The production of ultra-short electromagnetic waves by the retarding field method is analyzed. It is found that to generate oscillations of very short wave lengths, it is more effective to reduce the size of the electrodes of the vacuum tube and to design the tubes to oscillate higher orders than to increase the grid potential.
Experiments were made with the Pliotron FP-126 tubes as retarding field oscillators. These tubes generated strong normal and higher order oscillations. The wave length of the normal oscillations differed considerably from the values calculated from the Barkhausen and Scheibe equations. For the higher order oscillations, the observed wave lengths were approximately equal to values calculated according to Potapenko’s formula: n2λ2Eg=C. It was found that the predominating higher order oscillations were generated by the grid coil at its natural frequency. Its wave length agrees with that calculated from its dimensions.
Tubes with plate diameters as small as 0.05 cm. were made. They generated normal as well as higher order oscillations. They were designed so that the grid had a natural wave length of about 1 cm. The grid potentials calculated agree fairly well with the values observed. The energy of oscillations with these tubes was exceedingly small. The wave length of 1 cm. is about the shortest limit that can be obtained by the retarding field method.
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.
The growing interest in optical quantum systems has led to the exploration of multiple platforms. Though pioneering experiments were performed in trapped atom and trapped ion systems, solid state systems show promise of being scalable and robust. Rare earth dopants in crystalline hosts are an appealing option because they possess a rich spectrum of energy levels that result from a partially filled electron orbital. While level structure varies across the period, all elements possess crystal field splittings corresponding to near infra-red or optical frequencies, as well as Zeeman and often hyperfine levels separated by radio frequency and microwave frequencies. These levels demonstrate long excited-state lifetimes and coherence times and have been used in diverse applications, including demonstrating storage of a photonic state, converting of optical to microwave photons, and manipulating a single ion as a single qubit. The ions' weak interaction with their environment results in low coupling to optical fields, which had previously required measurements with macroscopically large ensembles of ions. Coupling the ions to an optical cavity enables the use of a smaller ensemble, which is required for the development of the aforementioned technologies in an on-chip scalable architecture.
This thesis contains recent progress towards fabricating optical micro and nanocavities coupled to ensembles of erbium ions, mainly erbium in yttrium orthosilicate. In one design, focused ion beam milling was used to create a triangular nanobeam photonic crystal cavity in a bulk erbium-doped substrate. A second design leveraged the fabrication capabilities of silicon photonics, defining amorphous silicon ring resonators using electron beam lithography and dry etching. These devices coupled evanescently to erbium ions below the ring, in the bulk substrate. Simulation, design, fabrication, and characterization of both resonators are discussed. Coupling between the ions and the resonator is demonstrated for each, and capabilities offered by these devices are described. Preliminary work implementing coherent control of erbium ions is presented. Lastly, alternative substrates are evaluated for possible future solid-state erbium systems.
Quantum chaos and the eigenstate thermalization hypothesis are based on the assumption of the validity of random matrix theory description on the spectrum and eigenstates. They provide the foundation and descriptions for the typical dynamics and thermalization in generic closed quantum systems. In this thesis, we investigate situations where the systems show atypical dynamics or anomalous thermalization, conflicting with the usual expectations from quantum chaos and eigenstate thermalization hypothesis.
We first examine weak thermalization in a nonintegrable spin chain. The system shows long-lived strong oscillations and relaxes to the thermal equilibrium weakly. We identify the dynamics describable by quasiparticles and recognize the oscillationfrequency to be the quasiparticle mass gap. We also estimate the damping time for the oscillations.
Next, we study prethermalization, a phenomenon where a system relaxes to an intermediate almost-equilibrium stage before reaching the true thermal equilibrium. We study a nonintegrable spin chain in the strong coupling limit, where an almost-conserved quantity emerges and gives rise to the prethermalization.
We also study a newly proposed diagnostic for quantum chaos: out-of-time-ordered correlators. Contrasting to the chaotic systems, we inspect their behaviors in various noninteracting integrable models.
