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.
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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.
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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
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