled with atom-trapping experiments in the Kimble Lab, we use these techniques to realize a new waveguide chip designed to address ultra-cold atoms along lithographically patterned nanobeams which have large atom-photon coupling and near 4π Steradian optical access for cooling and trapping atoms. We describe a fully integrated and scalable design where cold atoms are spatially overlapped with the nanostring cavities in order to observe a resonant optical depth of d₀ ≈ 0.15. The nanodevice illuminates new possibilities for integrating atoms into photonic circuits and engineering quantum states of atoms and light on a microscopic scale. We then describe our work with superconducting microwave resonators coupled to a phononic cavity towards the goal of building an integrated device for quantum-limited microwave-to-optical wavelength conversion. We give an overview of our characterizations of several types of substrates for fabricating a low-loss high-frequency electromechanical system. We describe our electromechanical system fabricated on a Si₃N₄ membrane which consists of a 12 GHz superconducting LC resonator coupled capacitively to the high frequency localized modes of a phononic nanobeam. Using our suspended membrane geometry we isolate our system from substrates with significant loss tangents, drastically reducing the parasitic capacitance of our superconducting circuit to ≈ 2.5$ fF. This opens up a number of possibilities in making a new class of low-loss high-frequency electromechanics with relatively large electromechanical coupling. We present our substrate studies, fabrication methods, and device characterization.

Acceleration Sensing, Feedback Cooling, and Nonlinear Dynamics with Nanoscale Cavity-Optomechanical Devices

Light has long been used for the precise measurement of moving bodies, but the burgeoning field of optomechanics is concerned with the interaction of light and matter in a regime where the typically weak radiation pressure force of light is able to push back on the moving object. This field began with the realization in the late 1960's that the momentum imparted by a recoiling photon on a mirror would place fundamental limits on the smallest measurable displacement of that mirror. This coupling between the frequency of light and the motion of a mechanical object does much more than simply add noise, however. It has been used to cool objects to their quantum ground state, demonstrate electromagnetically-induced-transparency, and modify the damping and spring constant of the resonator. Amazingly, these radiation pressure effects have now been demonstrated in systems ranging 18 orders of magnitude in mass (kg to fg).

In this work we will focus on three diverse experiments in three different optomechanical devices which span the fields of inertial sensors, closed-loop feedback, and nonlinear dynamics. The mechanical elements presented cover 6 orders of magnitude in mass (ng to fg), but they all employ nano-scale photonic crystals to trap light and resonantly enhance the light-matter interaction. In the first experiment we take advantage of the sub-femtometer displacement resolution of our photonic crystals to demonstrate a sensitive chip-scale optical accelerometer with a kHz-frequency mechanical resonator. This sensor has a noise density of approximately 10 micro-g/rt-Hz over a useable bandwidth of approximately 20 kHz and we demonstrate at least 50 dB of linear dynamic sensor range. We also discuss methods to further improve performance of this device by a factor of 10.

In the second experiment, we used a closed-loop measurement and feedback system to damp and cool a room-temperature MHz-frequency mechanical oscillator from a phonon occupation of 6.5 million down to just 66. At the time of the experiment, this represented a world-record result for the laser cooling of a macroscopic mechanical element without the aid of cryogenic pre-cooling. Furthermore, this closed-loop damping yields a high-resolution force sensor with a practical bandwidth of 200 kHZ and the method has applications to other optomechanical sensors.

The final experiment contains results from a GHz-frequency mechanical resonator in a regime where the nonlinearity of the radiation-pressure interaction dominates the system dynamics. In this device we show self-oscillations of the mechanical element that are driven by multi-photon-phonon scattering. Control of the system allows us to initialize the mechanical oscillator into a stable high-amplitude attractor which would otherwise be inaccessible. To provide context, we begin this work by first presenting an intuitive overview of optomechanical systems and then providing an extended discussion of the principles underlying the design and fabrication of our optomechanical devices.

Cavity Optomechanics at Millikelvin Temperatures

The field of cavity optomechanics, which concerns the coupling of a mechanical object's motion to the electromagnetic field of a high finesse cavity, allows for exquisitely sensitive measurements of mechanical motion, from large-scale gravitational wave detection to microscale accelerometers. Moreover, it provides a potential means to control and engineer the state of a macroscopic mechanical object at the quantum level, provided one can realize sufficiently strong interaction strengths relative to the ambient thermal noise. Recent experiments utilizing the optomechanical interaction to cool mechanical resonators to their motional quantum ground state allow for a variety of quantum engineering applications, including preparation of non-classical mechanical states and coherent optical to microwave conversion. Optomechanical crystals (OMCs), in which bandgaps for both optical and mechanical waves can be introduced through patterning of a material, provide one particularly attractive means for realizing strong interactions between high-frequency mechanical resonators and near-infrared light. Beyond the usual paradigm of cavity optomechanics involving isolated single mechanical elements, OMCs can also be fashioned into planar circuits for photons and phonons, and arrays of optomechanical elements can be interconnected via optical and acoustic waveguides. Such coupled OMC arrays have been proposed as a way to realize quantum optomechanical memories, nanomechanical circuits for continuous variable quantum information processing and phononic quantum networks, and as a platform for engineering and studying quantum many-body physics of optomechanical meta-materials.

