Fundamental quantum fluctuations caused by the Heisenberg principle limit measurement precision1. If the uncertainty is distributed equally between conjugate variables of the meter system, the measurement precision cannot exceed the standard quantum limit. When the meter is a large angular momentum, going beyond the standard quantum limit requires non-classical states such as squeezed states2,3,4 or Schrödinger-cat-like states5,6,7. However, the metrological use of the latter8,9,10 has been so far restricted to meters with a relatively small total angular momentum because the experimental preparation of these non-classical states is very challenging11,12. Here we report a measurement of an electric field based on an electrometer consisting of a large angular momentum (quantum number J ≈ 25) carried by a single atom in a high-energy Rydberg state. We show that the fundamental Heisenberg limit13 can be approached when the Rydberg atom undergoes a non-classical evolution through Schrödinger-cat states. Using this method, we reach a single-shot sensitivity of 1.2 millivolts per centimetre for a 100-nanosecond interaction time, corresponding to 30 microvolts per centimetre per square root hertz at our 3 kilohertz repetition rate. This highly sensitive, non-invasive space- and time-resolved field measurement extends the realm of electrometric techniques14,15,16,17 and could have important practical applications: detection of individual electrons in mesoscopic devices18,19,20,21 at a distance of about 100 micrometres with a megahertz bandwidth is within reach.
This is a preview of subscription content, access via your institution
Open Access articles citing this article.
Nature Communications Open Access 09 June 2022
npj Quantum Information Open Access 03 June 2021
Journal of Cluster Science Open Access 05 March 2021
Subscribe to Journal
Get full journal access for 1 year
only $3.90 per issue
All prices are NET prices.
VAT will be added later in the checkout.
Tax calculation will be finalised during checkout.
Get time limited or full article access on ReadCube.
All prices are NET prices.
Giovannetti, V., Lloyd, S. & Maccone, L. Quantum-enhanced measurements: beating the standard quantum limit. Science 306, 1330–1336 (2004).
Wasilewski, W. et al. Quantum noise limited and entanglement-assisted magnetometry. Phys. Rev. Lett. 104, 133601 (2010).
Müssel, W., Strobel, H., Linnemann, D., Hume, D. B. & Oberthaler, M. K. Scalable spin squeezing for quantum-enhanced magnetometry with Bose-Einstein condensates. Phys. Rev. Lett. 113, 103004 (2014).
Hosten, O., Engelsen, N. J., Krishnakumar, R. & Kasevich, M. A. Measurement noise 100 times lower than the quantum-projection limit using entangled atoms. Nature 529, 505–508 (2016).
Massar, S. & Polzik, E. S. Generating a superposition of spin states in an atomic ensemble. Phys. Rev. Lett. 91, 060401 (2003).
Lau, H. W., Dutton, Z., Wang, T. & Simon, C. Proposal for the creation and optical detection of spin cat states in Bose-Einstein condensates. Phys. Rev. Lett. 113, 090401 (2014).
Tanaka, T. et al. Proposed robust entanglement-based magnetic field sensor beyond the standard quantum limit. Phys. Rev. Lett. 115, 170801 (2015).
Leibfried, D. et al. Toward Heisenberg-limited spectroscopy with multiparticle entangled states. Science 304, 1476–1478 (2004).
Nagata, T., Okamoto, R., O’Brien, J. L., Sasaki, K. & Takeuchi, S. Beating the standard quantum limit with four-entangled photons. Science 316, 726–729 (2007).
Jones, J. A. et al. Magnetic field sensing beyond the standard quantum limit using 10-spin NOON states. Science 324, 1166–1168 (2009).
Monz, T. et al. 14-Qubit entanglement: creation and coherence. Phys. Rev. Lett. 106, 130506 (2011).
Signoles, A. et al. Confined quantum Zeno dynamics of a watched atomic arrow. Nat. Phys. 10, 715–719 (2014).
Giovannetti, V., Lloyd, S. & Maccone, L. Advances in quantum metrology. Nat. Photon. 5, 222–229 (2011).
Vamivakas, A. N. et al. Nanoscale optical electrometer. Phys. Rev. Lett. 107, 166802 (2011).
Houel, J. et al. Probing single-charge fluctuations at a GaAs/AlAs interface using laser spectroscopy on a nearby InGaAs quantum dot. Phys. Rev. Lett. 108, 107401 (2012).
Dolde, F. et al. Nanoscale detection of a single fundamental charge in ambient conditions using the NV− center in diamond. Phys. Rev. Lett. 112, 097603 (2014).
Arnold, C. et al. Cavity-enhanced real-time monitoring of single-charge jumps at the microsecond time scale. Phys. Rev. X 4, 021004 (2014).
