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Simultaneous observation of super-Heisenberg scaling and spin squeezing in a nonlinear measurement of atomic spins

R. J. Sewell, M. Napolitano, N. Behbood, Giorgio Colangelo, Ferran Martin Ciurana, Morgan W. Mitchell

Published Jan 1, 2013• 0 citations
Publisher

Abstract

We report a nonlinear alignment-to-orientation conversion measurement of atomic spins that simultaneously shows super-Heisenberg scaling and achieves projection-noise limited sensitivity of 990 spins, 20 dB more sensitive than the previous best nonlinear measurement. Using this technique, we have recently demonstrated conditional spin squeezing of the atomic ensemble, and entanglement-enhanced measurement sensitivity useful for optical magnetometry. In addition, we use a novel technique to explicitly certify that the measurement fulfills all the conditions required for quantum non-demolition measurement.

DOI
10.1364/cleo_qels.2013.qth1l.3

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We report a nonlinear alignment-to-orientation conversion measurement of atomic spins that simultaneously shows super-Heisenberg scaling and achieves projection-noise limited sensitivity of 990 spins, 20 dB more sensitive than the previous best nonlinear measurement. Using this technique, we have recently demonstrated conditional spin squeezing of the atomic ensemble, and entanglement-enhanced measurement sensitivity useful for optical magnetometry. In addition, we use a novel technique to explicitly certify that the measurement fulfills all the conditions required for quantum non-demolition measurement.
Techniques for making quantum-limited nonlinear measurements have attracted a great deal of recent attention because they allow a measurement sensitivity that improves as the number of measuring particles (e.g. photons) increases faster than an equivalent linear measurement. This super-Heisenberg scaling was recently demonstrated in a proof-of-principle experiment [1], in which a measurement Hamiltonian of the form studied in Ref. [2] was carefully engineered by exploiting nonlinearities in a Faraday rotation based measurement of atomic spins. However, despite the improved scaling, the absolute measurement sensitivity in this experiment remained significantly worse than a linear Faraday rotation measurement due to the weak atom-light coupling strength of the nonlinear Faraday rotation, and effect of higher-order nonlinearities at large photon number. This leaves open the question of whether it is possible to make a nonlinear measurement that both benefits from the improved scaling, and competes in absolute sensitivity with linear techniques.
We report the generation of spin squeezing and entanglement in a magnetically sensitive atomic ensemble, and entanglement-enhanced field measurements with this system. A maximal m(f) = ± 1 Raman coherence is prepared in an ensemble of 8.5 × 10(5) laser-cooled (87)Rb atoms in the f = 1 hyperfine ground state, and the collective spin is squeezed by synthesized optical quantum nondemolition measurement. This prepares a state with large spin alignment and noise below the projection-noise level in a mixed alignment-orientation variable. 3.2 dB of noise reduction is observed and 2.0 dB of squeezing by the Wineland criterion, implying both entanglement and metrological advantage. Enhanced sensitivity is demonstrated in field measurements using alignment-to-orientation conversion.
Quantum metrology uses quantum features such as entanglement and squeezing to improve the sensitivity of quantum-limited measurements. Long established as a valuable technique in optical measurements such as gravitational-wave detection, quantum metrology is increasingly being applied to atomic instruments such as matter-wave interferometers, atomic clocks, and atomic magnetometers. Several of these new applications involve dual optical/atomic quantum systems, presenting both new challenges and new opportunities. Here we describe an optical magnetometry system that achieves both shot-noise-limited and projection-noise-limited performance, allowing study of optical magnetometry in a fully-quantum regime [1]. By near-resonant Faraday rotation probing, we demonstrate measurement-based spin squeezing in a magnetically-sensitive atomic ensemble [2-4]. The versatility of this system allows us also to design metrologically-relevant optical nonlinearities, and to perform quantum-noise-limited measurements with interacting photons. As a first interaction-based measurement [5], we implement a non-linear metrology scheme proposed by Boixo et al. with the surprising feature of precision scaling better than the 1/N “Heisenberg limit” [6].
We demonstrate spin squeezing and entanglement in a large-spin system via quantum non-demolition measurement. We make non-destructive, projection-noise-limited collective spin measurements on an ensemble of up to in 8.4 × 105 laser-cooled 87Rb atoms in the f = 1 hyperfine ground state. A dynamically-decoupled probing scheme [Phys. Rev. Lett. 105, 093602 (2010)] prevents probe-induced decoherence. Repeated measurements show correlations beyond the standard quantum limit, indicating generation of a spin-squeezed state with up to −3.6 dB of noise reduction and −2.6 dB of metrologically-relevant squeezing.
A major challenge in quantum metrology is the generation of entangled states with a macroscopic atom number. Here, we demonstrate experimentally that atomic squeezing generated via nonlinear dynamics in Bose-Einstein condensates, combined with suitable trap geometries, allows scaling to large ensemble sizes. We achieve a suppression of fluctuations by 5.3(5) dB for 12,300 particles, from which we infer that similar squeezing can be obtained for more than 10(7) atoms. With this resource, we demonstrate quantum-enhanced magnetometry by swapping the squeezed state to magnetically sensitive hyperfine levels that have negligible nonlinearity. We find a quantum-enhanced single-shot sensitivity of 310(47) pT for static magnetic fields in a probe volume as small as 90 μm3.