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arXiv:1712.02071 · Physical Review A

Differential phase extraction in dual interferometers exploiting the correlation between classical and quantum sensors

Mehdi Langlois, Romain Caldani, Azer Trimeche, Sébastien Merlet, Franck Pereira dos Santos

Published Nov 20, 2017• 18 citations
arXivHTMLPDF

Abstract

We perform the experimental demonstration of the method proposed earlier [F. P. Dos Santos, Phys. Rev. A 91, 063615 (2015)] to extract the differential phase in dual atom interferometers. From a single magneto-optical trap, we generate two atomic sources, vertically separated and free falling synchronously, with the help of an accelerated lattice. We drive simultaneous Raman interferometers onto the two sources and use the correlation with the vibration signal measured by a seismometer to extract the phase of each interferometer. We demonstrate an optimal sensitivity of the extracted differential phase between the two interferometers, free from vibration noise and limited by detection noise, when the two interferometers are in phase.

DOI
10.1103/physreva.96.053624

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We perform the experimental demonstration of the method proposed earlier [F. P. Dos Santos, Phys. Rev. A 91, 063615 (2015)] to extract the differential phase in dual atom interferometers. From a single magneto-optical trap, we generate two atomic sources, vertically separated and free falling synchronously, with the help of an accelerated lattice. We drive simultaneous Raman interferometers onto the two sources and use the correlation with the vibration signal measured by a seismometer to extract the phase of each interferometer. We demonstrate an optimal sensitivity of the extracted differential phase between the two interferometers, free from vibration noise and limited by detection noise, when the two interferometers are in phase.
We present here a method for the extraction of the differential phase of an atom gradiometer that exploits the correlation of the vibration signal measured by an auxiliary classical sensor, such as a seismometer or an accelerometer. We show that sensitivities close to the quantum projection noise limit can be reached, even when the vibration noise induces phase fluctuations larger than $2\ensuremath{\pi}$. This method does not require the correlation between the atomic and classical signals to be perfect and allows for an exact determination of the differential phase, with no bias. It can also be applied to other configurations of differential interferometers, such as gyrometers, conjugate interferometers for the measurement of the fine-structure constant, or differential accelerometers for tests of the equivalence principle or detection of gravitational waves.
We present here a method for the extraction of the differential phase of an atom gradiometer that exploits the correlation of the vibration signal measured by an auxiliary classical sensor, such as a seismometer or an accelerometer. We show that sensitivities close to the quantum projection noise limit can be reached, even when the vibration noise induces phase fluctuations larger than 2πππ. This method doesn't require the correlation between the atomic and classical signals to be perfect and allows for an exact determination of the differential phase, with no bias. It can also be applied to other configurations of differential interferometers, such as for instance gyrometers, conjugate interferometers for the measurement of the fine structure constant, or differential accelerometers for tests of the equivalence principle or detection of gravitational waves.
A dual-atom-interferometer gyroscope has high sensitivity for accurate rotation measurements because of its immunity to common-mode noise. However, a measurement error is induced as the common phase noise, e.g., vibration noise, increases. In this work, we demonstrated a real-time compensation (RTC) scheme to improve the accuracy of measurements of the differential phase in dual atom interferometers. The vibration noise was measured by two seismometers and its induced phase shift was fed back to the Raman lasers after this shift was calculated based on the sensitivity function of the atom interferometers. After the RTC module was applied, the interference signals obtained via the square modulation method were stabilized at their midfringe points, which caused the vibration-induced phase noise for each of the atom interferometers to decrease from 495 mrad to 165 mrad. The differential phase error obtained by the dual atom interferometers and two seismometers was reduced from 114.8 mrad to 49.6 mrad, which implies that the rotation measurement error was improved by a factor of 2.3. This work paves the way to accurately measuring the rotation signal and has promising applications in fields of precision measurements.
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.
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.
We demonstrate a closed-loop light-pulse atom-interferometer inertial sensor that can realize continuous decoupled measurements of acceleration and rotation rate. The sensor operates with double-loop atom interferometers, which share the same Raman light pulses in a spatially separated Mach-Zehnder configuration and use continuous cold atomic beams propagating in opposite directions from two 2D+{\text{2D}}^{+}2D+ magneto-optical trappings. Acceleration and the rotation rate are decoupled and simultaneously measured by the sum and difference of dual-atom-interferometer signals, respectively. The sensitivities of inertial measurements are also increased to be approximately 1.86 times higher than that of a single atom interferometer. The acceleration phase shift is compensated in real time by phase locking these interferometers via the Raman laser phases from the sum-interferometer signal, and the gyroscope performance is improved. We achieve long-term stabilities of $6.1\phantom{\rule{0.2em}{0ex}}\text{\ensuremath{\mu}}\text{g}$ and 840 nrad/s for the acceleration and the rotation rate, respectively, using a short interrogation time of 0.87 ms (interference area A=0.097mm2A=0.097\phantom{\rule{0.2em}{0ex}}{\text{mm}}^{2}A=0.097mm2). This work provides a building block for an atomic interferometer-based inertial measurement unit for use in field applications that require a high data rate and high stability.