However, while ground state occupancies (that is, average phonon occupancies less than one) have been achieved in OMC cavities utilizing laser cooling techniques, parasitic absorption and the concomitant degradation of the mechanical quality factor fundamentally limit this approach. On the other hand, the high mechanical frequency of these systems allows for the possibility of using a dilution refrigerator to simultaneously achieve low thermal occupancy and long mechanical coherence time by passively cooling the device to the millikelvin regime. This thesis describes efforts to realize the measurement of OMC cavities inside a dilution refrigerator, including the development of fridge-compatible optical coupling schemes and the characterization of the heating dynamics of the mechanical resonator at sub-kelvin temperatures.

We will begin by summarizing the theoretical framework used to describe cavity optomechanical systems, as well as a handful of the quantum applications envisioned for such devices. Then, we will present background on the design of the nanobeam OMC cavities used for this work, along with details of the design and characterization of tapered fiber couplers for optical coupling inside the fridge. Finally, we will present measurements of the devices at fridge base temperatures of T_f = 10 mK, using both heterodyne spectroscopy and time-resolved sideband photon counting, as well as detailed analysis of the prospects for future quantum applications based on the observed optically-induced heating.

Quantum Electromechanics with Two Tone Drive

In the field of mechanics, it is a long standing goal to measure quantum behavior in ever larger and more massive objects. It may now seem like an obvious conclusion, but until recently it was not clear whether a macroscopic mechanical resonator -- built up from nearly 10¹³ atoms -- could be fully described as an ideal quantum harmonic oscillator. With recent advances in the fields of opto- and electro-mechanics, such systems offer a unique advantage in probing the quantum noise properties of macroscopic electrical and mechanical devices, properties that ultimately stem from Heisenberg's uncertainty relations. Given the rapid progress in device capabilities, landmark results of quantum optics are now being extended into the regime of macroscopic mechanics.

The purpose of this dissertation is to describe three experiments -- motional sideband asymmetry, back-action evasion (BAE) detection, and mechanical squeezing -- that are directly related to the topic of measuring quantum noise with mechanical detection. These measurements all share three pertinent features: they explore quantum noise properties in a macroscopic electromechanical device driven by a minimum of two microwave drive tones, hence the title of this work: "Quantum electromechanics with two tone drive".

In the following, we will first introduce a quantum input-output framework that we use to model the electromechanical interaction and capture subtleties related to interpreting different microwave noise detection techniques. Next, we will discuss the fabrication and measurement details that we use to cool and probe these devices with coherent and incoherent microwave drive signals. Having developed our tools for signal modeling and detection, we explore the three-wave mixing interaction between the microwave and mechanical modes, whereby mechanical motion generates motional sidebands corresponding to up-down frequency conversions of microwave photons. Because of quantum vacuum noise, the rates of these processes are expected to be unequal. We will discuss the measurement and interpretation of this asymmetric motional noise in a electromechanical device cooled near the ground state of motion.

Next, we consider an overlapped two tone pump configuration that produces a time-modulated electromechanical interaction. By careful control of this drive field, we report a quantum non-demolition (QND) measurement of a single motional quadrature. Incorporating a second pair of drive tones, we directly measure the measurement back-action associated with both classical and quantum noise of the microwave cavity. Lastly, we slightly modify our drive scheme to generate quantum squeezing in a macroscopic mechanical resonator. Here, we will focus on data analysis techniques that we use to estimate the quadrature occupations. We incorporate Bayesian spectrum fitting and parameter estimation that serve as powerful tools for incorporating many known sources of measurement and fit error that are unavoidable in such work.

Optomechanical Inertial Sensors and Feedback Cooling

The optomechanical interaction is an extremely powerful tool with which to measure mechanical motion. The displacement resolution of chip-scale optomechanical systems has been measured on the order of 1⁄10th of a proton radius. So strong is this optomechanical interaction that it has recently been used to remove almost all thermal noise from a mechanical resonator and observe its quantum ground-state of motion starting from cryogenic temperatures.

In this work, chapter 1 describes the basic physics of the canonical optomechanical system, optical measurement techniques, and how the optomechanical interaction affects the coupled mechanical resonator. In chapter 2, we describe our techniques for realizing this canonical optomechanical system in a chip-scale form factor.

