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Physical Review A

Proportional-scanning-phase method to suppress the vibrational noise in nonisotope dual-atom-interferometer-based weak-equivalence-principle-test experiments

Xi Chen, Jiaqi Zhong, Hongwei Song, Lei Zhu, Jin Wang, Mingsheng Zhan

Published Aug 7, 2014• 25 citations
Publisher

Abstract

Vibrational noise is one of the most important noises that limits the performance of the nonisotopes atom-interferometers (AIs) -based weak-equivalence-principle (WEP) -test experiment. By analyzing the vibration-induced phases, we find that, although the induced phases are not completely common, their ratio is always a constant at every experimental data point, which is not fully utilized in the traditional elliptic curve-fitting method. From this point, we propose a strategy that can greatly suppress the vibration-induced phase noise by stabilizing the Raman laser frequencies at high precision and controlling the scanning-phase ratio. The noise rejection ratio can be as high as ${10}^{15}$ with arbitrary dual-species AIs. Our method provides a Lissajous curve, and the shape of the curve indicates the breakdown of the weak-equivalence-principle signal. Then we manage to derive an estimator for the differential phase of the Lissajous curve. This strategy could be helpful in extending the candidates of atomic species for high-precision AIs-based WEP-test experiments.

DOI
10.1103/physreva.90.023609

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Vibrational noise is one of the most important noises that limits the performance of the nonisotopes atom-interferometers (AIs) -based weak-equivalence-principle (WEP) -test experiment. By analyzing the vibration-induced phases, we find that, although the induced phases are not completely common, their ratio is always a constant at every experimental data point, which is not fully utilized in the traditional elliptic curve-fitting method. From this point, we propose a strategy that can greatly suppress the vibration-induced phase noise by stabilizing the Raman laser frequencies at high precision and controlling the scanning-phase ratio. The noise rejection ratio can be as high as 1015{10}^{15}1015 with arbitrary dual-species AIs. Our method provides a Lissajous curve, and the shape of the curve indicates the breakdown of the weak-equivalence-principle signal. Then we manage to derive an estimator for the differential phase of the Lissajous curve. This strategy could be helpful in extending the candidates of atomic species for high-precision AIs-based WEP-test experiments.
Matter-wave interferometers utilizing different isotopes or chemical elements intrinsically have different sensitivities, and the analysis tools available until now are insufficient for accurately estimating the atomic phase difference under many experimental conditions. In this work, we describe and demonstrate two new methods for extracting the differential phase between dual-species atom interferometers for precise tests of the weak equivalence principle (WEP). The first method is a generalized Bayesian analysis, which uses knowledge of the system noise to estimate the differential phase based on a statistical model. The second method utilizes a mechanical accelerometer to reconstruct single-sensor interference fringes based on measurements of the vibration-induced phase. An improved ellipse-fitting algorithm is also implemented as a third method for comparison. These analysis tools are investigated using both numerical simulations and experimental data from simultaneous 87 Rb and 39 K interferometers, and both new techniques are shown to produce bias-free estimates of the differential phase. We also report observations of phase correlations between atom interferometers composed of different chemical species. This correlation enables us to reject common-mode vibration noise by a factor of 730, and to make preliminary tests of the WEP with a sensitivity of 1.6 × 10 − 6 per measurement with an interrogation time of T = 10 ms. We study the level of vibration rejection by varying the temporal overlap between interferometers in a symmetric timing sequence. Finally, we discuss the limitations of the new analysis methods for future applications of differential atom interferometry.
