Microwave electrometry with Rydberg atoms in a vapour cell using bright atomic resonances

Journal name:
Nature Physics
Volume:
8,
Pages:
819–824
Year published:
DOI:
doi:10.1038/nphys2423
Received
Accepted
Published online

Abstract

Atom-based standards for length and time as well as other physical quantities such as magnetic fields show clear advantages by enabling stable and uniform measurements. Here we demonstrate a new method for measuring microwave (MW) electric fields based on quantum interference in a rubidium atom. Using a bright resonance prepared within an electromagnetically induced transparency window we could achieve a sensitivity of ~30μVcm−1Hz−1/2 and demonstrate detection of MW electric fields as small as ~8μVcm−1 with a modest set-up. The sensitivity is limited, at present, by the stability of our lasers and can be significantly improved in the future. Our method can serve as a new atom-based traceable standard for MW electrometry, with its reproducibility, accuracy and stability promising advances towards levels comparable with those attained in magnetometry at present.

At a glance

Figures

  1. Level diagram and experimental set-up.
    Figure 1: Level diagram and experimental set-up.

    a, The energy level diagram for the four-level system used for the experiments. The top part of the inset shows an example EIT feature associated the three-level system without a MW electric field. The bottom part of the inset shows an example of the bright resonance that is produced within the EIT window when a MW electric field is present. b, The experimental set-up used for the experiments.

  2. Three-level EIT and splitting from the MW electric fields.
    Figure 2: Three-level EIT and splitting from the MW electric fields.

    a, The experimental bright resonance dip and attenuation of the EIT transmission signal for low MW electric field amplitudes (black) with theory curves (red). The differences in the theory and experiment in the lower curves are attributed to the fact that we are using a four-level theory in these plots rather than the full 52-level theory and to uncertainties in the transit-time broadening. b, Autler–Townes splitting of the 53D5/2right arrow54P3/2 Rydberg transition that occurs for larger MW electric field strengths. The experimental parameters can be found in Methods. The peak splitting corresponds to λc/λpΩMW/2π. The uncertainties in ΩMW are described in the text.

  3. Enhanced transmission of the four-level EIT signal due to the MW electric field.
    Figure 3: Enhanced transmission of the four-level EIT signal due to the MW electric field.

    a, Probe transmission on resonance due to the MW electric field. The experimental results show agreement with a four-level density matrix calculation. The red line is the theory and the black line is the experimental data. The parameters for the measurements are provided in Methods. The transmission at the line centre will continue to decrease as the electric field increases to the Autler–Townes regime. The MW electric field is tuned 1MHz off resonance. b, The enhancement of the EIT transmission when the MW electric field is applied for small MW electric field amplitudes. The MW electric field broadens the two-photon EIT transition in velocity space in a thermal vapour. This leads to enhanced transmission of the probe laser.

  4. Four-level EIT transmission signal as a function of MW electric field amplitude.
    Figure 4: Four-level EIT transmission signal as a function of MW electric field amplitude.

    a, Transmission line shapes for different values of MW electric field amplitude as a function of MW electric field detuning (ΔRF). The black curves are experimental data, and the red curves are Gaussian fits to the data. The graph shows the change in probe transmission as a function of MW electric field frequency. All of the data shown were taken under the same conditions as in Fig. 3, except the MW electric field was tuned to resonance. Each trace is the average of 9,000 scans. b, The on-resonance peak height taken from the traces in a as a function of MW electric field amplitude. The dashed red line is a theoretical four-level density matrix calculation. The vertical error bars in the figure represent the standard deviation of the fits to the peak heights. The horizontal axis is derived from the MW power applied to the horn antenna and the associated experimental geometry. The horizontal error bars are the uncertainty of calculating the MW electric field due to uncertainty in the output field of the MW generator, 5% accounting for both the calibration error to the Autler–Townes splitting at larger MW electric fields and the output setting error described in the text. The dashed blue (red) lines represent theoretical variation due to a change of ±10% in the coupling (probe) power.