In chapter 3, we describe an experiment where we used radiation pressure feedback to cool a mesoscopic mechanical resonator near its quantum ground-state from room-temperature. We cooled the resonator from a room temperature phonon occupation of <n> = 6.5 million to an occupation of <n> = 66, which means the resonator is in its ground state approximately 2% of the time, while being coupled to a room-temperature thermal environment. At the time of this work, this is the closest a mesoscopic mechanical resonator has been to its ground-state of motion at room temperature, and this work begins to open the door to room-temperature quantum control of mechanical objects.

Chapter 4 begins with the realization that the displacement resolutions achieved by optomechanical systems can surpass those of conventional MEMS sensors by an order of magnitude or more. This provides the motivation to develop and calibrate an optomechanical accelerometer with a resolution of approximately 10 micro-g/rt-Hz over a bandwidth of approximately 30 kHz. In chapter 5, we improve upon the performance and practicality of this sensor by greatly increasing the test mass size, investigating and reducing low-frequency noise, and incorporating more robust optical coupling techniques and capacitive wavelength tuning. Finally, in chapter 6 we present our progress towards developing another optomechanical inertial sensor - a gyroscope.

Reconfigurable Long-Range Phonon Dynamics in Optomechanical Arrays

We investigate periodic optomechanical arrays as reconfigurable platforms for engineering the coupling between multiple mechanical and electromagnetic modes and for exploring many-body phonon dynamics. Exploiting structural resonances in the coupling between light fields and collective motional modes of the array, we show that tunable effective long-range interactions between mechanical modes can be achieved. This paves the way towards the implementation of controlled phononic walks and heat transfer on densely connected graphs as well as the coherent transfer of excitations between distant elements of optomechanical arrays.

Chaos suppression in NEMs resonators by using nonlinear control design

In this work the chaotic behavior of a micro-mechanical resonator with electrostatic forces on both sides is suppressed. The aim is to control the system in an orbit of the analytical solution obtained by the Method of Multiple Scales. Two control strategies are used for controlling the trajectory of the system, namely: State Dependent Riccati Equation (SDRE) Control and Optimal Linear Feedback Control (OLFC). The controls proved effectiveness in controlling the trajectory of the system. Additionally, the robustness of each strategy is tested considering the presence of parametric errors and measurement noise in control. © 2012 American Institute of Physics.

Contribución al diseño de lazos de realimentación electrónica para microsistemas electromecánicos (MEMS) resonantes: ruido de fase generado en lazos osciladores por sus realimentaciones

