#### Date of Award

Spring 1-1-2016

#### Document Type

Dissertation

#### Degree Name

Doctor of Philosophy (PhD)

#### Department

Physics

#### First Advisor

Dr. Ana Maria Rey

#### Second Advisor

Dr. Chris Oates

#### Abstract

Oscillators used in timing standards aim to provide a universal, well defined frequency output with minimal random fluctuations. The stability (precision) of an oscillator is highlighted by its quality factor Q = ν_{0}/δν, where ν_{0} is the output frequency with a frequency linewidth of δν. To achieve a high timekeeping precision, an oscillator can operate at high frequency, allowing each partition of time, defined by one oscillation, to be short in duration and thus highly precise. In a similar fashion, because oscillator linewidth determines resolution of the output frequency, a narrow linewidth will yield a highly precise measure of time or frequency. High quality factors are advantageous for two reasons: i) frequency stability sets a fundamental limit to the consistency a clock can partition units of time and ii) measurement precision aids in the the study of physical effects that shift the clock frequency, leading to improved oscillator output control. In the pursuit of high quality factors, state-of-the-art microwave clocks match microwave oscillators to narrow atomic transitions achieving starting oscillator quality factors approaching Q ~ 10^{10}. Exploiting their starting quality factor in tandem with atomic transition properties allows microwave standards to reach a clock frequency uncertainty and precision of a few parts in 10^{16} after a month of averaging. Indeed, with this level of timekeeping, microwave clocks now define the SI second and play central roles in network synchronization, global positioning systems, and tests of fundamental physics.

Naturally, a direct approach to better timekeeping is forming oscillators with higher quality factors, partitioning time into finer intervals. This is realized in the next generation of atomic clocks, based on ultra-narrow *optical* transitions in an atom, capable of reaching quality factors of Q > 4 x 10^{15}. Optical clock quality factors allow operation of frequency standards in a measurement regime unobtainable by microwave standards, promising orders of magnitude improvement in frequency metrology. This thesis describes the design and realization of an optical frequency standard based on an ensemble of optically trapped, laser-cooled ^{171}Yb atoms. The frequency stability between two ^{171}Yb clock systems is presented here, demonstrating the first realized 10^{-18} level measurement precision reaching 1.6 x 10^{-18} after 25,000 s of averaging, a 100 fold improvement over state-of-the-art microwave sources. Leveraging a much improved measurement precision allows a detailed investigation of key physical phenomena that shift the atomic transition frequency. An in-depth study of these systematic shifts is discussed in detail here, with a focus on blackbody radiation shift and trap light induced frequency shifts. This study results in a total fractional uncertainty in the ytterbium clock transition frequency of 2.1 x 10^{-18}. Finally, the robust operation of ^{171}Yb clock systems at the 10^{-18} fractional level is discussed in detail here.

#### Recommended Citation

Hinkley, Nathan, "An Atomic Clock for 10^-18 Timekeeping" (2016). *Physics Graduate Theses & Dissertations*. 191.

https://scholar.colorado.edu/phys_gradetds/191