Atom Interferometry Tests the Isotropy of Post-Newtonian Gravity

Abstract

We present a test of the local Lorentz invariance of post-Newtonian gravity by monitoring Earth's gravity with a Mach-Zehnder atom interferometer that features a resolution of about 8×10−9 g/ √ Hz, the highest reported thus far. Expressed within the standard model extension (SME) or Nordtvedt's anisotropic universe model, the analysis limits four coefficients describing anisotropic gravity at the ppb level and three others, for the first time, at the 10ppm level. Using the SME we explicitly demonstrate how the experiment actually compares the isotropy of gravity and electromagnetism.PACS numbers: 03.75. Dg, 11.30.Cp, 11.30.Qc, 04.25.Nx The description of gravitation by a dynamic geometry of space-time, Einstein's general relativity (GR), is based on the Einstein equivalence principle. This encompasses the universality of free fall (UFF), local position invariance (LPI), and local Lorentz invariance (LLI), which also underlies the non-gravitational standard model of particle physics. Attempts to unify GR and the standard model have failed so far. This suggests that one of their foundations might be violated at some level of precision [1]. So far, tests of the UFF and LPI have not identified violations [1]. LLI has been tested experimentally for many sectors of the standard model, such as for photons ('Maxwell sector'), electrons, protons, and neutrons [1,2,3]. No Lorentz violation has been identified, although the coverage of parameter space is still incomplete. Far less attention, however, has been paid to the LLI of the gravitational ('Einstein') sector, in spite of the pioneering work of Nordtvedt and Will in the 1970ies. Motivated by that fact that anisotropies arise in various theories of gravity other than GR [4], they have ruled out a Lorentz-violating anisotropy in gravity by searching for an anomalous time-dependence of the acceleration of free fall g on Earth [4,5,6].The success of GR and the standard model implies that any Lorentz violations are tiny. This and the relative weakness of gravity means that only exceptionally sensitive experiments can hope to detect Lorentz violation in gravity. A relatively recent addition to these is precision atom interferometry [7,8]. This has been serving, for example, in measurements of the fine structure constant [9], g [10] and its gradient [11], the Sagnac effect [12], and Newton's constant G [13] with sensitivities that compare favorably with other state-of-the-art instruments. One reason for its outstanding precision is that the motion of neutral atoms can realize a freely falling frame to a * Electronic address: holgerm@stanford.edu high accuracy and that this motion can be interrogated by laser radiation in a tremendously precise way. As a result, tests of post-Newtonian gravity with atom interferometry have been proposed that could rival or exceed the precision of classical ones [14].Here, we report on a first step in this direction: We describe the highest resolution atomic gravimeter reported thus far [15]. We then analyze the influence of Lorentz violat...

Coherent Stern–Gerlach momentum splitting on an atom chip

“…The theoretical prediction (shaded area) is based on a measured current in a resistor that mimics the chip wire (inset), taking into account errors of ± 2.5 mm (one pixel) in the initial cloud position, ± 0.2 O in the wire resistance and a 1 ms delay of the measured rise-time (due to the resistor's inductance). The linear dependence on T is to be expected from the solution of equation (2). The current 'overshoot' at short times is responsible for the larger acceleration for small T. (b) Numerical integration of equation (2) over T, using the experimental wire configuration and using a constant current of 3A.…”

“…The last line of equation (17) becomes cos(Dxz þ Dy/2) ¼ cos(mdz/:t þ f/2), where 2d ¼ Z 2 À Z 1 and f ¼ y 2 À y 1 . To obtain equation (3), we take the square absolute value of equation (17), and use Re{a(t)} ¼ 1/4s z (t) 2 and cos 2 ðx=2Þ ¼ 1 2 ½1 þ cosðxÞ. The visibility v is ideally equal to 1 and was included as a parameter in equation (3) in order to account for the real interference patterns whose visibility is lower than the ideal one.…”

“…T he development of atom interferometry over the last two decades has given rise to new insights into the tenets of quantum mechanics 1 as well as to ultra-high accuracy sensors for fundamental physics [2][3][4] and technological applications 5,6 . Examples range from the creation of momentum state superpositions by accurate momentum transfer of laser photons 7,8 allowing high precision measurements of rotation, acceleration and gravity 5,6,9,10 , to the splitting of trapped ultracold atoms by local potential barriers [11][12][13] allowing the investigation of fundamental properties of quantum systems of a few or many particles, such as decoherence and entanglement [14][15][16] .…”

High resolution atom interferometry with optical resonators

“…However, those techniques require high-power laser beams [9] that are currently limiting the maximum achievable LMT order. A solution to improve the available laser power is to perform atom interferometry with cavity enhanced pulses [10].…”

Geometrical Models of the Locally Anisotropic Space-Time

“…In the first of them [24], the precise atomic interfereometer was used to measure the phase shifts of the freely falling atoms. The local Lorentz symmetry break larger than 2 standard errors was found, which means that there exists an anisotropic condensate of unknown nature, and that, this interacts with the gravitation field in such a way, that the central symmetry of the gravitational potential is broken.…”