Cleland, A. N. & Roukes, M. L. A nanometre-scale mechanical electrometer. Nature 392, 160–162 (1998).
Bunch, J. S. et al. Electromechanical resonators from graphene sheets. Science 315, 490–493 (2007).
Yoo, M. J. et al. Scanning single-electron transistor microscopy: imaging individual charges. Science 276, 579–582 (1997).
Devoret, M. H. & Schoelkopf, R. J. Amplifying quantum signals with the single-electron transistor. Nature 406, 1039–1046 (2000).
Lo, H. Y. et al. Spin-motion entanglement and state diagnosis with squeezed oscillator wavepackets. Nature 521, 336–339 (2015).
Wollman, E. E. et al. Quantum squeezing of motion in a mechanical resonator. Science 349, 952–955 (2015).
Caves, C. M., Thorne, K. S., Drever, R. W., Sandberg, V. D. & Zimmermann, M. On the measurement of a weak classical force coupled to a quantum-mechanical oscillator. I. Issues of principle. Rev. Mod. Phys. 52, 341–392 (1980).
Kitagawa, M. & Ueda, M. Squeezed spin states. Phys. Rev. A 47, 5138–5143 (1993).
Arecchi, F., Courtens, E., Gilmore, R. & Thomas, H. Atomic coherent spin states in quantum optics. Phys. Rev. A 6, 2211–2237 (1972).
Osterwalder, A. & Merkt, F. Using high Rydberg states as electric field sensors. Phys. Rev. Lett. 82, 1831–1834 (1999).
Abel, R. P., Carr, C., Krohn, U. & Adams, C. S. Electrometry near a dielectric surface using Rydberg electromagnetically induced transparency. Phys. Rev. A 84, 023408 (2011).
Hempel, C. et al. Entanglement-enhanced detection of single-photon scattering events. Nat. Photon. 7, 630–633 (2013).
Hermann-Avigliano, C. et al. Long coherence times for Rydberg qubits on a superconducting atom chip. Phys. Rev. A 90, 040502(R) (2014).
Bollinger, J. J., Itano, W. M., Wineland, D. J. & Heinzen, D. J. Optimal frequency measurements with maximally correlated state. Phys. Rev. A 54, R4649–R4652 (1996).
Pauli, W. Jr Über das Wasserstoffspektrum vom Standpunkt der neuen Quantenmechanik. Z. Phys. 36, 336–363 (1926).
Gay, J. C., Delande, D. & Bommier, A. Atomic quantum states with localization on classical elliptical orbits. Phys. Rev. A 39, 6587–6590 (1989).
Bellomo, P., Stroud, C. R., Farrelly, D. & Uzer, T. Quantum-classical correspondence in the hydrogen atom in weak external fields. Phys. Rev. A 58, 3896–3913 (1998).
Bellomo, P. & Stroud, C. R. Jr Classical evolution of quantum elliptic states. Phys. Rev. A 59, 2139–2145 (1999).
We thank A. Cottet, T. Kontos and W. Munro for discussions. We acknowledge funding by the EU under the ERC project ‘DECLIC’ and the RIA project ‘RYSQ’.
Reviewer Information Nature thanks C. Adams, L. Maccone and the other anonymous reviewer(s) for their contribution to the peer review of this work.
The authors declare no competing financial interests.
Extended data figures and tables
The atoms are produced by excitation of a thermal rubidium beam (blue arrow) propagating along axis O–x. Two horizontal electrodes A and B (represented here as cut by a vertical plane) produce the directing electric field (F) along O–z. The gap between A and B is surrounded by four independent electrodes (1, 2, 3 and 4), on which we apply radio-frequency signals to produce σ+ fields with tunable phase and amplitude. Electrodes 1 and 4, not represented, are the mirror images of electrodes 2 and 3 (in yellow) with respect to the x–O–z plane. The laser excitation to the Rydberg states is performed using three laser beams that intersect in the centre O of the cavity. The 780 nm and 776 nm laser beams are collinear (red), the 1,259 nm laser is sent perpendicular to the other beams (green). Once the atoms have left the electrode structure, they enter the field-ionization detector D.
About this article
Cite this article
Facon, A., Dietsche, EK., Grosso, D. et al. A sensitive electrometer based on a Rydberg atom in a Schrödinger-cat state. Nature 535, 262–265 (2016). https://doi.org/10.1038/nature18327
Nature Communications (2022)
Journal of Cluster Science (2022)
npj Quantum Information (2021)
Nature Physics (2020)
Optical and Quantum Electronics (2020)