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arXiv:2001.10104

Phononic gravity gradiometry with Bose-Einstein condensates

Tupac Bravo, Dennis Rätzel, Ivette Fuentes

Published Jan 27, 2020• 7 citations
arXivHTMLPDF

Abstract

Gravity gradiometry with Bose-Einstein condensates (BECs) has reached unprecedented precisions. The basis of this technique is the measurement of differential forces by interference of single-atom wave functions. In this article, we propose a gradiometry scheme where phonons, the collective oscillations of a trapped BEC's atoms are used instead. We show that our scheme could, in principle, enable high-precision measurements of gravity gradients of bodies such as the Earth or small spheres with masses down to the milligram scale. The fundamental error bound of our gravity gradiometry scheme corresponds to a differential force sensitivity in the nano-gal range per experimental realization on the length scale of the BEC.

DOI
10.48550/arxiv.2001.10104

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Gravity gradiometry with Bose-Einstein condensates (BECs) has reached unprecedented precisions. The basis of this technique is the measurement of differential forces by interference of single-atom wave functions. In this article, we propose a gradiometry scheme where phonons, the collective oscillations of a trapped BEC's atoms are used instead. We show that our scheme could, in principle, enable high-precision measurements of gravity gradients of bodies such as the Earth or small spheres with masses down to the milligram scale. The fundamental error bound of our gravity gradiometry scheme corresponds to a differential force sensitivity in the nano-gal range per experimental realization on the length scale of the BEC.
A description of the dynamical response of uniformly trapped Bose–Einstein condensates (BECs) to oscillating external gravitational fields is developed, with the inclusion of damping. Two different effects that can lead to the creation of phonons in the BEC are identified; direct driving and parametric driving. Additionally, the oscillating gravitational field couples phonon modes, which can lead to the transition of excitations between modes. The special case of the gravitational field of a small, oscillating sphere located closely to the BEC is considered. It is shown that measurement of the effects may be possible for oscillating source masses down to the milligram scale, with a signal to noise ratio of the order of 10. To this end, noise terms and variations of experimental parameters are discussed and generic experimental parameters are given for specific atom species. The results of this article suggest the utility of BECs as sensors for the gravitational field of very small oscillating objects which may help pave the way towards gravity experiments with masses in the quantum regime.
Squeezed, nonclassical states are an integral tool of quantum metrology due to their ability to push the sensitivity of a measurement apparatus beyond the limits of classical states. While their creation in light has become a standard technique, the production of squeezed states of the collective excitations in gases of ultracold atoms, the phonons of a Bose-Einstein condensate (BEC), is a comparably recent problem. This task is continuously gaining relevance with a growing number of proposals for BEC-based quantum metrological devices and the possibility to apply them in the detection of gravitational waves. The objective of this thesis is to find whether the recently described effect of an oscillating external potential on a uniform BEC can be exploited to generate two-mode squeezed phonon states, given present day technology. This question brings together elements of a range of fields beyond cold atoms, such as general relativity and Efimov physics. To answer it, the full transformation caused by the oscillating potential on an initially thermal phononic state is considered, allowing to find an upper bound for the magnitude of this perturbation as well as to quantify the quality of the final state with respect to its use in metrology. These findings are then applied to existing experiments to judge the feasibility of the squeezing scheme and while the results indicate that they are not well suited for it, a setup is proposed that allows for its efficient implementation and seems within experimental reach. In view of the vast parameter space leaving room for optimization, the considered mechanism could find applications not only in the gravitational wave detector that originally motivated this work, but more generally in the field of quantum metrology based on ultracold atoms.
A Bose-Einstein condensate is used as an atomic source for a high precision sensor. A $5\ifmmode\times\else\texttimes\fi{}1{0}^{6}\text{ }\text{ }\mathrm{atom}$ F=1F=1F=1 spinor condensate of 87Rb^{87}\mathrm{Rb}87Rb is released into free fall for up to 750 ms and probed with a T=130  msT=130\text{ }\text{ }\mathrm{ms}T=130  ms Mach-Zehnder atom interferometer based on Bragg transitions. The Bragg interferometer simultaneously addresses the three magnetic states $|{m}_{f}=1,0,\ensuremath{-}1⟩$, facilitating a simultaneous measurement of the acceleration due to gravity with a 1000 run precision of $\mathrm{\ensuremath{\Delta}}g/g=1.45\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}$ and the magnetic field gradient to a precision of 120 pT/m120\text{ }\mathrm{pT}/\mathrm{m}120 pT/m.
Quasiparticles in a Bose-Einstein condensate are sensitive to space-time distortions. Gravitational waves can induce transformations on the state of phonons that can be observed through quantum state discrimination techniques. We show that this method is highly robust to thermal noise and depletion. We derive a bound on the strain sensitivity that shows that the detection of waves in the kHz regime is not significantly affected by temperature in a wide range of parameters that are well within current experimental reach.
Light-pulse atom interferometers are highly sensitive to inertial and gravitational effects. As such they are promising candidates for tests of gravitational physics. In this article the state-of-the-art and proposals for fundamental tests of gravity are reviewed. They include the measurement of the gravitational constant GGG, tests of the weak equivalence principle, direct searches of dark energy and gravitational-wave detection. Particular emphasis is put on long-time interferometry in microgravity environments accompanied by an enormous increase of sensitivity. In addition, advantages as well as disadvantages of Bose-Einstein condensates as atom sources are discussed.
We demonstrate the operation of an atom interferometer based on a weakly interacting Bose-Einstein condensate. We strongly reduce the interaction induced decoherence that usually limits interferometers based on trapped condensates by tuning the s-wave scattering length almost to zero via a magnetic Feshbach resonance. We employ a 39K condensate trapped in an optical lattice, where Bloch oscillations are forced by gravity. The fine-tuning of the scattering length down to 0.1 a_(0) and the micrometric sizes of the atomic sample make our system a very promising candidate for measuring forces with high spatial resolution. Our technique can be in principle extended to other measurement schemes opening new possibilities in the field of trapped atom interferometry.