Levitation of very small but macroscopic objects is a rapidly developing interrogation technique for nanooptics and optomechanics. Paul traps are one mechanism for levitation of charged particles, which enables interrogation of novel materials or optically active samples in a virtually interaction-free environment, providing a test-bed for completely new experiments. Elementary traps have already been demonstrated for nano- and microparticles as a proof-of-principle for such experiments. We present a linear, segmented Paul trap with a printed-circuit-board-based design for levitation of nano- and microparticles, as a step toward the more sophisticated tools needed for advanced experiments. We describe the trap design, construction, and characterization and address the challenging phenomena associated with such a system. This trap provides a step toward designing an ideal environment for studies using a variety of isolated particles to enable advances in areas including magnetometry, thermodynamics, and optomechanics.

We report on the development of a highly miniaturized vacuum package for use in an atomic clock utilizing trapped ytterbium-171 ions. The vacuum package is approximately 1 cm(3) in size and contains a linear quadrupole RF Paul ion trap, miniature neutral Yb sources, and a non-evaporable getter pump. We describe the fabrication process for making the Yb sources and assembling the vacuum package. To prepare the vacuum package for ion trapping, it was evacuated, baked at a high temperature, and then back filled with a helium buffer gas. Once appropriate vacuum conditions were achieved in the package, it was sealed with a copper pinch-off and was subsequently pumped only by the non-evaporable getter. We demonstrated ion trapping in this vacuum package and the operation of an atomic clock, stabilizing a local oscillator to the 12.6 GHz hyperfine transition of (171)Y b(+). The fractional frequency stability of the clock was measured to be 2 × 10(-11)/τ(1/2).

We describe the development and frequency instability measurements of a highly miniaturized, buffer gas cooled, trapped-ion atomic clock. The clock utilizes the 12.6 GHz hyperfine transition of the 171 Yb + ion. A custom-built 3 cm 3 vacuum package containing the ion trap is integrated with other key elements of the atomic frequency standard, including a photo multiplier tube, miniaturized laser sources at 369 nm and 935 nm, a local oscillator, and control electronics. With the clock physics package assembled on a 10 cm × 15 cm breadboard, the long-term fractional frequency instability was measured to be 6 × 10 -14 at 25 days of integration. Later, the clock physics package was further miniaturized, and the frequency instability was measured to be 2 × 10 -11 /τ 1/2 at integration times up to 10,000 s.

As relative systematic frequency uncertainties in trapped-ion spectroscopy are approaching the low $10^{-18}$ range, motional frequency shifts account for a considerable fraction of the uncertainty budget. Micromotion, a driven motion fundamentally connected to the principle of the Paul trap, is a particular concern in these systems. In this article, we experimentally investigate at this level three common methods for minimizing and determining the micromotion amplitude. We develop a generalized model for a quantitative application of the photon-correlation technique, which is applicable in the commonly encountered regime where the transition linewidth is comparable to the rf drive frequency. We show that a fractional frequency uncertainty due to the 2nd-order Doppler shift below $1\times 10^{-20}$ can be achieved. The quantitative evaluation is verified in an interleaved measurement with the conceptually simpler resolved sideband method. If not performed deep within the Lamb-Dicke regime, a temperature-dependent offset at the level of $10^{-19}$ is observed in resolved sideband measurements due to sampling of intrinsic micromotion. By direct comparison with photon-correlation measurements, we show that the simple to implement parametric heating method is sensitive to micromotion at the level of $1\times 10^{-20}$ as well.

We use laser-cooled ion Coulomb crystals in the well-controlled environment of a harmonic radiofrequency ion trap to investigate phase transitions and defect formation. Topological defects in ion Coulomb crystals (kinks) have been recently proposed for studies of nonlinear physics with solitons and as carriers of quantum information. Defects form when a symmetry breaking phase transition is crossed nonadiabatically. For a second order phase transition, the Kibble–Zurek mechanism predicts that the formation of these defects follows a power law scaling in the rate of the transition. We demonstrate a scaling of defect density and describe kink dynamics and stability. We further discuss the implementation of mass defects and electric fields as first steps toward controlled kink preparation and manipulation.

