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Symposium on Frequency Standards and Metrology

PRECISE MEASUREMENTS OF S-WAVE SCATTERING PHASE SHIFTS WITH A JUGGLING ATOMIC CLOCK

S. D. Gensemer, Russell Hart, R.A. Martin, Xinye Xu, Ronald Legere, Kurt Gibble, S. J. J. M. F. Kokkelmans

Published May 1, 2009• 0 citations
Publisher

Abstract

We demonstrate an interferometric scattering technique that allows highly precise measurements of s-wave scattering phase shifts. We collide two clouds of cesium atoms in a juggling fountain clock. The atoms in one cloud are prepared in a coherent superposition of the two clock states and the atoms in the other cloud in an F,mF state. After the two clouds collide, we detect the scattered part of the clock atom's wavefunction for which the phase of the clock coherence is shifted by the difference of the s-wave phase shifts. In this way, we unambiguously observe the differences of scattering phase shifts. These phase shifts are independent of the atomic density to lowest order, enabling measurements of scattering phase shifts with clock accuracy. Recently, we have observed the changes in scattering phase shifts as a function of magnetic field over a range where Feshbach resonances may be expected and inelastic scattering channels open and close. Measurements like these will tightly constrain our knowledge of cesium-cesium interactions. With such knowledge, future measurements may place stringent limits on the time variation of fundamental constants, such as the electron-proton mass ratio, by precisely probing phase shifts near a Feshbach resonance.

DOI
10.1142/9789812838223_0009

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We demonstrate an interferometric scattering technique that allows highly precise measurements of s-wave scattering phase shifts. We collide two clouds of cesium atoms in a juggling fountain clock. The atoms in one cloud are prepared in a coherent superposition of the two clock states and the atoms in the other cloud in an F,mF state. After the two clouds collide, we detect the scattered part of the clock atom's wavefunction for which the phase of the clock coherence is shifted by the difference of the s-wave phase shifts. In this way, we unambiguously observe the differences of scattering phase shifts. These phase shifts are independent of the atomic density to lowest order, enabling measurements of scattering phase shifts with clock accuracy. Recently, we have observed the changes in scattering phase shifts as a function of magnetic field over a range where Feshbach resonances may be expected and inelastic scattering channels open and close. Measurements like these will tightly constrain our knowledge of cesium-cesium interactions. With such knowledge, future measurements may place stringent limits on the time variation of fundamental constants, such as the electron-proton mass ratio, by precisely probing phase shifts near a Feshbach resonance.
We scan the collision energy of two clouds of cesium atoms between 12 and 50 μK in an atomic fountain clock. By directly detecting the difference of s-wave scattering phase shifts, we observe a rapid variation of a scattering phase shift through a series of Feshbach resonances. At the energies we use, resonances that overlap at threshold become resolved. Our statistical phase uncertainty of 8 mrad can be improved in future precision measurements of Feshbach resonances to accurately determine the Cs-Cs interactions, which may provide stringent limits on the time variation of fundamental constants.
We use an atomic fountain clock to measure quantum scattering phase shifts precisely through a series of narrow, low-field Feshbach resonances at average collision energies below 1 μK. Our low spread in collision energy yields phase variations of order ±π/2 for target atoms in several F, m_{F} states. We compare them to a theoretical model and establish the accuracy of the measurements and the theoretical uncertainties from the fitted potential. We find overall excellent agreement, with small statistically significant differences that remain unexplained.
We present a new method based on a transfer of population by adiabatic passage that allows one to prepare cold atomic samples with a well-defined ratio of atomic density and atom number. This method is used to perform a measurement of the cold collision frequency shift in a laser cooled cesium clock at the percent level, which makes the evaluation of the cesium fountain accuracy at the 10(-16) level realistic. With improvements, the adiabatic passage would allow measurements of density-dependent phase shifts at the 10(-3) level in high precision experiments.
We demonstrate a juggling atomic fountain by launching two laser-cooled balls of 133Cs{}^{133}\mathrm{Cs}133Cs atoms in rapid succession. The atoms collide near the top of the fountain and, by varying the delay between launches, we scan the collision energy from 19 to $150\ensuremath{\mu}\mathrm{K}$. We measure the differential scattering cross section and isolate the contributions from different partial waves including their interferences. We observe the sss-wave energy dependence and the ppp-wave scattering threshold. We infer a triplet sss-wave scattering length of ${\ensuremath{-}400a}_{0}$ and a ppp wave of $({\ensuremath{-}107a}_{0}{)}^{3}$ for ∣F=4,m=4〉+∣3,3〉|F\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}4,m\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}4〉+|3,3〉∣F=4,m=4〉+∣3,3〉.