The wave-front aberration of Raman beams induces phase noise in atom interferometers and thus limits the performance of atom interferometers. We theoretically analyze the wave-front-aberration phase noise in weak-equivalence-principle tests using dual-species atom interferometers, and propose an expansion-rate-selection method to suppress the wave-front-aberration phase noise in both isotopic and nonisotopic atom interferometers. The suppression ratio is about 10 at the expense of half the number of atoms. The simulation based on appropriate experimental parameters shows that the wave-front aberration caused standard deviations to the E\"otv\"os coefficient in weak-equivalence-principle tests using $^{85}\mathrm{Rb}\text{\ensuremath{-}}^{87}\mathrm{Rb}$ and $^{41}\mathrm{K}\text{\ensuremath{-}}^{87}\mathrm{Rb}$ are $1.3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}$ and $3.0\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}$. Better results can be obtained by improving the wave-front quality and utilizing atom cloud with lower temperature. The analysis and suppression of wave-front-aberration phase noise will be useful for the design of high-precision atom interferometer--based weak-equivalence-principle tests both on ground and in space.
We theoretically investigate the application of the fringe-locking method (FLM) in the dual-species quantum test of the weak equivalence principle (WEP). With the FLM, the measurement is performed invariably at the midfringe, and the extraction of the phase shift for atom interferometers is linearized. For the simultaneous interferometers, this linearization enables a good common-mode rejection of vibration noise, which is usually the main limit for high precision WEP tests of dual-species kind. We note that this method also allows for an unbiased determination of the gravity accelerations difference, which meanwhile is readily to be implemented.
We report an improved test of the weak equivalence principle by using a simultaneous $^{85}\mathrm{Rb}\text{\ensuremath{-}}^{87}\mathrm{Rb}$ dual-species atom interferometer. We propose and implement a four-wave double-diffraction Raman transition scheme for the interferometer, and demonstrate its ability in suppressing common-mode phase noise of Raman lasers after their frequencies and intensity ratios are optimized. The statistical uncertainty of the experimental data for E\"otv\"os parameter $\ensuremath{\eta}$ is $0.8\ifmmode\times\else\texttimes\fi{}1{0}^{\ensuremath{-}8}$ at 3200 s. With various systematic errors corrected, the final value is $\ensuremath{\eta}=(2.8\ifmmode\pm\else\textpm\fi{}3.0)\ifmmode\times\else\texttimes\fi{}1{0}^{\ensuremath{-}8}$. The major uncertainty is attributed to the Coriolis effect.
We present here the performance of a simultaneous dual-species matter-wave accelerometer for measuring the differential acceleration between two different atomic species (87Rb^{87}\mathrm{Rb}87Rb and 85Rb^{85}\mathrm{Rb}85Rb). We study the expression and the extraction of the differential phase from the interferometer output. The differential accelerometer reaches a short-term sensitivity of $1.23\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}g/\sqrt{\mathrm{Hz}}$ limited by the detection noise and a resolution of $2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}g$ after 11 000 s, a very high sensitivity using a dual-species atom interferometer. Thanks to the simultaneous measurement, such resolution levels can still be achieved even with vibration levels up to $3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}g$, corresponding to a common-mode vibration noise rejection ratio of 94 dB (rejection factor of 50 000). These results prove the ability of such atom sensors for realizing a quantum-based test of the weak equivalence principle at a level of $\ensuremath{\eta}\ensuremath{\sim}{10}^{\ensuremath{-}9}$ even with high vibration levels and a compact sensor.
Coriolis effect is an important error source in the weak equivalence principle (WEP) test using atom interferometer. In this paper, the problem of Coriolis error in WEP test is studied theoretically and experimentally. In theoretical simulation, the Coriolis effect is analyzed by establishing an error model. The measurement errors of Eötvös coefficient (η) in WEP test related to experimental parameters, such as horizontal-velocity difference and horizontal-position difference of atomic clouds, horizontal-position difference of detectors, and rotation compensation of Raman laser’s mirror are calculated. In experimental investigation, the position difference between 85Rb and 87Rb atomic clouds is reduced to 0.1 mm by optimizing the experimental parameters, an alternating detection method is used to suppress the error caused by detection position difference, thus the Coriolis error related to the atomic clouds and detectors is reduced to 1.1× 10−9. This Coriolis error is further corrected by compensating the rotation of Raman laser’s mirror, and the total uncertainty of η measurement related to the Coriolis effect is reduced as δη = 4.4 × 10−11.