Finally, we dig into the quantum many-body scar states in the PXP model which describes a Rydberg atom chain. These special states do not satisfy the random matrix theory description nor the eigenstate thermalization hypothesis, therefore defying quantum chaos.
The interaction between an electron beam and the plasma oscillations it excites in traversing a plasma region effectively changes the magnitude and direction of the force between beam electrons. This effect has been studied theoretically and experimentally by computing and observing beam electron velocities and phases for a beam which is initially velocity modulated at frequency ω and allowed to drift through a plasma filled region of plasma frequency ω_p. When ω > ω_p the force between electrons is repulsive and effectively increases in magnitude as ω approaches ω_p. When ω < ω_p, the force between electrons becomes a force of attraction, to within a given inter-electron spacing, and the maximum effect is also at the resonance condition ω ~ ω_p. This property could be used to improve the efficiency of electron bunching in a klystron type amplifier by filling the drift space with a plasma of appropriate density.
The beam behavior is studied theoretically by computing in an exact, nonlinear manner, the trajectories of a disc model electron beam which traverses a linear, dielectric model plasma. The parameters varied are the beam space charge conditions (beam current), the degree of initial velocity modulation, and the ratio of modulation frequency to plasma frequency (ω/ω_p). Computations show that it is possible to bunch the beam electrons to within 85% of delta function bunching under some beam and plasma conditions. The electron beam behavior is studied experimentally by observing the beam electron velocity phase distribution with a crossed-field velocity analyzer, and observing the beam current waveform (density-phase distribution) using a wide-band sampling oscilloscope. Experimental results show essentially the same beam behavior as predicted by the computations with some differences which are attributed to variation in the plasma density along the beam path.,Electron Tube and Microwave Laboratory Technical Report 33,
There has been a barrage of interest in recent years to marry the fields of nanomechanics and quantum optics. Mechanical systems provide sensitive and scalable architectures for sensing applications ranging from atomic force microscopy to gravity wave interferometry. Optical resonators driven by low noise lasers provide a quiet and well-understood means to read-out and manipulate mechanical motion, by way of the radiation pressure force. Taken to an extreme, a device consisting of a high-Q nanomechanical oscillator coupled to a high-finesse optical cavity may enable ground-state preparation of the mechanical element, thus paving the way for a new class of quantum technology based on chip-scale phononic devices coupled to optical photons. By way of mutual coupling to the optical field, this architecture may enable coupling of single phonons to real or artificial atoms, an enticing prospect because of the vast "quantum optics toolbox" already developed for cavity quantum electrodynamics. The first step towards these goals --- ground-state cooling of the mechanical element in a "cavity optomechanical" system --- has very recently been realized in a cryogenic setup. The work presented in this thesis describes an effort to extend this capability to a room temperature apparatus, so that the usual panoply of table-top optical/atomic physics tools can be brought to bear. This requires a mechanical oscillator with exceptionally low dissipation, as well as careful attention to extraneous sources of noise in both the optical and mechanical componentry. Our particular system is based on a high-Q, high-stress silicon nitride membrane coupled to a high-finesse Fabry-Perot cavity. The purpose of this thesis is to record in detail the procedure for characterizing/modeling the physical properties of the membrane resonator, the optical cavity, and their mutual interaction, as well as extraneous sources of noise related to multimode thermal motion of the oscillator, thermal motion of the cavity apparatus, optical absorption, and laser phase fluctuations. Our principle experimental result is the radiation pressure-based cooling of a high order, 4.8 MHz drum mode of the membrane from room temperature to ~ 100 mK (~ 500 phonons). Secondary results include an investigation of the Q-factor of membrane oscillators with various geometries, some of which exhibit state-of-the-art Q x frequency products of 3 x 10^13 Hz, and a novel technique to suppress extraneous radiation pressure noise using electro-optic feedback.