References

  1. Hall, J. L. Nobel lecture: Defining and measuring optical frequencies. Rev. Mod. Phys. 78, 12791295 (2006).
  2. Savukov, I. M., Seltzer, S. J., Romalis, M. V. & Sauer, K. L. Tunable atomic magnetometer for detection of radio-frequency magnetic fields. Phys. Rev. Lett. 95, 063004 (2005).
  3. Balabas, M. V., Karaulanov, T., Ledbetter, M. P. & Budker, D. Polarized alkali-metal vapor with minute-long transverse spin-relaxation time. Phys. Rev. Lett. 105, 070801 (2010).
  4. Wasilewski, W. et al. Quantum noise limited and entanglement-assisted magnetometry. Phys. Rev. Lett. 104, 133601 (2010).
  5. Koschorreck, M., Napolitano, M., Dubost, B. & Mitchell, M. W. Sub-projection-noise sensitivity in broadband atomic magnetometry. Phys. Rev. Lett. 104, 093602 (2010).
  6. Hanneke, D., Fogwell, S. & Gabrielse, G. New measurement of the electron magnetic moment and the fine structure constant. Phys. Rev. Lett. 100, 120801 (2008).
  7. Tishchenko, V. A., Tokatly, V. I. & Luk’yanov, V. I. The beginning of the metrology of radio frequency electromagnetic fields and the first standards of electric field strength. Meas. Tech. 46, 7684 (2003).
  8. Kanda, M. & Orr, R. D. Generation of standard electromagnetic fields in a TEM cell. NBS Technical note 1319 (1988).
  9. Kanda, M. Standard probes for electromagnetic field measurements. IEEE Trans. Antennas Propag. 41, 13491364 (1993).
  10. Kanda, M. Standard antennas for electromagnetic interference measurements and methods to calibrate them. IEEE Trans. Electromagn. Compat. 36, 261273 (1994).
  11. Mal’ter, I. G., Pavlovskii, O. P., Korshunov, V. A. & Voronov, V. L. Russian and foreign millimeter band radio measuring instruments. Meas. Tech. 52, 9971005 (2009).
  12. Tishchenko, V. A., Tokalty, V. I. & Luk’yanov, V. I. Upgrading radio frequency electromagnetic field standards part I. Meas. Tech. 46, 796801 (2003).
  13. Tishchenko, V. A., Tokalty, V. I. & Luk’yanov, V. I. Upgrading radio frequency electromagnetic field standards part II. Meas. Tech. 46, 903911 (2003).
  14. Electro-optical Sensor for Detecting Electric Fields; http://www.kyosemi.co.jp/en/.
  15. Sriram, S., Kingsley, S. A. & Boyd, J. T. Electro-optical sensor for detecting electric fields. US patent 5,267,336 (1992).
  16. Camparo, J. C. Atomic stabilization of electromagnetic field strength using Rabi resonances. Phys. Rev. Lett. 80, 222225 (1998).
  17. Swan-Wood, T., Coffer, J. G. & Camparo, J. C. Precision measurements of absorption and refractive index using an atomic candle. IEEE Trans. Inst. Meas. 50, 12291233 (2001).
  18. Gordon, J. A., Holloway, C. L., Jefferts, S. & Heavner, T. 2010 Int. Symp. on Electromagnetic Compatibility 321324 (2010).
  19. Kübler, H., Shaffer, J. P., Baluksian, T., Löw, R. & Pfau, T. Coherent excitation of Rydberg atoms in micrometre-sized atomic vapour cells. Nature Photon. 4, 112116 (2010).
  20. Fleischhauer, M., Imamoglu, A. & Marangos, J. P. Electromagnetically induced transparency: Optics in coherent media. Rev. Mod. Phys. 77, 633673 (2005).
  21. Mohapatra, A. K., Jackson, T. R. & Adams, C. S. Coherent optical detection of highly excited Rydberg states using electromagnetically induced transparency. Phys. Rev. Lett. 98, 113003 (2007).
  22. Bason, M. G. et al. Enhanced electric field sensitivity of rf-dressed Rydberg dark states. New J. Phys. 12, 065015 (2010).
  23. Tanasittikosol, M. et al. Microwave dressing of Rydberg dark states. J. Phys. B 44, 184020 (2011).
  24. Gallagher, T. F. Rydberg Atoms 1st edn (Cambridge Univ. Press, 1994).
