Systematics of zero-energy phase shifts for atomic ions

Aaron M. Hankin, Ethan Clements, Yao Huang +5 more

We describe a framework for calculating the frequency shift and uncertainty of trapped-ion optical atomic clocks caused by background-gas collisions, and apply this framework to an $^{27}\mathrm{Al}^{+}$ clock to enable a total fractional systematic uncertainty below ${10}^{\ensuremath{-}18}$. For this clock, with 38(19) nPa of room-temperature ${\mathrm{H}}_{2}$ background gas, we find that collisional heating generates a non-thermal distribution of motional states with a mean time-dilation shift of order ${10}^{\ensuremath{-}16}$ at the end of a 150 ms probe, which is not detected by sideband thermometry energy measurements. However, the contribution of collisional heating to the spectroscopy signal is highly suppressed and we calculate the BGC shift to be $\ensuremath{-}0.6(2.4)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}19}$, where the shift is due to collisional heating time dilation and the uncertainty is dominated by the worst case $\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2$ bound used for collisional phase shift of the $^{27}\mathrm{Al}^{+}$ superposition state. We experimentally validate the framework and determine the background-gas pressure in situ using measurements of the rate of collisions that cause reordering of mixed-species ion pairs.

Sabre Kais, Juan Pablo Neirotti, Pablo Serra

Charles Potter Holmes

Raisa Trubko

This Dissertation describes how I used a three nanograting Mach-Zehnder atom beam interferometer to precisely measure a wavelength of light, known as a tune-out wavelength, that causes zero energy shift for an atom. I also describe how such measurements can be remarkably sensitive to rotation rates. It is well known that atom interferometry can be used to measure accelerations and rotations, but it was a surprise to find out that tune-out wavelength measurements can under certain conditions be used to report the absolute rotation rate of the laboratory with respect to an inertial frame of reference. I also describe how we created conditions which improve the accuracy of tune out wavelength measurements. These measurements are important because they serve as a benchmark test for atomic structure calculations of line strengths, oscillator strengths, and dipole matrix elements. I present a new measurement of the longest tune-out wavelength in potassium, λzero = 768.9701(4) nm. To reach sub-picometer precision, an optical cavity surrounding the atom beam paths of the interferometer was used. Although this improved the precision of our experiment by increasing the light-induced phase shifts, the cavity also brought several systematic errors to our attentions. For example, I found that large ±200 pm shifts in tune-out wavelengths can occur due to the Earth's rotation rate. To solve this problem, I demonstrated that controlling the optical polarization, the magnetic field, and the atom beam velocity distribution can either suppress or enhance these systematic shifts. Suppressing these systemic shifts in tune-out wavelengths is useful for precision measurements used to test atomic structure calculations. By enhancing these systematic shifts, the interferometer can be a gyroscope that utilizes tune-out wavelengths.

Ming Li

Amar C. Vutha, Tom Kirchner, P. Dubé

Summary form only given. As the performance of optical atomic clocks improves steadily, new sources of systematic errors need to be evaluated with increasingly higher accuracy. At present, the collisional frequency shift (CFS), due to interactions with background gas atoms in the environment of the clock ions, is in some cases the next-to-leading source of systematic uncertainty for trapped-ion optical clocks. Existing approaches towards evaluating the CFS have either assumed that only glancing-angle collisions are relevant, or assumed a worst-case scenario for the phase shift imparted to clock state superposition by a collision. The former approach, which was developed for laser-cooled cesium clocks, is not applicable to the deeply trapped atomic ions used in optical clocks, while the latter approach is likely to significantly overestimate the CFS. To address this problem we have developed a framework, based on a non-perturbative quantum channel description of the collision process. Our method leads to a convenient master equation and a compact expression for the CFS. In particular, this framework can be used to estimate the CFS in situations involving many partial waves and large collisional phase shifts, which is the case with thermal background gas atoms scattering off a clock ion. Our method lends itself to practical evaluations of the CFS, by using readily calculated molecular potential curves for the ion-background gas system to extract the collisional phase shifts which lead to the CFS. As an application of this method to a realistic and relevant situation, we have numerically estimated the frequency shift of the 674 nm clock transition in Sr+due to collisions with background helium gas. We find that the CFS is much smaller than the worst-case estimate. In this talk, we describe the theoretical background and motivate the steps that lead to our framework for calculating the CFS. Following this, we present our calculations for the Sr+-He system as an example of the general method, and discuss possible extensions and improvements that will allow us to evaluate the CFS for the Sr+clock at the National Research Council Canada.