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arXiv:2011.09779 · Physical Review A

Single-shot Stern-Gerlach magnetic gradiometer with an expanding cloud of cold cesium atoms

Katja Gosar, Tina Arh, Tadej Mežnaršič, Ivan Kvasič, Dušan Ponikvar, Tomaz Apih, Rainer Kaltenbaek, Rok Žitko, Erik Zupanič, Samo Beguš, P. Jeglič

Published Feb 19, 2021• 6 citations

Abstract

We combine the Ramsey interferometry protocol, the Stern-Gerlach detection scheme, and the use of elongated geometry of a cloud of fully polarized cold cesium atoms to measure the selected component of the magnetic-field gradient along the atomic cloud in a single shot. In contrast to the standard method where the precession of two spatially separated atomic clouds is simultaneously measured to extract their phase difference, which is proportional to the magnetic-field gradient, we here demonstrate a gradiometer using a single image of an expanding atomic cloud with the phase difference imprinted along the cloud. Using resonant radio-frequency pulses and Stern-Gerlach imaging, we first demonstrate nutation and Larmor precession of atomic magnetization in an applied magnetic field. Next, we let the cold atom cloud expand in one dimension and apply the protocol for measuring the magnetic-field gradient. The resolution of our single-shot gradiometer is not limited by thermal motion of atoms and has an estimated absolute accuracy below $\ifmmode\pm\else\textpm\fi{}0.2$ mG/cm ($\ifmmode\pm\else\textpm\fi{}20$ nT/cm).

DOI: 10.1103/physreva.103.022611

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International Conference on Photonics and Optical Engineering•Jan 24, 2019•0 citations

We combine the Ramsey interferometry protocol, the Stern-Gerlach detection scheme, and the use of elongated geometry of a cloud of fully polarized cold cesium atoms to measure the selected component of the magnetic-field gradient along the atomic cloud in a single shot. In contrast to the standard method where the precession of two spatially separated atomic clouds is simultaneously measured to extract their phase difference, which is proportional to the magnetic-field gradient, we here demonstrate a gradiometer using a single image of an expanding atomic cloud with the phase difference imprinted along the cloud. Using resonant radio-frequency pulses and Stern-Gerlach imaging, we first demonstrate nutation and Larmor precession of atomic magnetization in an applied magnetic field. Next, we let the cold atom cloud expand in one dimension and apply the protocol for measuring the magnetic-field gradient. The resolution of our single-shot gradiometer is not limited by thermal motion of atoms and has an estimated absolute accuracy below

\ifmmode\pm\else\textpm\fi{}0.2

mG/cm (

\ifmmode\pm\else\textpm\fi{}20

nT/cm).

We demonstrate an atomic magnetic gradiometer based on self-sustaining Larmor precession. By coherent optical pumping, we measure the phase of the Larmor precession directly and observe that the gradiometer shows a 1/τ improvement in magnetic field gradient uncertainty over time τ. Since the measurement gives frequency signals, the gradiometer can be easily implemented by mixing and filtering the different frequency signals from two adjacent magnetometers. A gradient sensitivity of 186 fT/Hz/cm−1) is realized, which is close to the shot-noise limit. In a noisy environment, the gradiometer can still maintain its 1/τ behavior by suppressing 90% of the common-mode noise. This method should be widely applicable to the measurement of magnetic field gradients owing to its simplicity and outstanding performance.

We demonstrate a technique for imaging magnetic fields using velocity-selective two-photon resonances in a cold atom cloud. Freely expanding (85)Rb atoms released from a magneto-optical trap are exposed to a brief (approximately 1 ms), off-resonant, retro-reflected laser pulse in a lin-perp-lin configuration. Two-photon resonance between magnetic sublevels occurs only for atoms in narrow velocity classes dependent on the magnetic field strength. The momentum of resonant atoms is altered by the pulse, and this two-photon momentum change is easily visible after further ballistic expansion. When the momentum pulse is applied to an atom cloud with finite size, magnetic field variations across the sample result in position-dependent features in images of the expanded cloud. We demonstrate the technique by imaging magnetic field variations over approximately 5 mm with approximately 250 microm spatial resolution.

Summary form only given. Spatial coherences are measured by means of a new atom interferometry technique. First, a coherent superposition of the Zeeman components of the atom is built by means of well-controlled magnetic interactions. Second, pulsed inhomogeneous magnetic fields are employed to coherently separate and reunite the atomic substates via the Stern-Gerlach induced forces. Finally, atomic interference fringes are recorded on the state-selected outcoming sample by changing the spatial separation. This method bears strong similarities with the Fourier-transform spectroscopy of light. The interferogram visibility curve yields the atom sample spatial coherences. For example, when the applied magnetic gradients are parallel to the atom trajectory, one gets the coherence length by varying the overlap of the separated wavepackets. Several experiments on cold cesium atoms have been performed and are presented. Furthermore, we have used our magnetic cooling method to prepare the atom cloud upstream from the interferometer. Large enhancements of the coherence length are demonstrated.

Radio-frequency pulses are applied to probe and control the Larmor precession of a spin-2 Bose–Einstein condensate subject to a magnetic field gradient. Using the techniques of Ramsey interferometry and Stern–Gerlach absorption imaging, a helical spin pattern was clearly observed as spatial variations in the atomic density distribution. We experimentally show that the spin echo technique reduces the effects of spatially inhomogeneous and temporally fluctuating spin evolution, and improves the repeatability of the interferometry.

We have realized a magnetic tensor gradiometer by interferometrically measuring the relative phase between two spatially separated Bose-Einstein condensates (BECs). We perform simultaneous Ramsey interferometry of the proximate

^{87}\mathrm{Rb}

spin-1 condensates in free fall and infer their relative Larmor phase, and thus the differential magnetic-field strength, with a common-mode phase noise suppression exceeding

50\phantom{\rule{0.28em}{0ex}}\mathrm{dB}

. By appropriately biasing the magnetic field and separating the BECs along orthogonal directions, we measure in vacuo the magnetic-field-gradient tensor of ambient and applied magnetic fields with a nominal precision of $0.30\phantom{\rule{0.28em}{0ex}}\mathrm{nT}\phantom{\rule{0.16em}{0ex}}{\mathrm{mm}}^{\ensuremath{-}1}$ and a sensor volume of $2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}\phantom{\rule{0.28em}{0ex}}{\mathrm{mm}}^{3}$. We predict a spin-projection noise-limited magnetic energy resolution of order $\ensuremath{\sim}10\ensuremath{\hbar}$ for typical Zeeman coherence times of trapped condensates with this scheme, even with the low measurement duty cycle of current BEC experiments.

The magnetic field is one of the most important physical observables with about all electromagnetic information. Larmor precession atomic magnetometers based on optical pumping experienced considerable attention recently. However, the sensitivity of this kind of atomic magnetometers is limited by their spin coherence time and the systematic noise. Here, we propose a self-sustaining atomic magnetic gradiometer that shows a superior 1/τ behavior in the magnetic field uncertainty measurement over time. The gradiometer is implemented by mixing and filtering the different frequency signals from two adjacent spin self-sustaining magnetometers with a baseline equal to 1 cm. The common-mode noise is suppressed and a gradient sensitivity of 200 fT/(√Hz=cm) is realized, being close to the shot noise limit.