  25. Herrmann, P. P., Hoffnagle, J., Schlumpf, N., Telegdi, V. L. & Weis, A. Stark spectroscopy of forbidden two-photon transitions: A sensitive probe for the quantitative measurement of small electric fields. J. Phys. B 19, 12711280 (1986).
  26. Schramm, A. et al. Laser photoelectron attachment to molecules in a skimmed supersonic beam: Diagnostics of weak electric fields and attachment cross sections down to 20μeV. Phys. Rev. Lett. 81, 778781 (1998).
  27. Tauschinsky, A., Thijssen, R. M. T., Whitlock, S., van Linden van den Heuvell, H. B. & Spreeuw, R. J. C. Spatially resolved excitation of Rydberg atoms and surface effects on an atom chip. Phys. Rev. A 81, 063411 (2010).
  28. Frey, M. T., Ling, X., Lindsay, B. G., Smith, K. A. & Dunning, F. B. Use of the Stark effect to minimize residual electric fields in an experimental volume. Rev. Sci. Instum. 64, 36493650 (1993).
  29. Osterwalder, A. & Merkt, F. Using high Rydberg states as electric field sensors. Phys. Rev. Lett. 82, 18311834 (1999).
  30. Auzinsh, M., Jayasinghe, L., Oelke, L., Ferber, R. & Shafer-Ray, N. Strobe imaging of electric fields by depolarization of Rydberg states of Hg. J. Phys. D 34, 19331938 (2001).
  31. Figger, H., Leuchs, G., Straubinger, R. & Walther, H. A photon detector for submillimetre wavelengths using Rydberg atoms. Opt. Commun. 33, 3741 (1980).
  32. Goy, P. et al. Rydberg atom masers. II. Triggering by external radiation and applications to millimeter-wave detectors. Phys. Rev. A 27, 20652081 (1983).
  33. Arora, B., Safronova, M. S. & Clark, C. W. Determination of electric dipole matrix elements in K and Rb from Stark shift measurements. Phys. Rev. A 76, 052516 (2007).
  34. Li, W., Mourachko, I., Noel, M. W. & Gallagher, T. F. Millimeter-wave spectroscopy of cold Rb Rydberg atoms in a magneto-optical trap: Quantum defects of the ns, np, and nd series. Phys. Rev. A 67, 052502 (2003).
  35. Mack, M. et al. Measurement of absolute transition frequencies of 87Rb to nS and nD Rydberg states by means of electromagnetically induced transparency. Phys. Rev. A 83, 052515 (2011).
  36. Steck, D. A. Rubidium 87 D line data. available online at http://steck.us//alkalidata (Revision 2.1.4,23 December 2010).
  37. HP 8340B, HP 8341B Synthesized Sweepers, Hewlett-Packard Company, 1400 Fountaingrove Parkway, Santa Rosa, CA (1986).
  38. Piotrowicz, M. J. et al. Measurement of the electric dipole moments for transitions to Rubidium Rydberg states via Autler–Townes splitting. New J. Phys. 13, 093012 (2011).
  39. Schwettmann, A., Crawford, J., Overstreet, K. R. & Shaffer, J. P. Cold Cs Rydberg-gas interactions. Phys. Rev. A 74, 020701 (2006).
  40. Thomas, J. E. & Quivers, W. W. Transit-time effects in optically pumped coupled three-level systems. Phys. Rev. A 22, 21152121 (1980).

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Author information

Affiliations

  1. Homer L. Dodge Department of Physics and Astronomy, The University of Oklahoma, 440 West Brooks Street, Norman, Oklahoma 73019, USA

    • Jonathon A. Sedlacek,
    • Arne Schwettmann,
    • Harald Kübler &
    • James P. Shaffer
  2. 5. Physikalisches Institut, Universität Stuttgart, Pfaffenwaldring, 57 D-70550 Stuttgart, Germany

    • Harald Kübler,
    • Robert Löw &
    • Tilman Pfau

Contributions

J.P.S. and T.P. conceived the idea. J.P.S. led the project and wrote the paper. J.A.S., A.S. and H.K. carried out the experiments and reduced the data. A.S. and J.A.S. wrote the simulation programs. R.L. contributed useful ideas to the analysis of the experiment. All authors contributed extensively to the work.

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The authors declare no competing financial interests.

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