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Physical Review A

Precisely mapping the magnetic field gradient in vacuum with an atom interferometer

Min-Kang Zhou, Zhong-Kun Hu, Xiao‐Chun Duan, Bu-Liang Sun, Jinbo Zhao, Jun Luo

Published Dec 10, 2010• 61 citations
Publisher

Abstract

The magnetic field gradient has been measured with an atom interferometer using the magnetic sublevels of $^{87}\mathrm{Rb}$ atoms. The Doppler-insensitive measurement effectively eliminates the contribution from gravity and background vibration noise, and the differential measurement also can reject some systematic errors. A resolution of $300$ pT/mm has been demonstrated with a $90$-s integration time and a spatial resolution of $1.4$ mm. The gradiometer was then used to measure the magnetic field gradient in an ultrahigh-vacuum environment. The technique will also be very useful to subtract the systematic error arising from the magnetic field inhomogeneity in precision atom-interferometry experiments, such as gravity measurement.

DOI
10.1103/physreva.82.061602

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The magnetic field gradient has been measured with an atom interferometer using the magnetic sublevels of 87Rb^{87}\mathrm{Rb}87Rb atoms. The Doppler-insensitive measurement effectively eliminates the contribution from gravity and background vibration noise, and the differential measurement also can reject some systematic errors. A resolution of 300300300 pT/mm has been demonstrated with a 909090-s integration time and a spatial resolution of 1.41.41.4 mm. The gradiometer was then used to measure the magnetic field gradient in an ultrahigh-vacuum environment. The technique will also be very useful to subtract the systematic error arising from the magnetic field inhomogeneity in precision atom-interferometry experiments, such as gravity measurement.
Precisely measuring the magnetic-field gradient within a vacuum chamber is important for many precision experiments and can be realized by atom interferometry using magnetically sensitive sublevels at different times to make a differential measurement, which had been demonstrated in our previous work. In this paper, we demonstrate a differential method to measure the magnetic-field gradient by means of two simultaneously operated atom interferometers using double atomic fountains. By virtue of this simultaneous differential measurement to reject common-mode noise, the resolution can be improved by one order of magnitude for about a 1000-s integration time.
Atoms in magnetically sensitive sublevels constitute a natural sensor for absolute magnetic field measurements, which are explored here to form an optical Ramsey interferometer for determining the magnetic field distribution. An optical Ramsey atom interferometer provides a convenient way to map a magnetic field in vacuum. In comparison with the often used Raman spectroscopy method, a Ramsey interferometer can not only improve the sensitivity, but also dramatically suppress the contribution of the ac Stark effect. Furthermore, in this work, the magnetically sensitive atoms are velocity-selected, which improves the spatial resolution for the magnetometer as well as the contrast of the Ramsey fringes. A short-term sensitivity of 1.4nT/Hz1/21.4\phantom{\rule{0.2em}{0ex}}{\mathrm{nT/Hz}}^{1/2}1.4nT/Hz1/2 for magnetic field measurement is finally achieved even with an interrogation time as short as $500\phantom{\rule{0.2em}{0ex}}\ensuremath{\mu}\mathrm{s}$. The presented approach for absolute magnetic field measurement is expected to find wide applications in atom-interferometry-based precision measurements.
Precisely evaluating the systematic error induced by the quadratic Zeeman effect is important for developing atom interferometer gravimeters aiming at an accuracy in the $\ensuremath{\mu}\mathrm{Gal}$ regime ($1\ensuremath{\mu}\mathrm{Gal}={10}^{\ensuremath{-}8}\mathrm{m}/{\mathrm{s}}^{2}\ensuremath{\approx}{10}^{\ensuremath{-}9}\mathrm{g}$). This paper reports on the experimental investigation of Raman spectroscopy-based magnetic field measurements and the evaluation of the systematic error in the gravimetric atom interferometer (GAIN) due to quadratic Zeeman effect. We discuss Raman duration and frequency step-size-dependent magnetic field measurement uncertainty, present vector light shift and tensor light shift induced magnetic field measurement offset, and map the absolute magnetic field inside the interferometer chamber of GAIN with an uncertainty of 0.72 nT and a spatial resolution of 12.8 mm. We evaluate the quadratic Zeeman-effect-induced gravity measurement error in GAIN as $2.04\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{Gal}$. The methods shown in this paper are important for precisely mapping the absolute magnetic field in vacuum and reducing the quadratic Zeeman-effect-induced systematic error in Raman transition-based precision measurements, such as atomic interferometer gravimeters.
We propose the utilization of atom interferometry techniques for the measurement of magnetic fields in noisy environments. We find that the interferometer we propose is insensitive (to first order) to the magnetic field but is sensitive to the field gradient. We propose a technique by which a superposition of magnetically sensitive states (a beam splitter) can be achieved. We experimentally demonstrate our techniques to null the magnetic field at the location of a cold atom cloud and how we can probe the population of magnetic sublevels.
An atom interferometer using a Bose--Einstein condensate of 87Rb^{87}\mathrm{Rb}87Rb atoms is utilized for the measurement of magnetic-field gradients. Composite optical pulses are used to construct a spatially symmetric Mach--Zehnder geometry. By using a biased interferometer we demonstrate the ability to measure small residual forces in our system and discriminate between magnetic and inertial effects. These are a residual ambient magnetic-field gradient of $15\ifmmode\pm\else\textpm\fi{}2$ mG/cm and an inertial acceleration of $0.08\ifmmode\pm\else\textpm\fi{}0.02$ m/s2{\mathrm{s}}^{2}s2. Our method has important applications in the calibration of precision measurement devices and the reduction of systematic errors.
An atom interferometer using a Bose-Einstein condensate of 87^{87}87Rb atoms is utilized for the measurement of magnetic field gradients. Composite optical pulses are used to construct a spatially symmetric Mach-Zehnder geometry. Using a biased interferometer we demonstrate the ability to measure small residual forces in our system at the position of the atoms. These are a residual magnetic field gradient of 15$\pm2mG/cmandandaninertialaccelerationof0.082 mG/cm and and an inertial acceleration of 0.082mG/cmandandaninertialaccelerationof0.08\pm0.02m/s0.02 m/s0.02m/s^2$. Our method has important applications in the calibration of precision measurement devices and the reduction of systematic errors.