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arXiv:cond-mat/0612685 · Physical Review Letters

High-Resolution Magnetometry with a Spinor Bose-Einstein Condensate

Mukund Vengalattore, James Higbie, Sabrina R. Leslie, Jennie Guzman, Lorraine E. Sadler, Dan Stamper-Kurn

Published May 17, 2007• 245 citations
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Abstract

We demonstrate a precise magnetic microscope based on direct imaging of the Larmor precession of a $^{87}\mathrm{Rb}$ spinor Bose-Einstein condensate. This magnetometer attains a field sensitivity of $8.3\text{ }\text{ }\mathrm{pT}/{\mathrm{Hz}}^{1/2}$ over a measurement area of $120\text{ }\text{ }\ensuremath{\mu}{\mathrm{m}}^{2}$, an improvement over the low-frequency field sensitivity of modern SQUID magnetometers. The achieved phase sensitivity is close to the atom shot-noise limit, estimated as $0.15\text{ }\text{ }\mathrm{pT}/{\mathrm{Hz}}^{1/2}$ for a unity duty cycle measurement, suggesting the possibilities of spatially resolved spin-squeezed magnetometry. This magnetometer marks a significant application of degenerate atomic gases to metrology.

DOI
10.1103/physrevlett.98.200801

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•Jan 1, 2017•0 citations
We demonstrate a precise magnetic microscope based on direct imaging of the Larmor precession of a 87Rb^{87}\mathrm{Rb}87Rb spinor Bose-Einstein condensate. This magnetometer attains a field sensitivity of 8.3  pT/Hz1/28.3\text{ }\text{ }\mathrm{pT}/{\mathrm{Hz}}^{1/2}8.3  pT/Hz1/2 over a measurement area of 120  \ensuremathμm2120\text{ }\text{ }\ensuremath{\mu}{\mathrm{m}}^{2}120  \ensuremathμm2, an improvement over the low-frequency field sensitivity of modern SQUID magnetometers. The achieved phase sensitivity is close to the atom shot-noise limit, estimated as 0.15  pT/Hz1/20.15\text{ }\text{ }\mathrm{pT}/{\mathrm{Hz}}^{1/2}0.15  pT/Hz1/2 for a unity duty cycle measurement, suggesting the possibilities of spatially resolved spin-squeezed magnetometry. This magnetometer marks a significant application of degenerate atomic gases to metrology.
An improved spatial magnetometer using a spinor Bose-Einstein condensate of 87^{87}87Rb atoms is realized utilizing newly developed two-polarization phase contrast imaging. The optical shot noise is suppressed by carefully choosing the probe parameters. We attain a dc-magnetic field sensitivity of 7.7 pT/Hz{\rm pT/\sqrt{Hz}}pT/Hz​ over a measurement area of 28 μm2{\rm μm^{2}}μm2. The attained sensitivity per unit area is superior to that for other modern low-frequency magnetometers with micrometer-order spatial resolution. This result is a promising step for realizing quantum-enhanced magnetometry surpassing classical methods.
We demonstrate a sensitive spatially resolved magnetometer using a spinor Bose-Einstein condensate (BEC) of 87Rb^{87}\mathrm{Rb}87Rb atoms with increased probe fluence. By performing a probe parameter search using a two-polarization phase contrast imaging technique, we find that the probe-induced atom loss, a major constraint in optical magnetometry with high-density gas, can be reduced. We attain a sensitivity of 5.4(6) mrad for the phase measurement of Larmor precession using a measurement area of $1.4\ifmmode\times\else\texttimes\fi{}{10}^{2}\phantom{\rule{3.33333pt}{0ex}}\ensuremath{\mu}{\mathrm{m}}^{2}$ with a probe fluence of $4.1\ifmmode\times\else\texttimes\fi{}{10}^{5}\phantom{\rule{3.33333pt}{0ex}}\ensuremath{\mu}{\mathrm{m}}^{\ensuremath{-}2}$. A dc magnetic field sensitivity of 5.0(4)pT/Hz5.0(4)\phantom{\rule{3.33333pt}{0ex}}\mathrm{pT}/\sqrt{\mathrm{Hz}}5.0(4)pT/Hz​ is attained with a probe fluence of $3.9\ifmmode\times\else\texttimes\fi{}{10}^{5}\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}{\mathrm{m}}^{\ensuremath{-}2}$. The results should contribute to further enhancement of the sensitivity of a BEC magnetometer.
Polarization-dependent phase-contrast imaging is used to resolve the spatial magnetization profile of an optically trapped ultracold gas. This probe is applied to Larmor precession of degenerate and nondegenerate spin-1 87Rb gases. Transverse magnetization of the Bose-Einstein condensate persists for the condensate lifetime, with a spatial response to magnetic field inhomogeneities consistent with a mean-field model of interactions. In comparison, the magnetization of the non-condensed gas decoheres rapidly. Rotational symmetry implies that the Larmor frequency of a spinor condensate be density independent, and thus suitable for precise magnetometry with high spatial resolution.
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 87Rb^{87}\mathrm{Rb}87Rb 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 50dB50\phantom{\rule{0.28em}{0ex}}\mathrm{dB}50dB. 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.
