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arXiv:1406.4979 · Physical Review Letters

Quantum Test of the Universality of Free Fall

Dennis Schlippert, J. Hartwig, H. Albers, L. Richardson, Christian Schubert, Albert Roura, Wolfgang P. Schleich, Wolfgang A. Ertmer, Ernst Maria Rasel

Published May 22, 2014• 331 citations
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Abstract

We simultaneously measure the gravitationally-induced phase shift in two Raman-type matter-wave interferometers operated with laser-cooled ensembles of $^{87}$Rb and $^{39}$K atoms. Our measurement yields an Eötvös ratio of $η_{\text{Rb,K}}=(0.3\pm 5.4)\times 10^{-7}$. We briefly estimate possible bias effects and present strategies for future improvements.

DOI
10.1103/physrevlett.112.203002

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We simultaneously measure the gravitationally-induced phase shift in two Raman-type matter-wave interferometers operated with laser-cooled ensembles of 87^{87}87Rb and 39^{39}39K atoms. Our measurement yields an Eötvös ratio of ηRb,K=(0.3±5.4)×10−7η_{\text{Rb,K}}=(0.3\pm 5.4)\times 10^{-7}ηRb,K​=(0.3±5.4)×10−7. We briefly estimate possible bias effects and present strategies for future improvements.
We report a test of the universality of free fall by comparing the gravity acceleration of the ^{87}Rb atoms in m_{F}=+1 versus those in m_{F}=-1, of which the corresponding spin orientations are opposite. A Mach-Zehnder-type atom interferometer is exploited to alternately measure the free fall acceleration of the atoms in these two magnetic sublevels, and the resultant Eötvös ratio is η_{S}=(0.2±1.2)×10^{-7}. This also gives an upper limit of 5.4×10^{-6} m^{-2} for a possible gradient field of the spacetime torsion. The interferometer using atoms in m_{F}=±1 is highly sensitive to the magnetic field inhomogeneity. A double differential measurement method is developed to alleviate the inhomogeneity influence, of which the effectiveness is validated by a magnetic field modulating experiment.
Quantum Tests of the Universality of Free FallIn the process of formulating a "theory of everything" that aims to provide a self-contained model of modern physics by unifying all four fundamental interactions, two theoretical frameworks have yielded important contributions: quantum mechanics, which can explain the nature of physics at the most microscopic length scales such as the origin of spectra of electrons bound in atomic systems, and Einstein's general relativity, that conveys our understanding of gravity over the largest distances across the universe.Although no theory of "quantum gravity", that is consistent over all energy scales, exists to date, certain modifications may enable a reconciliation of quantum mechanics and general relativity.These approaches allow for violations of the universality of free fall (UFF), that among Lorentz invariance and local position invariance constitute Einstein's equivalence principle.The UFF states that all bodies, located at the same space-time point, experience the same acceleration in a gravitational field independently of their composition.Because of its central role in modern physics the UFF has been tested extensively in many experiments, most of which utilized classical test masses.Quantum mechanical tests of the UFF differ from classical ones in various aspects such as the coherence length and spin polarization of the test masses.In this thesis, the first inertial-sensitive matter wave interferometer comparing the free fall of two different elements, 87 Rb and 39 K, was realized.This quantum test of the UFF yielded an Eötvös ratio 𝜂 Rb,K = (0.3 ± 5.4) × 10 -7 , and was limited by statistical uncertainty.In this work, an existing apparatus for rubidium interferometry was extended to the use of potassium and the first inertial-sensitive potassium matter wave interferometer with a resolution to gravitational acceleration of 𝜎 K = 3 × 10 -6 m/s 2 after 4096 s integration has been demonstrated.A description of the experiment including the technical realization and the techniques used is provided.Specifically, the challenges imposed by the use of potassium, which in comparison to rubidium has a smaller mass and lower hyperfine energy splitting, are examined.The thesis furthermore discusses an assessment of the systematic effects influencing the dual species measurement and presents future strategies to further improve the performance of the apparatus.As a preliminary result, it was possible to improve the potassium short-term sensitivity to gravitational acceleration to 𝜎 K = 2.1 × 10 -5 m/s 2 / √ Hz.The results of this thesis pave the way for exciting future experiments to be performed in large-scale apparatuses and in space.
We perform a precision atom interferometry experiment to test the universality of free fall. Our experiment employs the Bragg atom interferometer with 87Rb atoms either in hyperfine state F = 1 , m F = 0 or F = 2 , m F = 0 , and the wave packets in these two states are diffracted by one pair of Bragg beams alternatively, which is helpful for suppressing common-mode systematic errors. We obtain an Eötvös ratio η 1 − 2 = 0.9 ± 2.7 × 10 − 10 , and set a new record on the precision with improvement of nearly 5 times. This measurement also provides constraint on the difference of the diagonal terms of the mass-energy operator.
To date, no framework combining quantum field theory and general relativity and hence unifying all four fundamental interactions, exists. Violations of the Einstein's equivalence principle (EEP), being the foundation of general relativity, may hold the key to a theory of quantum gravity. The universality of free fall (UFF), which is one of the three pillars of the EEP, has been extensively tested with classical bodies. Quantum tests of the UFF, e.g. by exploiting matter wave interferometry, allow for complementary sets of test masses, orders of magnitude larger test mass coherence lengths and investigation of spin-gravity coupling. We review our recent work towards highly sensitive matter wave tests of the UFF on ground. In this scope, the first quantum test of the UFF utilizing two different chemical elements, Rb-87 and K-39, yielding an Eötvös ratio η Rb,K=(0.3±5.4)×10−7η_{\,\text{Rb,K}}=(0.3\pm 5.4)\times 10^{-7}ηRb,K​=(0.3±5.4)×10−7 has been performed. We assess systematic effects currently limiting the measurement at a level of parts in 10810^8108 and finally present our strategies to improve the current state-of-the-art with a test comparing the free fall of rubidium and ytterbium in a very long baseline atom interferometry setup. Here, a 10 m baseline combined with a precise control of systematic effects will enable a determination of the Eötvös ratio at a level of parts in 101310^{13}1013 and beyond, thus reaching and overcoming the performance limit of the best classical tests.
We demonstrate how simultaneously operated 39K–87Rb interferometers exhibiting a high level of correlation can be used to make competitive tests of the university of free fall. This work provides an overview of our experimental apparatus and data analysis procedure, including a detailed study of systematic effects. With a total interrogation time of 2T=40 ms in a compact apparatus, we reach a statistical uncertainty on the measurement of the Eötvös parameter of 7.8×10−8 after 2.4×104 s of integration. The main limitations of our measurements arise from a combination of wavefront aberrations, the quadratic Zeeman effect in 39K, parasitic interferometers in 87Rb, and the velocity sensitivity of our detection system. These systematic errors limit the accuracy of our measurement to η=0.9(1.6)×10−6. We discuss prospects for improvements using ultracold atoms at extended interrogation times.