Efficient quantification of non-gaussian spin distributions.

We study theoretically and experimentally the quantification of non-gaussian distributions via nondestructive measurements. Using the theory of cumulants, their unbiased estimators, and the uncertainties of these estimators, we describe a quantification which is simultaneously efficient, unbiased by measurement noise, and suitable for hypothesis tests, e.g., to detect nonclassical states. The theory is applied to cold 87Rb spin ensembles prepared in non-gaussian states by optical pumping and measured by nondestructive Faraday rotation probing. We find an optimal use of measurement resources under realistic conditions, e.g., in atomic ensemble quantum memories.

Magnetic sensitivity beyond the projection noise limit by spin squeezing.

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.

Interaction-based quantum metrology showing scaling beyond the Heisenberg limit.

Quantum metrology aims to use entanglement and other quantum resources to improve precision measurement. An interferometer using N independent particles to measure a parameter χ can achieve at best the standard quantum limit of sensitivity, δχ ∝ N(-1/2). However, using N entangled particles and exotic states, such an interferometer can in principle achieve the Heisenberg limit, δχ ∝ N(-1). Recent theoretical work has argued that interactions among particles may be a valuable resource for quantum metrology, allowing scaling beyond the Heisenberg limit. Specifically, a k-particle interaction will produce sensitivity δχ ∝ N(-k) with appropriate entangled states and δχ ∝ N(-(k-1/2)) even without entanglement. Here we demonstrate 'super-Heisenberg' scaling of δχ ∝ N(-3/2) in a nonlinear, non-destructive measurement of the magnetization of an atomic ensemble. We use fast optical nonlinearities to generate a pairwise photon-photon interaction (corresponding to k = 2) while preserving quantum-noise-limited performance. We observe super-Heisenberg scaling over two orders of magnitude in N, limited at large numbers by higher-order nonlinear effects, in good agreement with theory. For a measurement of limited duration, super-Heisenberg scaling allows the nonlinear measurement to overtake in sensitivity a comparable linear measurement with the same number of photons. In other situations, however, higher-order nonlinearities prevent this crossover from occurring, reflecting the subtle relationship between scaling and sensitivity in nonlinear systems. Our work shows that interparticle interactions can improve sensitivity in a quantum-limited measurement, and experimentally demonstrates a new resource for quantum metrology.

Quantum nondemolition measurement of large-spin ensembles by dynamical decoupling.

Quantum nondemolition (QND) measurement of collective variables by off-resonant optical probing has the ability to create entanglement and squeezing in atomic ensembles. Until now, this technique has been applied to real or effective spin one-half systems. We show theoretically that the buildup of Raman coherence prevents the naive application of this technique to larger spin atoms, but that dynamical decoupling can be used to recover the ideal QND behavior. We experimentally demonstrate dynamical decoupling by using a two-polarization probing technique. The decoupled QND measurement achieves a sensitivity 5.7(6) dB better than the spin projection noise.

Sub-projection-noise sensitivity in broadband atomic magnetometry.

We demonstrate sub-projection-noise sensitivity of a broadband atomic magnetometer using quantum nondemolition spin measurements. A cold, dipole-trapped sample of rubidium atoms provides a long-lived spin system in a nonmagnetic environment, and is probed nondestructively by paramagnetic Faraday rotation. The calibration procedure employs as known reference state, the maximum-entropy or "thermal" spin state, and quantitative imaging-based atom counting to identify electronic, quantum, and technical noise in both the probe and spin system. The measurement achieves a sensitivity 1.6 dB (2.8 dB) better than projection-noise (thermal state quantum noise) and will enable squeezing-enhanced broadband magnetometry.