We demonstrate detection of a weak alternate-current magnetic field by application of the spin-echo technique to F=2F=2F=2 Bose-Einstein condensates. A magnetic field sensitivity of 12 pT/Hz/\sqrt{\mathrm{Hz}}/Hz​ is attained for an atom number of $5\ifmmode\times\else\texttimes\fi{}{10}^{3}$ at a spatial resolution of 100 $\ensuremath{\mu}$m2{}^{2}2. Our observations indicate magnetic field fluctuations synchronous with the power supply line frequency. We show that this noise is greatly suppressed by application of a reverse phase magnetic field. Our technique is useful in order to create a stable magnetic field environment, which is an important requirement for atomic experiments which require a weak bias magnetic field.
Spinor Bose-Einstein condensates (BECs) are multi-component superfluids with magnetic interactions, formed from dilute gases of atoms in the Zeeman sublevels mF of a single hyperfine ground state F. Spinor BECs are inherently magnetic quantum objects, and exhibit a multitude of features such as spin domains, magnon excitations, and distinct magnetic phases. At the heart of the magnetic nature of a spinor BEC is the spin-dependent collisional interaction c, which determines the overall magnetic behaviour of the superfluid. In conjunction with the quadratic Zeeman shift q, the magnitude and sign of c give rise to an intricate magnetic phase diagram. The magnetic phase of a spinor BEC is tunable, and c and q are the knobs. In addition to realising quantum simulators of magnetism, spinor BECs are also precise magnetic sensors. Atomic magnetometry measures the Larmor precession frequency of atoms, which is proportional to the magnetic field strength. The sensitivity of an atomic magnetometer is principally dependent on the duration of the measurement (interrogation time) and number of atoms participating in the measurement. BECs are highly suitable as atomic magnetometers, allowing for long interrogation times and high atomic density, with microscopic sensor volumes. The latter is an important consideration, as measurement of small magnetic sources demand equally microscopic sensors. Established forms of magnetometry (such as warm vapour magnetometers) use large sensing volumes and are not trivially miniaturised. The exquisite sensitivity of a spinor BEC to magnetic fields becomes a liability when one studies low energy (~ 1 Hz) spinor physics over long evolution times (100 ms) in a typical laboratory environment. To first order, the spin-collisional interaction is independent of the magnetic field. However, spatially inhomogeneous magnetic fields are problematic, exerting mechanical forces on the magnetically sensitive spin components, suppressing spin collisions and possibly introducing relaxation mechanisms that confound the observation of intrinsic equilibration. Precise characterisation of magnetic field gradients and their cancellation is thus of paramount importance. In this thesis, the interaction of a spinor BEC with its environment is studied. The construction, operation and optimisation of a BEC machine is described in detail, as well as the quantum state preparation and control techniques used. Spin-mixing collisions were studied by observing population oscillations, the characteristic hallmark of such coherent phenomena. The observed population dynamics showed strong evidence of the deleterious effects of magnetic field gradients. A series of experiments were performed using spin-echo pulse sequences to decouple the evolving spinor condensate from the inhomogeneous magnetic environment with encouraging results, but which posed further questions. The fidelity of spin-echo pulses in the strong radiative coupling regime was also studied. Spinor condensates were then employed as sensitive magnetometers to characterise the magnetic landscape they inhabit. A new method of measuring magnetic field gradients was developed, using a pair of spinor BECs separated in space that are simultaneously addressed by a Ramsey interferometry sequence. Combined with a re-orientable magnetic bias field, the resulting gradiometer was used to measure the magnetic field gradient tensor in vacuo. This scheme can be extended to realise a high-precision vector co-magnetometer, with spatiotemporal sensitivity comparable to established forms of magnetometry. Vector light shifts (VLSs) are optically-induced energy shifts that result in effective magnetic fields, which in our case originate from the laser beams used to trap the atoms. The VLS vanishes for purely linearly polarised light, which is experimentally difficult to obtain in vacuo. Small elliptical polarisation imperfections originating from birefringent optics and the glass vacuum cell result in a non-zero shift that contaminates magnetometry measurements. The VLS is spatially varying due to the intensity gradient of the trapping light. Due to gravitational sag of the trapping potential, the spatial variation of the VLS is accentuated, resulting in an effective magnetic field gradient that contributes to dephasing and component separation. The simultaneous Ramsey interferometry experiments are then adapted to measure the VLS-induced Zeeman shift and diagnose its elimination. Up to 99.96% of the VLS is eliminated using this method, and extensions to the technique are described.