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Entanglement-Based dc Magnetometry with Separated Ions*

T. Ruster, H. Kaufmann, M. A. Luda†, V. Kaushal, C. T. Schmiegelow‡, F. Schmidt-Kaler, and U. G. Poschinger

  • Institut für Physik, Universität Mainz, Staudingerweg 7, 55128 Mainz, Germany

  • †Present address: DEILAP, CITEDEF & CONICET, J.B. de La Salle 4397, 1603 Villa Martelli, Buenos Aires, Argentina.
  • ‡Present address: Departamento de Física, FCEyN, UBA and IFIBA, Conicet, Pabellón 1, Ciudad Universitaria, 1428 Buenos Aires, Argentina.
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Phys. Rev. X 7, 031050 – Published 21 September, 2017

DOI: https://doi.org/10.1103/PhysRevX.7.031050

Abstract

We demonstrate sensing of inhomogeneous dc magnetic fields by employing entangled trapped ions, which are shuttled in a segmented Paul trap. As sensor states, we use Bell states of the type |↑↓⟩+eiφ|↓↑⟩ encoded in two Ca+40 ions stored at different locations. The linear Zeeman effect leads to the accumulation of a relative phase φ, which serves for measuring the magnetic-field difference between the constituent locations. Common-mode magnetic-field fluctuations are rejected by the entangled sensor state, which gives rise to excellent sensitivity without employing dynamical decoupling and therefore enables accurate dc sensing. Consecutive measurements on sensor states encoded in the S1/2 ground state and in the D5/2 metastable state are used to separate an ac Zeeman shift from the linear dc Zeeman effect. We measure magnetic-field differences over distances of up to 6.2 mm, with accuracies down to 300 fT and sensitivities down to 12  pT/Hz. Our sensing scheme features spatial resolutions in the 20-nm range. For optimizing the information gain while maintaining a high dynamic range, we implement an algorithm for Bayesian frequency estimation.

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  • *The U.S. Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright annotation thereon. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the view of the U.S. Army Research Office.

Popular Summary

Precise magnetic-field sensors are essential for many applications in modern technology as well as applied and fundamental research. With recent advances in quantum technology, highly sensitive magnetometers based on the spins of single electrons have become available. In an external magnetic field, the spin orientation wobbles at a frequency that is set by the field’s strength. This frequency can be determined with high accuracy by creating a superposition of the spin-up and spin-down states—states where quantum mechanics allows the spin to point up and down at the same time. Being highly sensitive to magnetic fields, these states are fragile and easily destroyed by noise. We have designed a magnetometer that is resilient to specific sources of noise by using quantum entanglement.

We entangle the valence electrons of two calcium ions such that their spins are always aligned in opposite directions, while the state of each individual spin is completely undetermined. This shields the quantum state from magnetic noise acting on both ions so that the difference in the magnetic field between the two locations can be measured with high precision. We use a segmented linear ion trap to move entangled ions freely along the trap axis, separating them by macroscopic distances of up to 6.2 mm. Our measurement scheme enables us to measure inhomogeneous direct-current magnetic fields with spatial resolution at the 20-nm level, reaching accuracies down to 310 fT.

For future work, our device could be extended to measure magnetic fields in any direction (not just along the trap axis) as well as to probe the magnetic properties of miniscule objects such as additional ions or single-molecule magnets.

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  59. All quantities with a “Δ” denote differences with respect to sensing positions x1 and x2; we consistently omit these arguments.

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Phys. Rev. X 7, 031050– Published 21 September, 2017
  • Received 6 April 2017
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