Ultrasensitive Magnetometer using a Single Atom

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Ultrasensitive Magnetometer using a Single Atom

I. Baumgart, J.-M. Cai, A. Retzker, M. B. Plenio, and Ch. Wunderlich

Phys. Rev. Lett. 116, 240801 – Published 17 June 2016

Abstract

Precision sensing, and in particular high precision magnetometry, is a central goal of research into quantum technologies. For magnetometers, often trade-offs exist between sensitivity, spatial resolution, and frequency range. The precision, and thus the sensitivity of magnetometry, scales as $1 / \sqrt{T_{2}}$ with the phase coherence time $T_{2}$ of the sensing system playing the role of a key determinant. Adapting a dynamical decoupling scheme that allows for extending $T_{2}$ by orders of magnitude and merging it with a magnetic sensing protocol, we achieve a measurement sensitivity even for high frequency fields close to the standard quantum limit. Using a single atomic ion as a sensor, we experimentally attain a sensitivity of $4.6 pT / \sqrt{Hz}$ for an alternating-current magnetic field near 14 MHz. Based on the principle demonstrated here, this unprecedented sensitivity combined with spatial resolution in the nanometer range and tunability from direct current to the gigahertz range could be used for magnetic imaging in as of yet inaccessible parameter regimes.

Received 10 December 2014

DOI:https://doi.org/10.1103/PhysRevLett.116.240801

Physics Subject Headings (PhySH)

Coherent control Metrology

General PhysicsAtomic, Molecular & Optical

Authors & Affiliations

I. Baumgart¹, J.-M. Cai², A. Retzker³, M. B. Plenio⁴, and Ch. Wunderlich^1,*

¹Department Physik, Naturwissenschaftlich-Technische Fakultät, Universität Siegen, 57068 Siegen, Germany
²School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China
³Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem 91904, Givat Ram, Israel
⁴Institut für Theoretische Physik, Universität Ulm, 89069 Ulm, Germany

^*Corresponding author. christof.wunderlich@uni-siegen.de

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Issue

Vol. 116, Iss. 24 — 17 June 2016

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Images

Figure 1
Level scheme for magnetometry. (a) Hyperfine levels for magnetic sensing (not to scale). The signal field to be measured creates rotations between the states $| 0^{'} ⟩$ and $| B ⟩ \equiv (| - 1 ⟩ + | + 1 ⟩) / \sqrt{2}$ , while the microwave fields at frequencies $ω_{+ 1}$ and $ω_{- 1}$ and with Rabi frequency $Ω$ decouple the $| B ⟩$ state from the orthogonal superposition of the Zeeman sublevels, $| D ⟩ \equiv (| - 1 ⟩ - | + 1 ⟩) / \sqrt{2}$ . The clock transition $| 0 ⟩ \leftrightarrow | 0^{'} ⟩$ at frequency $ω_{0}$ is insensitive to magnetic field fluctuations to first order. (b) Partial ${}^{171}{Yb}^{+}$ level structure (not to scale). The four hyperfine states of the electronic ground state are used to implement the level structure shown in (a). The optical transition near 369 nm is used for Doppler cooling, state preparation, and state-selective readout.
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Figure 2
Coherence time of dressed and bare states. A coherent superposition of $| B ⟩$ and $| 0^{'} ⟩$ is prepared and probed after time $T_{R}$ (red data points and black fit, $10^{2} ms < T_{R} < 2 \times 10^{3} ms$ ). For comparison, the result of a Ramsey-type experiment between the bare states $| - 1 ⟩ \leftrightarrow | 0 ⟩$ (blue data points and green fit, $0 ms < T_{R} < 10^{1} ms$ ) is shown. For the dressed states a rf field implements two $π / 2$ pulses separated by time $T_{R}$ of free evolution. The rf frequency is slightly detuned from resonance yielding Ramsey oscillations with a period of $1 / (0.52 Hz)$ between 0.1 and 2000 ms. Each of the 11 measurement points (dressed states, red data points) consists of 10 repetitions. In the case of the bare states, the 51 measurement points between 0.1 and 10 ms are repeated 50 times each. The error bars indicate 1 standard deviation.
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Figure 3
Qubit rotation between coherence protected states $| B ⟩$ and $| 0^{'} ⟩$ . Rabi oscillations take place between 0.1 and 500 ms with a Rabi frequency $Ω_{g} = 2 π (7.54 \pm 0.12) Hz$ . Each of the 21 measurement points consists of 30 repetitions. The solid line is a fit to the data yielding $Ω_{g}$ . The error bars indicate 1 standard deviation.
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Figure 4
Sensitivity of the dressed state magnetometer. (a) Rabi signal measured for various pulse durations $T$ and different values of $Ω_{g}$ plotted versus $φ = Ω_{g} T$ . The range of $Ω_{g}$ extends from $2 π \times 2 Hz$ to $2 π \times 3336 Hz$ [34]. The derivative of the blue fitted curve gives the slope $\partial P (φ) / \partial φ$ . Each data point is the average of $n$ repetitions. (b) Sensitivity $S$ for variation in $Ω_{g}$ as a function of the total measurement time $T_{tot} / n = (T + T_{add})$ , where $T_{add}$ is the additional time needed for state preparation, readout, and laser cooling. The sensitivity derived for three exemplary data points in (a) is shown with different color coding and marker symbol. For an experimental time $T = 500 ms$ and $Ω_{g} = 2 π (7.54 \pm 0.12) Hz$ (see Fig. 3), a sensitivity of $S = (0.278 \pm 0.017) Hz / \sqrt{Hz}$ is achieved (cyan rectangle). For $T = 1000 ms$ and $Ω_{g} = 2 π (6.74 \pm 0.10) Hz$ , a sensitivity of $S = (0.200 \pm 0.004) Hz / \sqrt{Hz}$ is derived (red triangle). The best sensitivity, $S = (0.130 \pm 0.036) Hz / \sqrt{Hz}$ , is reached for an experimental time $T = 1500 ms$ and $Ω_{g} = 2 π (1.86 \pm 0.10) Hz$ (green circle). The solid blue line indicates the standard quantum limit given by $1 / \sqrt{T}$ .
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