Symmetry breaking phase transitions play an important role in nature. When a system traverses such a transition at a finite rate, its causally disconnected regions choose the new broken symmetry state independently. Where such local choices are incompatible, topological defects can form. The Kibble-Zurek mechanism predicts the defect densities to follow a power law that scales with the rate of the transition. Owing to its ubiquitous nature, this theory finds application in a wide field of systems ranging from cosmology to condensed matter. Here we present the successful creation of defects in ion Coulomb crystals by a controlled quench of the confining potential, and observe an enhanced power law scaling in accordance with numerical simulations and recent predictions. This simple system with well-defined critical exponents opens up ways to investigate the physics of non-equilibrium dynamics from the classical to the quantum regime.

We study experimentally and theoretically the properties of structural defects (kink solitons) in two-dimensional ion Coulomb crystals. We show how different types of kink solitons with different physical properties can be realized, and transformed from one type into another by varying the aspect ratio of the trap confinement. Further, we discuss how impurities in ion Coulomb crystals, such as mass defects, can modify the dynamics of kink creation and their stability. For both pure and impure crystals, the experimentally observed kink dynamics are analyzed in detail and explained theoretically by numerical simulations and calculations of the Peierls-Nabarro potential. Finally, we show that static electric fields provide a handle to vary the influence of mass defects on kinks in a controlled way and allow for deterministic manipulation and creation of kinks.

Femtosecond laser structuring is applied to produce linear ion traps of AlN ceramics. Such ion trap can serve as an optical clock with exceptionally high long term stability. The selection of techniques, applicable to the high precision microstructuring of AlN ceramics, is limited due to high hardness and fragility of the material. Laser structuring is very attractive for this application. However, long laser pulses cause thermal decomposition and surface metallization of AlN ceramics. A femtosecond laser allows material removal without adverse heat effects. At the same time high quality surface finish together with aspect ratios and precision as required for optical ion trap clocks are ensured. Here, a high process throughput of up to 400 μm3/pulse and a sub-pristine surface roughness down to 350 nm Ra were achieved. The novelty of this structuring technique lies in the separation of processing stages and the application of two distinctive femtosecond laser induced phenomena: ablation and plasma etching. Rapid material removal for the rough contouring is achieved by material ablation with a focused laser beam. The remaining rough surface is further refined to the required specifications by plasma polishing. The laser beam then acts indirectly and serves as a source of energy to sustain a plasma plume in the near vicinity of the substrate.

This dissertation reports on the development of a low-power, high-stability miniature atomic frequency standard based on 171Yb+ ions. The ions are buffer-gas cooled and held in a linear quadrupole trap that is integrated into a sealed, getter-pumped vacuum package, and interrogated on the 12.6 GHz hyperfine transition. We hope to achieve a long-term fractional frequency stability of 10^-14 with a miniature clock that consumes only 50 mW of power and occupies a volume of 5 cm^3. I discuss our progress over several years of work on this project. We began by building a conventional tabletop clock to use as a test bed while developing several designs of miniature ion-trap vacuum packages, while also developing techniques for various aspects of the clock operation, including ion loading, laser and magnetic field stabilization, and a low power ion trap drive. The ion traps were modeled using boundary element software to assist with the design and parameter optimization of new trap geometries. We expect a novel trap geometry that uses a material new to ion traps to lead to an exceptionally small ion trap vacuum package in the next phase of the project. To achieve the long-term stability required, we have also considered the sensitivity of the clock frequency to magnetic fields. A study of the motion of the individual ions in a room-temperature cloud in the trap was performed with the purpose of understanding the effect of both spatially varying and constant magnetic fields on the clock resonance and therefore the operation of the clock. These effects were studied experimentally and theoretically for several traps. In summary, this dissertation is a contribution to the design, development, and testing of a 171Yb+ ion cloud frequency standard and related techniques, including analyses of trap geometries and parameters, modeling of the ion motion, and the practical operation of the clock.

We report a demonstration of a very small microwave atomic clock using the 12.6 GHz hyperfine transition of the trapped 171Yb ions inside a miniature, completely sealed-off 3 cm3 ion-trap vacuum package. In the ion clock system, all of the components are highly miniaturized with low power consumption except the 369 nm optical pumping laser still under development for miniaturization. The entire clock, including the control electronics, consumes <300 mW. The fractional frequency instability of the miniature Yb+ clock reaches the 10−14 range after a few days of integration.