En 1966, D. B. Leeson publicó el artículo titulado “A simple model of feedback oscillator noise spectrum” en el que, mediante una ecuación obtenida de forma heurística y basada en parámetros conocidos de los osciladores, proponía un modelo para estimar el espectro de potencia que cuantifica el Ruido de Fase de estos osciladores. Este Ruido de Fase pone de manifiesto las fluctuaciones aleatorias que se producen en la fase de la señal de salida de cualquier oscilador de frecuencia f_0. Desde entonces, los adelantos tecnológicos han permitido grandes progresos en cuanto a la medida del Ruido de Fase, llegando a encontrar una estrecha “zona plana”, alrededor de f_0, conocida con el nombre de Ensanchamiento de Línea (EL) que Leeson no llegó a observar y que su modelo empírico no recogía. Paralelamente han ido surgiendo teorías que han tratado de explicar el Ruido de Fase con mayor o menor éxito. En esta Tesis se propone una nueva teoría para explicar el espectro de potencia del Ruido de Fase de un oscilador realimentado y basado en resonador L-C (Inductancia-Capacidad). Al igual que otras teorías, la nuestra también relaciona el Ruido de Fase del oscilador con el ruido térmico del circuito que lo implementa pero, a diferencia de aquellas, nuestra teoría se basa en un Modelo Complejo de ruido eléctrico que considera tanto las Fluctuaciones de energía eléctrica asociadas a la susceptancia capacitiva del resonador como las Disipaciones de energía eléctrica asociadas a su inevitable conductancia G=1⁄R, que dan cuenta del contacto térmico entre el resonador y el entorno térmico que le rodea. En concreto, la nueva teoría que proponemos explica tanto la parte del espectro del Ruido de Fase centrada alrededor de la frecuencia portadora f_0 que hemos llamado EL y su posterior caída proporcional a 〖∆f〗^(-2) al alejarnos de f_0, como la zona plana o pedestal que aparece en el espectro de Ruido de Fase lejos de esa f_0. Además, al saber cuantificar el EL y su origen, podemos explicar con facilidad la aparición de zonas del espectro de Ruido de Fase con caída 〖∆f〗^(-3) cercanas a la portadora y que provienen del denominado “exceso de ruido 1⁄f” de dispositivos de Estado Sólido y del ruido “flicker” de espectro 1⁄f^β (0,8≤β≤1,2) que aparece en dispositivos de vacío como las válvulas termoiónicas. Habiendo mostrado que una parte del Ruido de Fase de osciladores L-C realimentados que hemos denominado Ruido de Fase Térmico, se debe al ruido eléctrico de origen térmico de la electrónica que forma ese oscilador, proponemos en esta Tesis una nueva fuente de Ruido de Fase que hemos llamado Ruido de Fase Técnico, que se añadirá al Térmico y que aparecerá cuando el desfase del lazo a la frecuencia de resonancia f_0 del resonador no sea 0° o múltiplo entero de 360° (Condición Barkhausen de Fase, CBF). En estos casos, la modulación aleatoria de ganancia de lazo que realiza el Control Automático de Amplitud en su lucha contra ruidos que traten de variar la amplitud de la señal oscilante del lazo, producirá a su vez una modulación aleatoria de la frecuencia de tal señal que se observará como más Ruido de Fase añadido al Térmico. Para dar una prueba empírica sobre la existencia de esta nueva fuente de Ruido de Fase, se diseñó y construyó un oscilador en torno a un resonador mecánico “grande” para tener un Ruido de Fase Térmico despreciable a efectos prácticos. En este oscilador se midió su Ruido de Fase Técnico tanto en función del valor del desfase añadido al lazo de realimentación para apartarlo de su CBF, como en función de la perturbación de amplitud inyectada para mostrar sin ambigüedad la aparición de este Ruido de Fase Técnico cuando el lazo tiene este fallo técnico: que no cumple la Condición Barkhausen de Fase a la frecuencia de resonancia f_0 del resonador, por lo que oscila a otra frecuencia. ABSTRACT In 1966, D. B. Leeson published the article titled “A simple model of feedback oscillator noise spectrum” in which, by means of an equation obtained heuristically and based on known parameters of the oscillators, a model was proposed to estimate the power spectrum that quantifies the Phase Noise of these oscillators. This Phase Noise reveals the random fluctuations that are produced in the phase of the output signal from any oscillator of frequencyf_0. Since then, technological advances have allowed significant progress regarding the measurement of Phase Noise. This way, the narrow flat region that has been found around f_(0 ), is known as Line Widening (LW). This region that Leeson could not detect at that time does not appear in his empirical model. After Leeson’s work, different theories have appeared trying to explain the Phase Noise of oscillators. This Thesis proposes a new theory that explains the Phase Noise power spectrum of a feedback oscillator around a resonator L-C (Inductance-Capacity). Like other theories, ours also relates the oscillator Phase Noise to the thermal noise of the feedback circuitry, but departing from them, our theory uses a new, Complex Model for electrical noise that considers both Fluctuations of electrical energy associated with the capacitive susceptance of the resonator and Dissipations of electrical energy associated with its unavoidable conductance G=1/R, which accounts for the thermal contact between the resonator and its surrounding environment (thermal bath). More specifically, the new theory we propose explains both the Phase Noise region of the spectrum centered at the carrier frequency f_0 that we have called LW and shows a region falling as 〖∆f〗^(-2) as we depart from f_0, and the flat zone or pedestal that appears in the Phase Noise spectrum far from f_0. Being able to quantify the LW and its origin, we can easily explain the appearance of Phase Noise spectrum zones with 〖∆f〗^(-3) slope near the carrier that come from the so called “1/f excess noise” in Solid-State devices and “flicker noise” with 1⁄f^β (0,8≤β≤1,2) spectrum that appears in vacuum devices such as thermoionic valves. Having shown that the part of the Phase Noise of L-C oscillators that we have called Thermal Phase Noise is due to the electrical noise of the electronics used in the oscillator, this Thesis can propose a new source of Phase Noise that we have called Technical Phase Noise, which will appear when the loop phase shift to the resonance frequency f_0 is not 0° or an integer multiple of 360° (Barkhausen Phase Condition, BPC). This Phase Noise that will add to the Thermal one, comes from the random modulation of the loop gain carried out by the Amplitude Automatic Control fighting against noises trying to change the amplitude of the oscillating signal in the loop. In this case, the BPC failure gives rise to a random modulation of the frequency of the output signal that will be observed as more Phase Noise added to the Thermal one. To give an empirical proof on the existence of this new source of Phase Noise, an oscillator was designed and constructed around a “big” mechanical resonator whose Thermal Phase Noise is negligible for practical effects. The Technical Phase Noise of this oscillator has been measured with regard to the phase lag added to the feedback loop to separate it from its BPC, and with regard to the amplitude disturbance injected to show without ambiguity the appearance of this Technical Phase Noise that appears when the loop has this technical failure: that it does not fulfill the Barkhausen Phase Condition at f_0, the resonance frequency of the resonator and therefore it is oscillating at a frequency other than f_0.