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arXiv:1708.03715 · Physical Review Letters

Atomic Clock Measurements of Quantum Scattering Phase Shifts Spanning Feshbach Resonances at Ultralow Fields

Aaron Bennett, Kurt Gibble, S. J. J. M. F. Kokkelmans, Jeremy M. Hutson

Published Sep 15, 2017• 7 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.119.113401

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Abstract : The grant as in support of a research program to explore the possibility of a microwave atomic clock based on an atomic fountain of cesium atoms. During the two year granting period, the following work was done: A large magneto-optic trap in a vapor cell was constructed where over 4x 10(exp 10) atoms were trapped at a density on the order of 10(exp 11) atoms/cu cm. This work increased the number of atoms optically trapped by a factor of -400 compared to previous work. The optical density of the atoms in this trap has a peak attenuation of e(-175). In an invited review article we examined the prospects for slow atom frequency standards. Most of the systematic effects that limit the current accuracy today's frequency standards decrease as the velocity of the atoms is reduced. We identified the one possible exception: collisions between ultra-cold atom in an atomic fountain could induce a phase shift that would ultimately limit the accuracy of the fountain clock. We brought the problem to the attention of B. Verhaar, who began a series of calculations on the effects of low energy collisions. jg p.4

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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 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 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 have observed Feshbach resonances for 133Cs{}^{133}\mathrm{Cs}133Cs atoms in two different hyperfine states at static magnetic fields of a few milligauss. These resonances are unusual for two main reasons. First, they are the lowest static-field resonances investigated up to now, and we explain their multipeak structure in these ultralow fields. Second, they are robust with respect to temperature effects. We have measured them using an atomic fountain clock and reproduced them using coupled-channels calculations, which are in excellent agreement with our measurements. We show that these are sss-wave resonances due to a very weakly bound state of the triplet molecular Hamiltonian. We also describe a model explaining their asymmetric shape in the regime where the kinetic energy dominates over the coupling strength.
One of the main limitations of cesium atomic fountains has been the cold collision frequency shift. By using a method based on a transfer of population by adiabatic passage allowing to prepare cold atomic samples with a well defined ratio of atomic density as well as atom number the collisional shift is controlled at the 10E-3 of its value. A calibration of Zeeman sub-states contribution to the clock shift as a function of the field has been performed. Feshbach resonances have been observed for the first time at very low magnetic field and with a very good resolution. A Monte Carlo simulation has been performed and could fit properly some of experimental data. This constrains some parameters of the theory of collisions.
Abstract : The grant as in support of a research program to explore the possibility of a microwave atomic clock based on an atomic fountain of cesium atoms. During the two year granting period, the following work was done: A large magneto-optic trap in a vapor cell was constructed where over 4x 10(exp 10) atoms were trapped at a density on the order of 10(exp 11) atoms/cu cm. This work increased the number of atoms optically trapped by a factor of -400 compared to previous work. The optical density of the atoms in this trap has a peak attenuation of e(-175). In an invited review article we examined the prospects for slow atom frequency standards. Most of the systematic effects that limit the current accuracy today's frequency standards decrease as the velocity of the atoms is reduced. We identified the one possible exception: collisions between ultra-cold atom in an atomic fountain could induce a phase shift that would ultimately limit the accuracy of the fountain clock. We brought the problem to the attention of B. Verhaar, who began a series of calculations on the effects of low energy collisions. jg p.4