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.
Atom interferometers typically use the total populations at the interferometer's output ports as the signal, but useful information can be encoded into spatial phase patterns. An interferometer translates the phase pattern into a measurable pattern in the atomic density that we use to perform a direct precision measurement of the
7Li tune-out wavelength near 671 nm. Expressed as a detuning from the $|2{S}_{1/2},F=2\ensuremath{\rangle}\ensuremath{\rightarrow}|2{P}_{1/2},{F}^{\ensuremath{'}}=2\ensuremath{\rangle}$ transition, we find 3329.5(1.4) MHz for the tensor-shifted tune out of the $|2{S}_{1/2},F=2,{m}_{F}=0\ensuremath{\rangle}$ state with ${\ensuremath{\sigma}}^{\ifmmode\pm\else\textpm\fi{}}$ light polarization and 3310.6(4.9) MHz for the tune out of the scalar polarizability. This technique may be generalized for directly sensing spatially varying phase profiles.
We have measured the tune-out wavelength of lithium isotope
7Li at 671 nm. We have used our atom interferometer to measure the phase shift due to the dynamical Stark effect as a function of the laser frequency when a laser beam was focused on a single interferometer arm. The tune-out wavelength is a function of the hyperfine
F,mF sublevel, and we have prepared the atoms in the sublevel
F=2,mF=+2 or $\ensuremath{-}2$. We find that the tune-out frequency of the
F=2,mF=+2 sublevel is at
3388(8)MHz to the blue of the $^{2}S_{1/2},F=1\ensuremath{\rightarrow}^{2}P_{1/2},{F}^{\ensuremath{'}}=2$ transition, the accuracy of this measurement being limited by imperfect optical pumping. This measurement is in excellent agreement with its theoretical value, and, once corrected for different tensorial contributions, our measurement agrees with the more precise measurement of Copenhaver et al. [Phys. Rev. A 100, 063603 (2019)], who also used atom interferometry but different experimental conditions.