BRIEF COMMUNICATIONS NATURE|Vol 435|26 May 2005 440 7. Kundel, H. L. in Medical Imaging 2000: Image Perception and Performance (ed. Krupinski, E. A.) 135–144 (2000). 8. Gur, D., Rockette, H. E., Warfel, T., Lacomis, J. M. & Fuhrman, C. R. Acad. Radiol. 10, 1324–1326 (2003). doi:435439a Supplementary information accompanies this communication on Nature’s website. Competing financial interests: declared none. by charging the probed structure electrically. This measurement is more sensitive than the one discussed above because the trapping parameters can be adjusted independently from the measured potential landscape by using a separate wire for holding the BEC. The optimal potential sensitivity of a BEC used as a field sensor, ǵBǃȍǵN/z 0 3 , is achieved if the trapping parameters are adjusted so that the cloud’s transverse size matches the desired spatial resolution z 0 . Here ǵN is the minimal atom-number variation resolved by the imaging system, and ȍ contains all the atomic-physics parameters of the spe- cific atom (ȍǃ8.63ǂ10 ǁ29 tesla cubic metres for the 87 Rb used in our experiment). Currently available CCD (charge-coupled device) cam- eras allow atom-shot noise-limited detection with a ǵN value of better than 10 atoms per pixel in absorption imaging, so that a sensitiv- ity, ǵB, of 1 nanotesla is possible even at a high spatial resolution of 1 Ȗm (or 1 picotesla at 10 Ȗm). By changing to a different atom with higher mass and/or by reducing the inter- atomic interaction, a significant increase in sensitivity can be achieved. A comparison of different magnetic-field measurement techniques 1–4,12 (see supplemen- tary information) shows that BECs as mag- netic sensors could reach unprecedented sensitivity over a large range of spatial resolu- tion. The sample measurements we present here reach higher sensitivities than those obtained with established techniques operat- ing at the same spatial resolution. Stephan Wildermuth*, Sebastian Hofferberth*, Igor Lesanovsky*, Elmar Haller*, L. Mauritz Andersson*, Sönke Groth*†, Israel Bar-Joseph†, Peter Krüger*, Jörg Schmiedmayer* *Physikalisches Institut, Universität Heidelberg, Philosophenweg 12, 69120 Heidelberg, Germany e-mail: schmiedmayer@atomchip.org †Department of Condensed Matter Physics, The Weizmann Institute of Science, Rehovot 76100, Israel 1. Bending, S. J. Adv. Phys. 48, 499–535 (1999). 2. Freeman, M. R. & Choi, B. C. Science 294, 1484–1488 (2001). 3. Faley, M. I. et al. Supercond. Sci. Technol. 17, 324–327 (2004). 4. Kominis, I. K., Kornack, T. W., Allred, J. C. & Romalis, M. V. Nature 422, 596–599 (2003). 5. Fortagh, J., Ott, H., Kraft, S., Günther, A. & Zimmermann, C. Phys. Rev. A 66, 041604 (2002). 6. Esteve, J. et al. Phys. Rev. A 70, 043629 (2004). 7. Leanhardt, A. E. et al. Phys. Rev. Lett. 89, 040401 (2002). 8. Jones, M. P. A. et al. Phys. Rev. Lett. 91, 080401 (2003). 9. Dunjko, V., Lorent, V. & Olshanii, M. Phys. Rev. Lett. 86, 5413–5416 (2001). 10. Folman, R., Krüger, P., Schmiedmayer, J., Denschlag, J. & Henkel, C. Adv. At. Mol. Opt. Phys. 48, 263–356 (2002). 11. Rous, P. J., Yongsunthon, R., Stanishevsky, A. & Williams, E. D. J. Appl. Phys. 95, 2477–2486 (2004). 12. Oral, A. et al. IEEE Trans. Magn. 38, 2438–2440 (2002). doi:435440a Supplementary information accompanies this communication on Nature’s website . Competing financial interests: declared none. BRIEF COMMUNICATIONS ARISING online ➧ www.nature.com/bca see Contents pages. BOSE–EINSTEIN CONDENSATES Microscopic magnetic-field imaging Today’s magnetic-field sensors 1 are not capa- ble of making measurements with both high spatial resolution and good field sensitivity. For example, magnetic force microscopy 2 allows the investigation of magnetic structures with a spatial resolution in the nanometre range, but with low