We used an atom interferometer for atom optical shop testing of lenses for atomic de Broglie waves. We measured focal lengths and spherical aberrations of electrostatic lenses in three independent ways based on contrast data, phase data, or calculations of de Broglie wavefront curvature. We report focal lengths of -2.5 km and -21.7 km with 5% uncertainty for different lenses. All three methods give consistent results. Understanding how lenses magnify and distort atom interference fringes helps improve atom beam velocity measurements made with phase choppers [New J. Phys. 13, 115007 (2011)], which in turn will improve the accuracy of atomic polarizability measurements.
We used an atom interferometer for atom optical shop testing of lenses for atomic de Broglie waves. We measured focal lengths and spherical aberrations of electrostatic lenses in three independent ways based on contrast data, phase data, or calculations of de Broglie wavefront curvature. We report focal lengths of -2.5 km and -21.7 km with 5% uncertainty for different lenses. All three methods give consistent results. Understanding how lenses magnify and distort atom interference fringes helps improve atom beam velocity measurements made with phase choppers [New J. Phys. 13, 115007 (2011)], which in turn will improve the accuracy of atomic polarizability measurements.
To improve precision measurements made with atom interferometers, the effect of de Broglie wave-front curvature induced by a lens inside an atom interferometer is experimentally demonstrated and theoretically analyzed. Electrostatic lenses shift, magnify, and distort atom interference fringes, which modifies the phase and the contrast of the interference signals. Informed by these observations, an improved method is presented for analyzing measurements of atomic beam velocity distributions using phase choppers [W. F. Holmgren, I. Hromada, C. E. Klauss, and A. D. Cronin, New J. Phys. 13, 115007 (2011)].
Atom interferometers, in which de Broglie waves are coherently split and recombined to make interference fringes, now serve as precision measurement tools for several quantities in physics. Examples include measurements of Newton's constant, the fine structure constant, van der Waals potentials, and atomic polarizabilities. To make next-generation measurements of static electric dipole atomic polarizabilities with an atom beam interferometer, I worked on new methods to precisely measure the velocity distribution for atom beams. I will explain how I developed and used phase choppers to measure lithium, sodium, potassium, and cesium atomic beam velocities with 0.07% accuracy. I also present new measurements of polarizability for these atoms. I classify systematic errors into two broad categories: (1) fractional errors that are similar for all different types of atoms in our experiments, and (2), errors that scale with de Broglie wavelength or inverse atomic momentum in our experiments. This distinction is important for estimating the uncertainty in our measurements of ratios of atomic polarizabilities, e.g., αCs / αNₐ = 2.488(12).
We describe a new method to measure atom beam velocity in an atom interferometer using phase choppers. Phase choppers are analogous to mechanical chopping discs, but rather than being transmitted or blocked by mechanical choppers, an atom receives different differential phase shifts (e.g. zero or π radians) from phase choppers. Phase choppers yield 0.1% uncertainty measurements of beam velocity in our interferometer with 20 min of data and enable new measurements of polarizability with unprecedented precision.
We have built an atom interferometer and, by applying an electric field on one of the two interfering beams, we have measured the static electric polarizability of lithium $\ensuremath{\alpha}=(24.33\ifmmode\pm\else\textpm\fi{}0.16)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}30}\phantom{\rule{0.3em}{0ex}}{\mathrm{m}}^{3}$ with a 0.66% uncertainty. Our experiment is similar to an experiment done on sodium in 1995 by Pritchard and co-workers, with several improvements: the electric field can be calculated analytically and the interference signals have a large intensity and a high visibility, resulting in accurate phase measurements. This experiment illustrates the extreme sensitivity of atom interferometry: when the atom enters the electric field, its velocity increases and the fractional change, equal to $4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}$ for our largest field, is measured with a ${10}^{\ensuremath{-}3}$ accuracy.
I used a Mach-Zehnder atom interferometer to measure the static electric-dipole polarizabilities of K, Rb, and Cs atoms with 0.11\% uncertainty. Static polarizability measurements serve as benchmark tests for 𝑎𝑏 𝑖𝑛𝑖𝑡𝑖𝑜 atomic structure calculations. Calculating atomic properties such as polarizabilities, van der Waals coefficients, state lifetimes, or oscillator strengths involves accurately calculating the valence electrons' electric-dipole transition matrix elements. Additionally, testing Cs atomic structure calculations helps interpret the results of parity non-conservation experiments, which in turn places constraints on beyond-the-standard-model physics. I discuss improvements to our experiment that allowed us to measure static polarizabilities with 0.11% uncertainty, and we present our results in the context of recent 𝑎𝑏 𝑖𝑛𝑖𝑡𝑖𝑜 and semi-empirical static polarizabilities and recent, high-precision measurements of excited state lifetimes and van der Waals C₆ coefficients. I also used our interferometer to develop a new technique for inertial sensing. High precision, portable, atom-interferometer gyroscopes and accelerometers are desirable for self-contained inertial navigation and in the future may be used for tests of General Relativity and searches for gravitational waves using satellite-mounted inertial sensors. Satellite-mounted atom interferometers are challenging to build because of size, weight, power, and reliability constraints. Atom interferometers that use nanogratings to diffract atoms are attractive for satellite-mounted inertial sensing applications because nanogratings weigh approximately nothing and require no power. We developed a new 𝑖𝑛 𝑠𝑖𝑡𝑢 measurement technique using our nanograting atom interferometer, and we used it to measure inertial forces for the benefit of our static polarizability measurements. I also review how to calculate the sensitivity of a nanograting atom interferometer, and I employed these calculations in order to design a portable, nanograting atom interferometer inertial sensor.
Atom interferometers have been successfully applied for precision measurements and the realization of basic gedanken experiments [1]. They consist of three or more atom optical elements to split, redirect, and recombine the motional state of the atoms. These elements are implemented either by freestanding microstructures or by light fields. For high precision applications, such as gyroscopes [2–5], a large throughput of the initial atomic flux is advantageous [6]. In order to efficiently use all atoms in an uncollimated thermal atomic beam, the ideal atom interferometer should produce equally spaced fringes for a wide range of transverse and longitudinal velocities. So called “white light” interferometers solve the problem for different longitudinal velocities by the recombination of only two velocity independent transverse momentum states at the output of the interferometer. Examples for this are the three-grating interferometer [7], operating with a transversely collimated beam, and the Raman interferometer [8]. Operation using a transversely uncollimated atomic beam can also be realized by the Raman interferometer and, for interferometers that do not require light, by the Talbot-Lau interferometer [9]. The latter, in contrast to Ref. [7], operates with three gratings in the Fresnel regime of matter wave diffraction. Since, in this case, many different momentum components build up the interference pattern, the typical length scale of the setup, the Talbot length, depends on the atomic velocity. The Talbot-Lau interferometer is, therefore, chromatic. In this work, we study a charged wire as the central element in an atom interferometer that requires only microstructures, operates in the Fresnel regime, and accepts, therefore, an uncollimated beam of atoms. At the same time, it has essentially white light character over the range of the atomic velocities in our thermal atomic beam. This makes future extensions of our approach based on microstructures potentially as powerful as, for example, the Raman interferometer gyroscope [5]. The attractive interaction between the induced dipole and the charged wire redirects the atomic trajectories to form a simple interferometer with two spatially separated paths. It can, therefore, also be used to measure the recently proposed topological phase shifts for moving electric dipoles [10–13].