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Magnetic Resonance Based Atomic Magnetometers

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High Sensitivity Magnetometers

Part of the book series: Smart Sensors, Measurement and Instrumentation ((SSMI,volume 19))

Abstract

The chapter gives a comprehensive account of the theory of atomic magnetometers deploying optically detected magnetic resonance (ODMR) in spin-polarized atomic ensembles, and of the practical realization of such magnetometers. We address single laser beam experiments throughout, but give explicit hints on how the results can be extended to pump-probe configurations. After a general introduction and the presentation of a classification of atomic magnetometer principles, we address the three major processes, viz., polarization creation, atom-field interaction, and optical detection that occur in the subclass of magnetic resonance-based magnetometers. The time-independent signals on which so-called Hanle magnetometers built are also reviewed for both spin-oriented and spin-aligned media. In the extended central part we derive an algebraic master expression (valid for all ODMR magnetometers) that expresses the signal, i.e., the detected time-dependent light power in terms of all system parameters. We then give explicit algebraic results for the absolute signals observed in the so-called Mz- and Mx-configurations for various geometries with arbitrary relative orientations of the static field, the oscillating field and the light propagation direction. Although the chapter’s main focus is on magnetic resonance processes driven by oscillating magnetic fields (we treat both spin-oriented and spin-aligned media), we also address magnetometers in which the magnetic resonance is driven by amplitude-, frequency-, or polarization-modulated light. The final section of the chapter gives a detailed account of the physical realization of an Mx-magnetometer array and the electronics used for its operation. We demonstrate that the observed resonance signals have the predicted spectral shapes and illustrate procedures for optimizing the magnetometric sensitivity.

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Notes

  1. 1.

    Free spin precession magnetometers discussed in Chap. 16 form an exception from this general rule.

  2. 2.

    Here also the 3He magnetometers described by W. Heil elsewhere in this book are a most notable exception.

  3. 3.

    The non-absorbing state \( |1/2, + 1/2\rangle \) is called a ‘dark’ state since atoms in that state do not fluoresce, while the \( |1/2, - 1/2\rangle \) state is a ‘bright’ state. In this sense the oscillatory time-dependence of the magnetometer principles discussed below in this chapter can be understood as resulting from coherent oscillations between dark and bright states.

  4. 4.

    Note that \( S_{z} \) and \( A_{zz} \) in Eq. 9 refer to a quantization axis along the \( {\mathbf{k}} \)-vector, while the quantization axis defining \( A_{{z^{{\prime }} z^{{\prime }} }}^{{\prime }} \) in Eq. 10 is along the light polarization as shown in Fig. 2.

  5. 5.

    Magnetic resonance transitions can also be driven between atomic fine or hyperfine structure components, in which case the characteristic frequencies, \( \omega_{\text{fs}} = \varDelta E_{\text{fs}} /\hbar \) and \( \omega_{\text{hfs}} = \varDelta E_{\text{hfs}} /\hbar \), respectively, are determined by internal magnetic fields.

  6. 6.

    The neglected component induces a systematic red shift \( \varDelta \omega_{L} \) (Bloch-Siegert shift) of the magnetic resonance frequency \( \omega_{L} \) that is on the order of \( \varDelta \omega_{L} \sim \gamma^{2} /\omega_{L} \). where \( \gamma \) is the polarization relaxation rate.

  7. 7.

    The results given below are easily extended to magnetometers using a probe beam that propagates along a direction \( {\mathbf{k}}_{\text{probe}} \ne {\mathbf{k}}_{\text{pump}} \). For this one has to project \( \mathbf{S}(t) \) onto the probe beam by \( S_{\text{probe}} (t) = \mathbf{S}(t) \cdot {\mathbf{k}}_{\text{probe}} /|{\mathbf{k}}_{\text{probe}} | \) and replace in the subsequent equations \( S_{k} (t) \) by \( S_{\text{probe}} (t) \).

  8. 8.

    Besides its dependence on the field orientation, the phase offset \( \phi_{0} \) may be affected by additional phase shifts arising, e.g., from complex impedances in the coil driving and photo-detector circuits, or geometrical alignment uncertainties of the rf coils.

  9. 9.

    We note that the modulation frequency \( \omega_{\bmod } \) used in this section plays an equivalent role than the rf frequency \( \omega_{\text{rf}} \) in the ‘true’ magnetic resonance magnetometrs discussed in the previous sections.

  10. 10.

    For polarization modulation we use the acronym SM---meaning Stokes (parameter) modulation---since the acronym \( PM \) might be mistaken with the standing acronym for phase modulation.

  11. 11.

    In alkali atoms the \( F \to F - 1 \) hyperfine component of the \( |n^{2} S_{1/2} \rangle \to |n^{2} P_{1/2} \rangle \) transition yields the largest signals.

  12. 12.

    Here we used the proportionality between \( P_{0} \) and \( P_{\text{DC}} \) to write the scaling of the noise with respect to \( P_{0} \).

  13. 13.

    Lookup table based implementations of the sin and cos functions [55] profit from this representation since the two most significant bits of \( \phi \) correspond to its quadrant.

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Author information

Authors and Affiliations

  1. Physics Department, University of Fribourg, 1700, Fribourg, Switzerland

    Antoine Weis & Zoran D. Grujić

  2. Paul Scherrer Institut, 5232, Villigen, Switzerland

    Georg Bison

Authors
  1. Antoine Weis
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  2. Georg Bison
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  3. Zoran D. Grujić
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Correspondence to Antoine Weis .

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Editors and Affiliations

  1. Ben-Gurion University of the Negev , Beer-Sheva, Israel

    Asaf Grosz

  2. Northern Illinois University, DeKalb, Illinois, USA

    Michael J. Haji-Sheikh

  3. Massey University (Manawatu), Palmerston North, New Zealand

    Subhas C. Mukhopadhyay

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Weis, A., Bison, G., Grujić, Z.D. (2017). Magnetic Resonance Based Atomic Magnetometers. In: Grosz, A., Haji-Sheikh, M., Mukhopadhyay, S. (eds) High Sensitivity Magnetometers. Smart Sensors, Measurement and Instrumentation, vol 19. Springer, Cham. https://doi.org/10.1007/978-3-319-34070-8_13

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  • DOI: https://doi.org/10.1007/978-3-319-34070-8_13

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