Sub-Projection-Noise Sensitivity in Broadband Atomic Magnetometry

Koschorreck, M.; Napolitano, M.; Dubost, B.; Mitchell, Morgan W.

doi:10.1103/physrevlett.104.093602

Cited by 161 publications

(239 citation statements)

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“…We note also that H (4) eff is sensitive to more spin degrees of freedom than is H ( Before each polarisation step, the state of the ensemble is reset to a fully-mixed state by repeated pumping from F = 1 to F = 2 and back, using resonant lasers from the MOT beams as described in Koschorreck et al 8 . During the reset process, about 10% of the atoms escape from Modelling.…”

Section: Supplementary Discussionmentioning

confidence: 99%

“…1, uses pulses of near-resonant light to measure the collective spinF of an ensemble of N A ∼ 10 6 cold rubidium-87 atoms, probed on the 5S 1/2 → 5P 3/2 D 2 line. The experimental system is described in detail in the references 8,23 . The on-axis atomic magnetisation F z , which plays the role of X in this measurement, is prepared in the initial state F z = N A by optical pumping with resonant circularly polarised light propagating along the trap axis z.…”

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confidence: 99%

“…i.e., linear estimation and, as described by Koschorreck et al 8 , provides a projection-noise-limited quantum-non-demolition (QND) measurement 24 ofF z , with uncertainty at the parts-per-thousand level 8 . The nonlinear probe consists of a single τ NL = 54 ns FWHM, Gaussian-shaped, highintensity pulse with N NL photons and detuning ∆ 0 , so that A N NL B. Crucially, having two probes allows us to precisely calibrate the nonlinear measurement using a highly sensitive and well characterised independent measurement of the same sample.…”

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confidence: 99%

“…To generate pairwise photon-photon interactions, we use fast nonlinear optical effects in a cold atomic ensemble and measure the ensemble magnetisation F z with super-Heisenberg sensitivity δF z ∝ N −3/2 . To rigorously quantify the photon-photon interaction and the sensitivity, we calibrate against a precise, non-destructive, linear measurement of the same atomic quantity 8 , demonstrate quantum-noise-limited performance of the optical instrumentation, and place an upper limit on systematic, i.e., non-atomic, nonlinearities at the few-percent level. The experiment demonstrates the use of inter-particle interactions as a new resource for quantum metrology.…”

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Interaction-based quantum metrology showing scaling beyond the Heisenberg limit

Napolitano

Koschorreck

Dubost

et al. 2011

Nature

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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...

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Section: Supplementary Discussionmentioning

confidence: 99%

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confidence: 99%

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confidence: 99%

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confidence: 99%

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Interaction-based quantum metrology showing scaling beyond the Heisenberg limit

Napolitano

Koschorreck

Dubost

et al. 2011

Nature

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“…In this paper we revisit the three-dimensional atomlight interface with particular emphasis on spin squeezing through QND measurement of the collective spin via the Faraday effect [30][31][32], shown schematically in Fig. 1.…”

Section: Arxiv:13112328v2 [Quant-ph] 17 Dec 2013mentioning

confidence: 99%

Three-dimensional light-matter interface for collective spin squeezing in atomic ensembles

et al. 2014

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We study the three-dimensional nature of the quantum interface between an ensemble of cold, trapped atomic spins and a paraxial laser beam, coupled through a dispersive interaction. To achieve strong entanglement between the collective atomic spin and the photons, one must match the spatial mode of the collective radiation of the ensemble with the mode of the laser beam while minimizing the effects of decoherence due to optical pumping. For ensembles coupling to a probe field that varies over the extent of the cloud, the set of atoms that indistinguishably radiates into a desired mode of the field defines an inhomogeneous spin wave. Strong coupling of a spin wave to the probe mode is not characterized by a single parameter, the optical density, but by a collection of different effective atom numbers that characterize the coherence and decoherence of the system. To model the dynamics of the system, we develop a full stochastic master equation, including coherent collective scattering into paraxial modes, decoherence by local inhomogeneous diffuse scattering, and backaction due to continuous measurement of the light entangled with the spin waves. This formalism is used to study the squeezing of a spin wave via continuous quantum nondemolition (QND) measurement. We find that the greatest squeezing occurs in parameter regimes where spatial inhomogeneities are significant, far from the limit in which the interface is well approximated by a one-dimensional, homogeneous model.

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Microchip‐Based Trapped‐Atom Clocks

2011

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Basic principlesA two-level quantum system in vacuum-in the absence of any perturbing fields-constitutes an ideal clock whose oscillation frequency ω = E/h is given by the energy difference E between the two levels |1 , |2 . In a single measurement of duration T performed on a single particle this frequency can be determined with an uncertainty ∆ω = 1/T. If the measurement is performed simultaneously on N independent identical particles, and this measurement is repeated with a cycle time T c > T for a total averaging time τ > T c , the fundamental quantum uncertainty of the frequency determination is given by the standard quantum limit [1]The N −1/2 scaling arises because the quantities to be measured are the nonzero probabilities to find a particle in either of the clock states |1 , |2 : when the independent particles in the ensemble are read out, the observed populations of the two clock states are binomially distributed, leading to so-called projection noise on the estimation of those probabilities [2,3]. The √ T c /τ scaling arises because the sequential measurement repeated τ/T c times using N particles each is equivalent to a single measurement using Nτ/T c atoms. For a given total measurement time τ the stability improves as the duration T of the single measurement is increased. The latter is limited by the coherence time of the transition. While the absolute stability does not depend on the transition frequency ω, the fractional stability improves with higher transition frequency.

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Sub-Projection-Noise Sensitivity in Broadband Atomic Magnetometry

Cited by 161 publications

References 28 publications

Interaction-based quantum metrology showing scaling beyond the Heisenberg limit

Interaction-based quantum metrology showing scaling beyond the Heisenberg limit

Three-dimensional light-matter interface for collective spin squeezing in atomic ensembles

Microchip‐Based Trapped‐Atom Clocks

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