Progress on indium and barium single ion optical frequency standards

We report progress on 115In+ and 137Ba+ single ion optical frequency standards using all solid-state sources. Both are free from quadrupole field shifts and together enable a search for drift in fundamental constants.Comment: 2 pages, 1 figure, submitted to IEEE/LEOS Summer 2005 Topicals conference proceeding

Laser Phase and Frequency Stabilization Using Atomic Coherence

We present a novel and simple method of stabilizing the laser phase and frequency by polarization spectroscopy of an atomic vapor. In analogy to the Pound-Drever-Hall method, which uses a cavity as a memory of the laser phase, this method uses atomic coherence (dipole oscillations) as a phase memory of the transmitting laser field. A preliminary experiment using a distributed feedback laser diode and a rubidium vapor cell demonstrates a shot-noise-limited laser linewidth reduction (from 2 MHz to 20 kHz). This method would improve the performance of gas-cell-based optical atomic clocks and magnetometers and facilitate laser-cooling experiments using narrow transitions.Comment: 7 pages, 6 figures, appendix on the derivation of Eq.(3) (transfer function for a polarization-spectroscopy-based frequency discriminator) has been adde

Precision measurement of light shifts in a single trapped Ba+^+ ion

Using a single trapped barium ion we have developed an rf spectroscopy technique to measure the ratio of the off-resonant vector ac Stark effect (or light shift) in the 6S_{1/2} and 5D_{3/2} states to 0.1% precision. We find R = Delta_S / Delta_D = -11.494(13) at 514.531 nm where Delta_{S,D} are the light shifts of the m = +/- 1/2 splittings due to circularly polarized light. Comparison of this result with an ab initio calculation of R would yield a new test of atomic theory. By appropriately choosing an off-resonant light shift wavelength one can emphasize the contribution of one or a few dipole matrix elements and precisely determine their values.Comment: 4 pages, 5 figures, in submission to PR

High-Q Fused Silica Micro-Shell Resonators for Navigation-Grade MEMS Gyroscopes

This research aims to develop the resonator for a navigation-grade microelectromechanical system (MEMS) Coriolis vibratory gyroscope (CVG) that will bring inertial navigation capabilities to a wider range of applications by reducing gyroscope size and cost. To achieve the desired gyroscope performance, the gyroscope resonator must have low energy dissipation and a highly symmetric structure. Several challenges arise at the micro-scale due to the increased sensitivity to imperfections and increased susceptibility to energy loss mechanisms. This work investigates the lower limit on energy dissipation in a micro-shell resonator known as the birdbath (BB) resonator. The BB resonator is designed to mitigate the energy loss mechanisms that commonly limit MEMS resonators, including anchor loss and thermoelastic dissipation, through a unique shape and fabrication process and through the use of fused silica as the structural material. A blowtorch molding process is used to form high aspect ratio fused silica shells with a range of wall profiles, providing a high level of control in three dimensions that is not possible with conventional micromachining techniques. Prototype BB resonators were developed prior to this dissertation work but they achieved low quality factors (Q) and low ring-down time constants (T) on the order of 100 thousand and 1 s, respectively. The goal of this work is to drastically increase performance above these initial results. Each relevant energy loss mechanism is considered in order to identify the dominant loss mechanism for a given device. Process improvements are implemented to mitigate each loss mechanism, including improved thermal management during blowtorch molding, cleaner lapping and polishing, reduced upfront surface contamination, and methods to remove contaminants after fabrication. Following optimization, Qs up to 10 million and Ts up to 500 s are measured, representing a marked improvement over the prototype resonators. It is found that BB resonators are now limited by surface loss, as indicated by the observed inverse relationship between Q and surface-to-volume ratio. The surface-loss-limited regime results in a high sensitivity to added surface layers. The addition of a conductive layer to enable electrostatic transduction is found to have a large impact, decreasing Q by 50% with the addition of only 30 angstroms of metal. It is suggested that the origin of this loss may be interfacial slippage due to a large increase in stress that occurs at the interface during oscillation. Experimental investigation into the dependence of Q on conductive layer composition, thickness, deposition conditions, and post-deposition treatments is carried out. Following treatments to removed adsorbed contaminants from the surface, resonators with a 15/50 angstrom Ti/Pt layer are found to maintain 60% of their initial Qs. Indium tin oxide (ITO) is identified as a promising conductive layer candidate, with initial experiments producing shells that maintain 70% of their initial Q. The values of Q and T produced in this work are unprecedented for MEMS resonators. Even accounting for the losses that accompany conductive layer deposition, birdbath resonator gyroscopes are expected to achieve navigation-grade performance.PHDElectrical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/146096/1/taln_1.pd

Optical clocks based on ultra-narrow three-photon resonances in alkaline earth atoms

A sharp resonance line that appears in three-photon transitions between the $^{1}S_{0}$ and $^{3}P_{0}$ states of alkaline earth and Yb atoms is proposed as an optical frequency standard. This proposal permits the use of the even isotopes, in which the clock transition is narrower than in proposed clocks using the odd isotopes and the energy interval is not affected by external magnetic fields or the polarization of trapping light. The method has the unique feature that the width and rate of the clock transition can be continuously adjusted from the $MHz$ level to sub-$mHz$ without loss of signal amplitude by varying the intensities of the three optical beams. Doppler and recoil effects can be eliminated by proper alignment of the three optical beams or by point confinement in a lattice trap. The three beams can be mixed to produce the optical frequency corresponding to the $^{3}P_{0}$ - $^{1}S_{0}$ clock interval.Comment: 10 pages, 4 figures, submitted to PR

Precision measurement of light shifts at two off-resonant wavelengths in a single trapped Ba+ ion and determination of atomic dipole matrix elements

We define and measure the ratio (R) of the vector ac-Stark effect (or light shift) in the 6S_1/2 and 5D_3/2 states of a single trapped barium ion to 0.2% accuracy at two different off-resonant wavelengths. We earlier found R = -11.494(13) at 514.531nm and now report the value at 1111.68nm, R = +0.4176(8). These observations together yield a value of the matrix element, previously unknown in the literature. Also, comparison of our results with an ab initio calculation of dynamic polarizability would yield a new test of atomic theory and improve the understanding of atomic structure needed to interpret a proposed atomic parity violation experiment.Comment: 12 pages, 11 figures, in submission to PR

Studies of the 1^{1}S0_{0}--3^3P0_0 transition in atomic ytterbium for optical clocks and qubit arrays

We report an observation of the weak $6^{1}$S$_{0}$-$6^3$P$_0$ transition in $^{171,173}$Yb as an important step to establish Yb as a primary candidate for future optical frequency standards, and to open up a new approach for qubits using the $^{1}$S$_{0}$ and $^3$P$_0$ states of Yb atoms in an optical lattice.Comment: 5 pages, 3 figure

Preparation of Schr\"odinger cat states with cold ions beyond the Lamb-Dicke limit

A scheme for preparing Schr\"odinger cat (SC) states is proposed beyond the Lamb-Dicke limit in a Raman-$\Lambda$-type configuration. It is shown that SC states can be obtained more efficiently with our scheme than with the former ones.Comment: RevTex 9 pages, no figures and table