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arXiv:cond-mat/0502517 · Physical Review Letters

Direct Nondestructive Imaging of Magnetization in a Spin-1 Bose-Einstein Gas

James Higbie, Lorraine E. Sadler, S. Inouye, A. P. Chikkatur, Sabrina R. Leslie, Kevin L. Moore, V. Savalli, Dan Stamper-Kurn

Published Jul 26, 2005• 225 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.95.050401

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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 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 $120\text{ }\text{ }\ensuremath{\mu}{\mathrm{m}}^{2}$, 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  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.
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.
Spinor Bose Einstein condensates have widely been sought after as perfect emulators of condensed matter phenomena, providing widely tunable and highly controlled systems. Utilizing a novel spin sensitive phase contrast imaging technique, the vector magnetization is measured in-situ with high spatial and temporal resolution and applied to a number of experiments. Using optically trapped F = 1 87Rb spinor condensates, the equilibrium phase diagram of a spin-1 Bose gas is quantitatively explored by observing the evolution of unmagnetized spin textures and their thermal equilibrium properties. Spin domain coarsening and a strong dependence of the spin configuration on the quadratic Zeeman shift is observed, supporting the predicted mean-field equilibrium phase diagram for small values of the quadratic shift. Additionally, spinor Bose gases are demonstrated to be an effective tool in calibrating and characterizing experimental imaging systems. Sinusoidal test patterns of varying pitch are created and used to extract the modulation transfer function and quantify optical aberrations which are of immense importance in systems which claim to have high spatial resolution. Lastly we realize an optical kagome geometry in a two-dimensional optical superlattice with a scalar Bose gases. The optical superlattice can be tuned between various geometries, including kagome, one-dimensional stripe, and decorated triangular lattice. Using atom optics we characterize the various geometries and demonstrate the versatility of this optical superlattice. The kagome geometry presents a new experimental arena for studies of geometrically frustrated systems.
We present coherence-enhanced imaging, an in situ technique that uses Raman superradiance to probe the spatial coherence of an ultracold gas. Applying this technique, we identify the coherent portion of an inhomogeneous degenerate (87)Rb gas and obtain a spatially resolved measurement of the first-order spatial correlation function. We find that the decay of spin gratings is enhanced in high density regions of a Bose-Einstein condensate, and ascribe the enhancement to collective atom-atom scattering. Further, we directly observe spatial inhomogeneities that arise generally in the course of extended-sample superradiance.
This thesis presents a novel magnetic resonance imaging (MRI) technique for spinor Bose-Einstein condensates (BEC) with the paramagnetic Faraday effect. This quantum-photon interface couples the spin of the BEC to the polarisation of an off-resonant laser, which in a magnetic field gradient allows a 1D density profile of the BEC to be reconstructed. As opposed to conventional imaging techniques that are destructive or diffraction limited, this technique is minimally destructive to the BEC and not diffraction limited. Multishot in situ imaging of a single condensate is therefore possible, paving the way for time-resolved studies and 2D/3D reconstructions. A theoretical model for Faraday imaging is developed using the tensor polarisability formalism for the atom-light interaction, and the signal-to-noise ratio is derived. Resolution limits induced by Stern-Gerlach separation are considered, encouraging rapid measurements with strong magnetic field gradients. Analysing the trapping potential reveals that the `magic-zero' wavelength 790nm produces no dipole force and enables a tightly focused probe laser to be used without perturbing the trap. Polarisation-maintaining fibers were seen to impart large fluctuations depending on the incident polarisation, which were minimised. The broad diode laser emission background is seen to reduce the lifetime of the BEC, which was corrected with an interference filter. Short-time Fourier transforms are used to process the photodetected signal, showing the evolution of the polarisation rotation frequency and amplitude. Frequency-modulation is observed at the power line frequency, corresponding to magnetic field fluctuations induced by nearby equipment. Birefringence of optical elements results in elliptical polarisation of the probe and an effective magnetic field, which is cancelled using a quarter-waveplate. The quadratic Zeeman effect causes rapid amplitude modulation, and is eliminated by applying a microwave dressing field. Radiative spin echo is achieved in a magnetic field gradient, proving that dephasing is coherent, and that multishot imaging possible. Magnetic resonance imaging (MRI) is performed on a partially-evaporated atom cloud, distinguishing the thermal and condensed fractions. A split dipole trap is used to create two spatially separated BECs, which are individually resolved during MRI. The resolution is only limited by the strength of the applied magnetic field gradient, and is not subject to the diffraction limit. Custom coils will enable MRI of condensates at the sub-micron scale.
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.