14-Qubit entanglement: creation and coherence. Magnetic field sensing beyond the standard quantum limit using 10-spin NOON states. Beating the standard quantum limit with four-entangled photons. Toward Heisenberg-limited spectroscopy with multiparticle entangled states. Proposed robust entanglement-based magnetic field sensor beyond the standard quantum limit. Proposal for the creation and optical detection of spin cat states in Bose-Einstein condensates. Generating a superposition of spin states in an atomic ensemble. Measurement noise 100 times lower than the quantum-projection limit using entangled atoms. Scalable spin squeezing for quantum-enhanced magnetometry with Bose-Einstein condensates. Müssel, W., Strobel, H., Linnemann, D., Hume, D. Quantum noise limited and entanglement-assisted magnetometry.

Quantum-enhanced measurements: beating the standard quantum limit. This highly sensitive, non-invasive space- and time-resolved field measurement extends the realm of electrometric techniques 14, 15, 16, 17 and could have important practical applications: detection of individual electrons in mesoscopic devices 18, 19, 20, 21 at a distance of about 100 micrometres with a megahertz bandwidth is within reach. 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. We show that the fundamental Heisenberg limit 13 can be approached when the Rydberg atom undergoes a non-classical evolution through Schrödinger-cat states. 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. However, the metrological use of the latter 8, 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 challenging 11, 12. When the meter is a large angular momentum, going beyond the standard quantum limit requires non-classical states such as squeezed states 2, 3, 4 or Schrödinger-cat-like states 5, 6, 7. If the uncertainty is distributed equally between conjugate variables of the meter system, the measurement precision cannot exceed the standard quantum limit. Fundamental quantum fluctuations caused by the Heisenberg principle limit measurement precision 1.

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