sensitivity, whereas SQUIDs 3 and atomic magnetometers 4 enable extremely sensitive magnetic-field measure- ments to be made, but at low resolution. Here we use one-dimensional Bose–Einstein con- densates in a microscopic field-imaging tech- nique that combines high spatial resolution (within 3 micrometres) with high field sensi- tivity (300 picotesla). Trapped cold atoms are ideal magnetic sensors as they are very sensitive to changes in magnetic-field landscapes, even in the pres- ence of large homogeneous offset fields. Den- sity modulations in trapped thermal atomic clouds have already been used as a measure of magnetic field variation caused by irregular current flow in nearby conductors 5–8 . We have produced a versatile, high-resolution sensor based on Bose–Einstein condensates (BECs). Its sensitivity is not limited by the temperature T of the cloud, but is rather determined by the chemical potential Ȗ of the condensate, which can be orders of magnitude lower than k B T (where k B is Boltzmann’s constant). The principles of the technique are shown in Fig. 1a. A BEC is trapped at the measurement site so that its density profile can be directly imaged. The spatially varying density is a mea- sure of the potential energy and hence of the local magnetic-field variation. To probe spatial magnetic-field variations, we start by confining a one-dimensional BEC (in which Ȗ is smaller than an energy quantum of transverse excita- tion) 9 in an elongated magnetic micro-trap with strong transverse and weak longitudinal confinement, created by small conductors mounted on the surface of an atom chip 10 . As a demonstration, we measured the magnetic-field variations above the 100-Ȗm- wide current-carrying wire used to create the trap itself. Scanning the position of the BEC enabled us to reconstruct a full two-dimen- sional magnetic-field profile (Fig. 1b) near the wire with unprecedented accuracy (sensi- tivity of 4 nanotesla) at the measurement resolution (3 Ȗm). From this map, we recon- structed the local current flow in the wire 11 and found extremely small angular deviations (2ǂ10 ǁ4 root-mean-square radians) from a straight current path (for details, see supple- mentary information). We also investigated an independent field landscape by placing a BEC close (5 Ȗm) to a test wire structure. As long as this structure is grounded and carries no current, the atomic- density profile is homogeneous within the detection sensitivity. This corresponds to an upper bound in potential roughness of less than 10 ǁ14 eV, corresponding to a temperature of 200 picokelvin (field sensitivity of 300 picotesla). As soon as a small current (about 5 mA) is passed through the wire, a characteristic field profile is imaged. The technique is applicable not only to mag- netic fields, but can also be used to detect vari- ations in electrostatic fields, as can be shown Probed sample Chip substrate Trapping wire Imaging laser beam CCD camera Probe BEC y z x –400 –200 0 B (nT) 200 300 200 100 0 0 50 –50 400 a b Figure 1 | One-dimensional Bose–Einstein condensate as a magnetic-field sensor. a, Experimental set-up. A Bose–Einstein condensate is created and trapped by a current- carrying wire mounted on a silicon surface (atom chip) and is positioned above the sample to be probed. b, Two-dimensional scan of the magnetic landscape (field component along the wire direction) above a 100-Ȗm-wide and 3.1-Ȗm-tall gold wire. This profile has been reconstructed from 28 equally spaced one- dimensional atomic-density traces measured 10 Ȗm above the current-carrying wire at a homogeneous offset field of 2 millitesla, so that relative field variations of only 4 p.p.m. stemming from slightly irregular current flow could be measured at a spatial resolution of 3 Ȗm. Nature Publishing Group ©2005