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 studies the use of entanglement and other quantum resources to improve precision measurement 1 . An interferometer using N independent particles to measure a parameter X can achieve at best the "standard quantum limit" (SQL) of sensitivity δX ∝ N −1/2 . The same interferometer 2 using N entangled particles can achieve in principle the "Heisenberg limit" δX ∝ N −1 , using exotic states 3 . Recent theoretical work argues that interactions among particles may be a valuable resource for quantum metrology, allowing scaling beyond the Heisenberg limit [4][5][6] . Specifically, a k-particle interaction will produce sensitivity δX ∝ N −k with appropriate entangled states and δX ∝ N −(k−1/2) even without entanglement 7 . Here we demonstrate this "super-Heisenberg" scaling in a nonlinear, nondestructive 8, 9 measurement of the magnetisation 10, 11 of an atomic ensemble 12 . We use fast optical nonlinearities to generate a pairwise photon-photon interaction 13 (k = 2) while preserving quantum-noise-limited performance 7,14 , to produce δX ∝ N −3/2 . We observe superHeisenberg scaling over two orders of magnitude in N , limited at large N by higher-order 1 arXiv:1012.5787v1 [quant-ph] 28 Dec 2010 nonlinear effects, in good agreement with theory 13 . 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 scenarios, however, higher-order nonlinearities prevent this crossover from occurring, reflecting the subtle relationship of scaling to sensitivity in nonlinear systems. This work shows that inter-particle interactions can improve sensitivity in a quantum-limited measurement, and introduces a fundamentally new resource for quantum metrology.The best instruments are interferometric in nature, and operate according to the laws of quantum mechanics. A collection of particles, e.g., photons or atoms, is prepared in a superposition state, allowed to evolve under the action of a Hamiltonian containing an unknown parameter X , and measured in agreement with quantum measurement theory. The complementarity of quantum measurements 15 determines the ultimate sensitivity of these instruments.Here we describe polarisation interferometry, used for example in optical magnetometry to detect atomic magnetisation 11,16,17 ; similar theory describes other interferometers 2 . A collection of N photons, with circular plus/minus polarisations |+ , |− is described by single-photon Stokeswhere the σ i are the Pauli matrices and σ 0 is the identity.In traditional quantum metrology, a Hamiltonian of the formĤ = X N j=1ŝ (j) z uniformly and independently couples the photons to X , the parameter to be measured 1 . If the input state consists of independent photons, the possible precision scales as δX ∝ N −1/2 , the shot-noise or standard quantum limit (SQL). The N −1/2 factor reflects the statistical averaging of independent results. 2In contrast, entangled states can be highly, even perfectly...

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.

We report the generation of a macroscopic singlet state in a cold atomic sample via quantum nondemolition measurement-induced spin squeezing. We observe 3 dB of spin squeezing and detect entanglement with 5σ statistical significance using a generalized spin-squeezing inequality. The degree of squeezing implies at least 50% of the atoms have formed singlets.

Quantum non-demolition (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 build-up 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.PACS numbers: 42.50. Lc, 07.55.Ge, 42.50.Dv, 03.67.Bg Quantum non-demolition measurement plays a central role in quantum networking and quantum metrology for its ability to simultaneously detect and generate non-classical quantum states. The original proposal by Braginsky [1] in the context of gravitational wave detection has been generalized to the optical [2, 3], atomic [4] and nano-mechanical [5] domains. In the atomic domain, QND by dispersive optical probing of spins or pseudospins has been demonstrated using ensembles of cold atoms on a clock transition [6,7], and with polarization variables [8,9], but thus far only with real or effective spin-1/2 systems.QND measurement of larger spin systems offers a metrological advantage, e.g., in magnetometry [10], and may be essential for the detection of different quantum phases of degenerate atomic gases that intrinsically rely on large-spin systems [11][12][13]. Dispersive interactions with large-spin atoms are complicated by the presence of non-QND-type terms in the effective Hamiltonian describing the interaction [14-16]. As we show, and contrary to what has often been assumed [11][12][13]17], these terms spoil the QND performance, even in the largedetuning limit. The non-QND terms introduce noise into the measured variable, or equivalently decoherence into the atomic state. The problem is serious for both large and small ensembles, so that naive application of dispersive probing fails for several of the above-cited proposals.We approach this problem using the methods of dynamical decoupling [18][19][20], which allow us to effectively cancel the non-QND terms in the Hamiltonian while retaining the QND term. To our knowledge, this is the first application of this method to quantum non-demolition measurements. Dynamical decoupling has been extensively applied in magnetic resonance [21,22], used to suppress collisional decoherence in a thermal vapor [23], to extend coherence times in solids [24], in Rydberg atoms [25], and with photon polarization [26]. Other approaches include application of a static perturbation [27,28].We consider an ensemble of spin-f atoms interacting with a pulse of near-resonant polarized light. As described in references [14][15][16], the light and atoms interact by the effective HamiltonianĤ effwhere τ is the duration of the pulse and G 1,2 are coupling constants that depend on the ato...