Measurement of magnetic fields permits identification of features below the earth's surface, with applications ranging from the detection of unexploded ordnance and buried hazardous waste containers to oil and mineral exploration. A high-resolution magnetic map (a collection of magnetic-field readings taken at different points in space) can pinpoint small-scale magnetic sources near the surface. However, for large or deeply buried objects, such readings are subject to systematic errors. These arise from the difficulty of accurately separating weak but large-scale magnetic field variations from the stronger but short-scale fields generated by nearby or near-surface objects.
By measuring at very high altitude, one can map magnetic fields with a deliberately lower spatial resolution and ‘see’ larger-scale and deeper objects. Such measurements can be implemented using satellites in low-earth orbit, but it is challenging to keep the stray magnetic fields produced by the satellite platform below the level required for useful measurements. Moreover, the cost of deploying spacecraft places limits on the number of available sensors.
We recently suggested an alternative magnetometry method.1 Although it makes use of the natural layer of atomic sodium in the mesosphere, located at around 90km, the scheme involves entirely ground-based apparatus. It takes advantage of the high-powered laser projection systems developed to create artificial laser ‘guide stars’ (LGSs) that are used in astronomical adaptive-optics imaging. The 100km-length-scale measurements permitted by this technique are applicable, for instance, to geological studies of the crust and outer mantle, determination of large-scale ocean currents relevant to climate, and calibration of magnetic maps for navigation.
Our method is based on the remote detection of a magneto-optical resonance. An atomic spin (for sodium, essentially the spin of the valence electron) precesses in a transverse magnetic field, that is, the spin axis rotates. The frequency of this precession, known as the Larmor frequency, is directly proportional to the magnitude of the field, with the proportionality given simply by fundamental constants. Therefore, determining this frequency is equivalent to measuring the magnetic field. Under normal circumstances, the spins in an atomic vapor are randomly oriented. But when the atoms interact with a laser beam, they can absorb angular momentum and be optically pumped into a definite state, that is, be forced to have their spins all point in the same direction. Larmor precession around a transverse field tends to ‘smear out’ the effects of optical pumping unless this pumping occurs synchronously with precession.2 When the frequencies match, the atomic polarization created during one cycle is in phase with that generated during previous cycles, and the atoms are efficiently polarized.
Moreover, laser-induced fluorescence intensity depends on atoms' spin state, so that the resonant match of frequencies results in a detectable change in the fluorescence. Thus, by varying the frequency at which the pumping laser beam is modulated in the neighborhood of the Larmor frequency and monitoring the fluorescence, we can determine the magnetic field experienced by sodium atoms. In this remote-detection scheme, only these particles need to be at high altitude: both pump laser and detector remain on the ground (see Figure 1).
Figure 1. Diagram of measurement scheme (not to scale). A modulated laser beam interacts with sodium atoms in the mesosphere. When the modulation frequency matches the atomic Larmor frequency, the atoms experience efficient optical pumping into a spin-polarized state. A detection telescope observes the modified fluorescence.
Recent advances in LGS technology greatly benefit this technique. Currently, most sodium LGS systems on astronomical telescopes project under 10W of average optical power per guide star on the sky. Based on Raman fiber lasers developed at the European Southern Observatory (ESO),3 for example, the next generation will raise this limit to 20W per guide star at a bandwidth of only a few megahertz. We have numerically optimized this laser format to achieve maximum photon return by optical pumping, and we anticipate it to yield about 12×106 photons/s/m2 on the ground (no modulation applied).4
The usefulness of the technique depends on its ability to detect small changes in the magnetic field. The attainable sensitivity, in turn, is determined by the number of sodium atoms that can be interrogated, the physics of atomic collisions in the mesosphere, and the quantity of fluorescence that can be detected. The number of usable atoms is limited by the available laser power and the requirement of sufficient intensity for optical pumping. Our numerical calculations show that collisions of sodium atoms with background atmospheric gas molecules are important. They limit to around 100μs the time during which an atomic spin can precess before decohering and, in turn, the sharpness of the magneto-optical resonance (see Figure 2). Finally, the fraction of captured fluorescence is very small at a distance of 90km, even with a large telescope. Nevertheless, we calculate an achievable sensitivity of better than 1nT (nanotesla) in a 1Hz bandwidth, suitable for the planned applications.
Figure 2. Representative resonance profiles for mesospheric sodium. The resonances shown correspond to distinct absorption lines of sodium, conventionally designated by D2(upper curve, blue diamonds) and D1 (lower curve, green circles). Symbols represent numerical calculations, and solid lines are Lorentzian fits to these results. The width of the resonances is determined by collisions with atmospheric molecules and by optical power broadening.
The numerical modeling of our high-precision technique to measure magnetic fields using ground-based lasers and mesospheric sodium shows promising results. Consequently, we are progressing toward a proof-of-principle measurement. We are currently preparing an experiment with a transportable 20W LGS projector system that can launch either a continuous-wave beam or a chopped beam with adjustable frequency in the range of the geomagnetic Larmor frequency. Both the projector and the receiving telescope have an aperture of about 40cm and can be pointed in any direction. Initial observations will be conducted in the summer of 2011 in southern Germany.
The authors are grateful for the support of the National Geospatial-Intelligence Agency University Research Initiatives program.
Ron Holzlöhner, Domenico Bonaccini Calia
European Southern Observatory
Garching bei München, Germany
Simon Rochester, Brian Patton, Dmitry Budker
University of California, Berkeley
1. J. M. Higbie, S. M. Rochester, B. Patton, R. Holzlöhner, D. Bonaccini Calia, D. Budker, Magnetometry with mesospheric sodium, Proc. Nat'l Acad. Sci. U.S.A.
108, no. 92011. doi:10.1073/pnas.1013641108
2. W. E. Bell, A. L. Bloom, Optically driven spin precession, Phys. Rev. Lett. 6, pp. 280-281, 1961.
3. D. Bonaccini Calia, Y. Feng, W. Hackenberg, R. Holzlöhner, L. Taylor, S. Lewis, Laser development for sodium laser guide stars at ESO, ESO Messenger 139, pp. 12-19, 2010.
4. R. Holzlöhner, S. M. Rochester, D. Budker, D. B. Calia, J. M. Higbie, W. Hackenberg, Optimization of cw sodium laser guide star efficiency, Astron. Astrophys
. 510, no. A202010. doi:10.1051/0004-6361/200913108