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arXiv:quant-ph/0305184 · Physical Review Letters

Dispersion Compensation for Atom Interferometry

Tony Roberts, Alexander D. Cronin, Martin V. Tiberg, David E. Pritchard

Published Feb 12, 2004• 23 citations
arXivHTMLPDF

Abstract

A new technique for maintaining high contrast in an atom interferometer is used to measure large de Broglie wave phase shifts. Dependence of an interaction induced phase on the atoms' velocity is compensated by applying an engineered counterphase. The counterphase is equivalent to a rotation, is precisely determined by a frequency, and can be used to measure phase shifts due to interactions of unknown strength. Phase shifts of 150 rad (5 times larger than previously possible) have now been measured in an atom beam interferometer, and we suggest that this technique can enable comparisons of atomic polarizability with precision of one part in 10,000.

DOI
10.1103/physrevlett.92.060405

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A new technique for maintaining high contrast in an atom interferometer is used to measure large de Broglie wave phase shifts. Dependence of an interaction induced phase on the atoms' velocity is compensated by applying an engineered counterphase. The counterphase is equivalent to a rotation, is precisely determined by a frequency, and can be used to measure phase shifts due to interactions of unknown strength. Phase shifts of 150 rad (5 times larger than previously possible) have now been measured in an atom beam interferometer, and we suggest that this technique can enable comparisons of atomic polarizability with precision of one part in 10,000.
We reanalyzed our atom interferometer measurement of the electric polarizability of lithium, now accounting for the Sagnac effect due to the Earth's rotation. The resulting correction to the polarizability is very small, but the visibility as a function of the applied phase shift is now better explained. The fact that the Sagnac and polarizability phase shifts are both proportional to ${v}^{\ensuremath{-}1}$, where vvv is the atom velocity, suggests that a phase shift of the Sagnac type could be used as a counterphase to compensate for the electric polarizability phase shift. This exact compensation opens the way to higher-accuracy measurements of atomic polarizabilities, and we discuss how this can be done in practice and the final limitations of the proposed technique.
We used the Toulouse atom interferometer to study how Van der Waals (VdW) interactions between atoms and surfaces cause velocity-dependent phase shifts for atomic de Broglie waves. By introducing a thin nano-grating in one branch of this interferometer, we observed a phase shift that depends on velocity to the power −0.49. This dispersion serves to measure both the strength and the position dependence of the atom-surface potential in the range from 5 to 10 nm from the surface, and it can also set new limits on non-Newtonian gravity in the 2 nm range.
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, 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).
Gravity gradients represent a major obstacle in high-precision measurements by atom interferometry. Controlling their effects to the required stability and accuracy imposes very stringent requirements on the relative positioning of freely falling atomic clouds, as in the case of precise tests of Einstein's equivalence principle. We demonstrate a new method to exactly compensate the effects introduced by gravity gradients in a Raman-pulse atom interferometer. By shifting the frequency of the Raman lasers during the central π pulse, it is possible to cancel the initial position- and velocity-dependent phase shift produced by gravity gradients. We apply this technique to simultaneous interferometers positioned along the vertical direction and demonstrate a new method for measuring local gravity gradients that does not require precise knowledge of the relative position between the atomic clouds. Based on this method, we also propose an improved scheme to determine the Newtonian gravitational constant G towards the 10 ppm relative uncertainty.