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Science

A quantum test of free fall

Ian S. Osborne

Published Jul 28, 2016• 0 citations
Publisher

Abstract

Physics![Figure][1] The Leaning Tower of Pisa, Italy PHOTO: © STEFANO POLITI MARKOVINA/ALAMY STOCK PHOTO Galileo Galilei is purported to have dropped objects of different mass from the Leaning Tower of Pisa to demonstrate that they fall at the same rate. In formulating his general theory of relativity, Einstein described this as the universality of free fall—that all objects, irrespective of their mass, will behave identically when subject to the same gravitational field. Taking this into the quantum regime, Duan et al. performed Galileo's drop experiment with rubidium atoms of different quantum mechanical spins. With a sensitive atom-interferometer setup, they showed that the atoms fall at the same rate to within one part in 10 million, upholding Einstein's universality proposition for now. While we await a theory that can unify relativity and the principles of quantum mechanics, such precision-based experimental tests should help place bounds on any proposed theories of quantum gravity. Phys. Rev. Lett. 117 , 023001 (2016). [1]: pending:yes

DOI
10.1126/science.353.6298.459-g

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•Jan 1, 2020•0 citations
PhysicsFigure
The Leaning Tower of Pisa, Italy
PHOTO: © STEFANO POLITI MARKOVINA/ALAMY STOCK PHOTO
Galileo Galilei is purported to have dropped objects of different mass from the Leaning Tower of Pisa to demonstrate that they fall at the same rate. In formulating his general theory of relativity, Einstein described this as the universality of free fall—that all objects, irrespective of their mass, will behave identically when subject to the same gravitational field. Taking this into the quantum regime, Duan et al. performed Galileo's drop experiment with rubidium atoms of different quantum mechanical spins. With a sensitive atom-interferometer setup, they showed that the atoms fall at the same rate to within one part in 10 million, upholding Einstein's universality proposition for now. While we await a theory that can unify relativity and the principles of quantum mechanics, such precision-based experimental tests should help place bounds on any proposed theories of quantum gravity.
Phys. Rev. Lett. 117 , 023001 (2016).
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.
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.
The quantum analogue of Galileo's leaning tower experiment is revisited using wave packets evolving under the gravitational potential. We first calculate the position detection probabilities for particles projected upwards against gravity around the classical turning point and also around the point of initial projection, which exhibit mass dependence at both these points. We then compute the mean arrival time of freely falling particles using the quantum probability current, which also turns out to be mass dependent. The mass dependence of both the position detection probabilities and the mean arrival time vanish in the limit of large mass. Thus, compatibility between the weak equivalence principle and quantum mechanics is recovered in the macroscopic limit of the latter.
Albert Einstein's insight that it is impossible to distinguish a local experiment in a "freely falling elevator" from one in free space led to the development of the theory of general relativity. The wave nature of matter manifests itself in a striking way in Bose-Einstein condensates, where millions of atoms lose their identity and can be described by a single macroscopic wave function. We combine these two topics and report the preparation and observation of a Bose-Einstein condensate during free fall in a 146-meter-tall evacuated drop tower. During the expansion over 1 second, the atoms form a giant coherent matter wave that is delocalized on a millimeter scale, which represents a promising source for matter-wave interferometry to test the universality of free fall with quantum matter.
The weak equivalence principle (WEP), that is, the universality of free fall, states that all point-like neutral particles in a gravitational field fall in the same way. This is the basis of the geometrization of the gravitational interaction. Together with further requirements on the behavior of point particles, light propagation and clocks one can show that gravity is modeled by a Riemannian geometry. Since in the quantum domain all objects are extended, it is not clear whether the notion of a WEP in the quantum domain makes sense at all. We show that for matter wave interferometry the notion of WEP still can be given a meaning. We give a short overview over schemes which allows a violation of the WEP and emphasize that there are also schemes which show that there might be violations of the WEP in the quantum regime which are not present classically. This makes a test of the WEP with quantum matter necessary. We also give a brief outline of the efforts made for testing the WEP with interferometry with cold atoms in the Bremen drop tower carried out by the QUANTUS and PRIMUS collaboration.
The search for a fundamental, self-consistent theoretical framework to cover phenomena over all energy scales is possibly the most challenging quest of contemporary physics. Approaches to reconcile quantum mechanics and general relativity entail the modification of their foundations such as the equivalence principle. This corner stone of general relativity is suspected to be violated in various scenarios and is therefore under close scrutiny. Experiments based on the manipulation of cold atoms are excellently suited to challenge its different facets. Freely falling atoms constitute ideal test masses for tests of the universality of free fall in interferometric setups. Moreover, the superposition of internal energy eigenstates provides the notion of a clock, which allows to perform tests of the gravitational redshift. Furthermore, as atom interferometers constitute outstanding phasemeters, they hold the promise to detect gravitational waves, another integral aspect of general relativity. In recent years, atom interferometers have developed into versatile sensors with excellent accuracy and stability, and allow to probe physics at the interface of quantum mechanics and general relativity without classical analog. In this thesis, various aspects regarding tests of general relativity with atom interferometry have been theoretically investigated. This includes the analysis of fundamental effects as well as feasibility studies of experimental configurations. The work is partially focussed on a space-borne mission scenario for a dedicated quantum test of the universality of free fall beyond state-of-the-art by dropping matter waves of different elements. To enable the target accuracy at the level of 10^(−17), a compensation scheme has been developed and discussed, mitigating the detrimental effects of imperfect test mass co-location upon release and relaxing the requirements on the source preparation by several orders of magnitude. In addition, it was demonstrated that the careful design of quantum degenerate sources is indispensable for these experiments, requiring tailored schemes to prepare miscible binary sources. The possibility to test the gravitational redshift with atom interferometers has also been examined in this thesis and connected to the ideas of clock interferometry. With the proof that closed light pulse atom interferometers without transitions between internal internal states are not sensitive to gravitational time dilation, an ongoing scientific debate has been resolved. Instead, certain configurations were shown to implement a quantum version of the special-relativistic twin paradox, for which an experiment has been proposed. Finally, requirements on atomic sources and atom optics for scenarios of gravitational wave detection on ground and in space have been investigated.