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Physical Review Letters

Sub-Projection-Noise Sensitivity in Broadband Atomic Magnetometry

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

Published Mar 3, 2010• 165 citations
Publisher

Abstract

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.

DOI
10.1103/physrevlett.104.093602

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•Oct 1, 2004•0 citations
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 measure the sensitivity of a broadband atomic magnetometer using quantum non-demolition spin measurements. A cold, dipole-trapped sample of rubidium atoms provides a long-lived spin system in a non-magnetic environment, and is probed non-destructively by paramagnetic Faraday rotation. The calibration procedure employs a 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 sensitivity 2.8 dB better than the projection noise level (6dB better if optical noise is suppressed) and will enable squeezing-enhanced broadband magnetometry [Geremia, et al. PRL 94, 203002 (2005)].
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 consider the limitations due to noise (e.g., quantum projection noise and photon shot-noise) on the sensitivity of an idealized atomic magnetometer that utilizes spin squeezing induced by a continuous quantum nondemolition measurement. Such a magnetometer measures spin precession of NNN atomic spins by detecting optical rotation of far-detuned light. We show that for very short measurement times, the optimal sensitivity scales as ${N}^{\ensuremath{-}3/4}$; if strongly squeezed probe light is used, the Heisenberg limit of ${N}^{\ensuremath{-}1}$ scaling can be achieved. However, if the measurement time exceeds ${\ensuremath{\tau}}_{\mathrm{r}\mathrm{e}\mathrm{l}}/{N}^{1/2}$ in the former case, or ${\ensuremath{\tau}}_{\mathrm{r}\mathrm{e}\mathrm{l}}/N$ in the latter, where ${\ensuremath{\tau}}_{\mathrm{r}\mathrm{e}\mathrm{l}}$ is the spin relaxation time, the scaling becomes ${N}^{\ensuremath{-}1/2}$, as for a standard shot-noise-limited magnetometer.
We consider the limitations due to noise (e.g., quantum projection noise and photon shot-noise) on the sensitivity of an idealized atomic magnetometer that utilizes spin squeezing induced by a continuous quantum nondemolition measurement. Such a magnetometer measures spin precession of N atomic spins by detecting optical rotation of far-detuned light. We show that for very short measurement times, the optimal sensitivity scales as N-3/4; if strongly squeezed probe light is used, the Heisenberg limit of N-1 scaling can be achieved. However, if the measurement time exceeds tau(rel)/N-1/2 in the former case, or tau(rel)/N in the latter, where tau(rel) is the spin relaxation time, the scaling becomes N-1/2, as for a standard shot-noise-limited magnetometer.