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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

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 May 1, 2013• 0 citations

Abstract

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.

DOI: 10.1109/cleoe-iqec.2013.6801619

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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

N

atomic spins by detecting optical rotation of far-detuned light. We show that for very short measurement times, the optimal sensitivity scales as ${N}^{\ensuremath{-}3/4}$; 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.

Super-Heisenberg scaling, which scales as N − β with β > 1 in terms of the number of particles N or T − β in terms of the evolution time T , is better than Heisenberg scaling in quantum metrology. It has been proven that super-Heisenberg scaling can be achieved when the Hamiltonian of the system involves many-body interactions or time-dependent terms. We demonstrate that nonlinear quantum scrambling facilitates the achievement of super-Heisenberg scaling T − β when the generator of the parameter is time-independent. More importantly, in dissipative systems, we can still obtain super-Heisenberg scaling. In the optical cavity system, an exponential improvement in measurement precision over time can be achieved by combining injected external squeezing and intracavity squeezing. Our work provides an optimal method for leveraging nonlinear resources to enhance the measurement precision of the driving field.