Effective Inertial Frame in an Atom Interferometric Test of the Equivalence Principle

Chris Overstreet, Peter Asenbaum, Tim Kovachy, Remy Notermans, Jason M. Hogan, and Mark A. Kasevich

Phys. Rev. Lett. 120, 183604 – Published 4 May 2018

Abstract

In an ideal test of the equivalence principle, the test masses fall in a common inertial frame. A real experiment is affected by gravity gradients, which introduce systematic errors by coupling to initial kinematic differences between the test masses. Here we demonstrate a method that reduces the sensitivity of a dual-species atom interferometer to initial kinematics by using a frequency shift of the mirror pulse to create an effective inertial frame for both atomic species. Using this method, we suppress the gravity-gradient-induced dependence of the differential phase on initial kinematic differences by 2 orders of magnitude and precisely measure these differences. We realize a relative precision of $Δ g / g \approx 6 \times 10^{- 11}$ per shot, which improves on the best previous result for a dual-species atom interferometer by more than 3 orders of magnitude. By reducing gravity gradient systematic errors to one part in $1 0^{13}$ , these results pave the way for an atomic test of the equivalence principle at an accuracy comparable with state-of-the-art classical tests.

Received 27 November 2017

DOI:https://doi.org/10.1103/PhysRevLett.120.183604

Physics Subject Headings (PhySH)

Atom interferometry Atom optics

Atomic, Molecular & Optical

Authors & Affiliations

Chris Overstreet, Peter Asenbaum, Tim Kovachy, Remy Notermans, Jason M. Hogan, and Mark A. Kasevich^*

Department of Physics, Stanford University, Stanford, California 94305, USA

^*kasevich@stanford.edu

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Vol. 120, Iss. 18 — 4 May 2018

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Images

Figure 1
Implementation of the FSGG-compensation scheme. (a) The interferometers in a dual-species differential accelerometer are separated by an initial displacement $Δ z$ . Because of the gravity gradient $T_{z z}$ , the interferometers experience a differential acceleration $T_{z z} Δ z$ and a differential phase shift $k T_{z z} Δ z T^{2}$ . To perform FSGG compensation, the effective wave vector of the interferometer mirror pulses is changed by $Δ k$ , which adds a differential phase shift $- 2 Δ k Δ z$ . For $Δ k / k = \frac{1}{2} T_{z z} T^{2}$ , the differential phase becomes insensitive to the initial displacement $Δ z$ . Alternatively, a scan of $Δ k$ provides information about $Δ z$ [23]. (b) Raw fluorescence image of the dual-species differential accelerometer operating at a LMT order of $10 ℏ k$ with initially overlapped clouds and $Δ f = 343 MHz$ , using phase shear readout to determine the differential phase.
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Figure 2
(a) Raw data from the ${}^{87}{Rb}$ -only ( $10 ℏ k$ momentum splitting, $T = 900 ms$ ) gravity gradiometer used to determine the optimal frequency shift $Δ f$ . The upper and lower pairs of output ports correspond to the two vertically displaced interferometers. The two interferometers use opposite input ports, which would give them a differential phase of $π$ in the absence of any gravity gradients. Upper image: without FSGG compensation. Lower image: with FSGG compensation. Without FSGG compensation, the differential phase is visibly shifted away from $π$ . With FSGG compensation, the differential phase is $π$ , illustrating the cancellation of the gravity gradient phase shift. (b) Gradiometer phase vs baseline for $Δ f = 0 MHz$ (blue points), $Δ f = 320 MHz$ (light red points), and $Δ f = 340 MHz$ (dark red points). Error bars are smaller than the points.
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Figure 3
Dependence of the differential phase on mirror pulse frequency shift $Δ f$ and initial separation $Δ z$ . (a) Differential phase as a function of $Δ f$ for two initial separations differing by 5.5 mm. The slope of each linear fit is used to determine the quantities $Δ \bar{z} = - 3.21 \pm 0.07 mm$ (red points) and $Δ \bar{z} = 2.3 \pm 0.1 mm$ (blue points). Each point is the average of $\sim 20$ experimental shots. For $Δ f = 345 \pm 11 MHz$ , the differential phase at the two separations is equal and, therefore, insensitive to the gravity gradient. (b) Differential phase as a function of relative position shift for $Δ f = 0 MHz$ (black points, $\sim 30$ shots per point), $Δ f = 510 MHz$ (blue points, $\sim 100$ shots per point), and $Δ f = 343 MHz$ (red points, $\sim 100$ shots per point). The intersection point of all three lines provides the relative position shift required to set $Δ \bar{z} = 0$ , $2.47 \pm 0.04 mm$ . The slope of the red linear fit is $(- 0.7 \pm 1.3) %$ of the slope of the black linear fit, demonstrating the reduction of differential phase sensitivity to initial kinematic mismatches. All differential phases are referenced to the differential phase at $Δ f = 0 MHz$ and $Δ \bar{z} = 2.3 \pm 0.1 mm$ .
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Figure 4
(a) Output ports of a ${}^{87}{Rb}$ interferometer with (blue) and without (red) a phase shift in the vertical direction. Each port is divided into four vertical bins. (b) Phase shift as a function of vertical position at two LMT orders ( $12 ℏ k$ , light blue points; $20 ℏ k$ , dark blue and red points) with (red) and without (light blue, dark blue) FSGG compensation. Distances are referenced to the top of each port. The ratio of the slopes of the light blue and dark blue linear fits is $0.62 \pm 0.03$ , consistent with the ratio of the LMT orders. The slope of the red linear fit is $(- 3 \pm 3) %$ of the slope of the dark blue linear fit. All phase shifts are referenced to the phase shift at the same cloud position of a $12 ℏ k$ interferometer with FSGG compensation.
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