We are developing a highly miniaturized trapped ion clock to probe the 12.6 GHz hyperfine transition in the 171Yb+ ion. The clock development is being funded by the Integrated Micro Primary Atomic Clock Technology (IMPACT) program from DARPA where the stated goals are to develop a clock that consumes 50 mW of power, has a size of 5 cm3, and has a long-term frequency stability of 10-14 at one month. One of the significant challenges will be to develop miniature single-frequency lasers at 369 nm and 935 nm and the optical systems to deliver light to the ions and to collect ion fluorescence on a detector.

We report a simple, efficient, high voltage radio frequency (RF) generator powered by a single voltage source (1.5-7 V) to resonantly drive ion traps or other capacitive loads. Our circuit is able to deliver RF voltages > 500 V(p-p) at frequencies ranging from 0.1 to 10 MHz. This RF oscillator uses low-cost, commercially available components, and can be easily assembled onto a circuit board of a few cm(2). Because of its simplicity and good efficiency, this circuit is useful in applications requiring small size and low power consumption such as portable ion trap systems where the duration of operation under battery power is of concern.

: We are developing a highly miniaturized trapped ion clock to probe the 12.6 GHz hyperfine transition in the (sup 171)Yb+ ion. The clock development is being funded by the Integrated Micro Primary Atomic Clock Technology (IMPACT) program from DARPA, where the stated goals are to develop a clock that consumes 50 mW of power, has a size of 5 cubic cm, and has a long-term frequency stability of 10(exp -14) at 1 month. Trapped ion systems are an excellent candidate for such extreme miniaturization, because ions are well isolated from the environment independently of the size of the trap. Trapped ion clocks are characterized by quality factors, Q, in excess of 10(exp 12) and excellent long-term stability, and the Q will be minimally degraded upon miniaturization. To realize the clock in a small package will require the miniaturization of several technologies. One of the primary technologies will be the miniaturized ion trap and vacuum package. Linear RF Paul traps routinely have dimensions of a couple millimeters, but miniaturizing the vacuum package with an integral trap, Yb source, and pump will require a novel design. Integrating the miniature, low-power light sources for state detection at 369 nm and 935 nm and for photoionization at 399 nm will also be critical. The 369 nm laser will be a frequency-doubled vertical external cavity surface-emitting laser (VECSEL). A low-phasenoise local oscillator at 12.6 GHz will also be developed using a micro resonator based on exciting acoustic resonances in aluminum nitride. We will present our proposed approach to developing the micro ion frequency standard and relevant current results.

We argue that it is possible in principle to reduce the uncertainty of an atomic magnetometer by double-passing a far-detuned laser field through the atomic sample as it undergoes Larmor precession. Numerical simulations of the quantum Fisher information suggest that, despite the lack of explicit multi-body coupling terms in the system's magnetic Hamiltonian, the parameter estimation uncertainty in such a physical setup scales better than the conventional Heisenberg uncertainty limit over a specified but arbitrary range of particle number N. Using the methods of quantum stochastic calculus and filtering theory, we demonstrate numerically an explicit parameter estimator (called a quantum particle filter) whose observed scaling follows that of our calculated quantum Fisher information. Moreover, the quantum particle filter quantitatively surpasses the uncertainty limit calculated from the quantum Cramer-Rao inequality based on a magnetic coupling Hamiltonian with only single-body operators. We also show that a quantum Kalman filter is insufficient to obtain super-Heisenberg scaling, and present evidence that such scaling necessitates going beyond the manifold of Gaussian atomic states.

We provide evidence, based on direct simulation of the quantum Fisher information, that 1/N scaling of the sensitivity with the number of atoms N in an atomic magnetometer can be surpassed by double-passing a far-detuned laser through the atomic system during Larmor precession. Furthermore, we predict that for N>>1, the proposed double-pass atomic magnetometer can essentially achieve 1/N scaling without requiring any appreciable amount of entanglement.

We provide evidence, based on direct simulation of the quantum Fisher information, that 1/N scaling of the sensitivity with the number of atoms N in an atomic magnetometer can be surpassed by double-passing a far-detuned laser through the atomic system during Larmor precession. Furthermore, we predict that for N>>1, the proposed double-pass atomic magnetometer can essentially achieve 1/N scaling without requiring any appreciable amount of entanglement.