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arXiv:2407.18670

Measuring a single atom's position with extreme sub-wavelength resolution and force measurements in the yoctonewton range

Patrick H. Huber, Barthel, P., Theeraphot Sriarunothai, Gouri Shankar Giri, Sabine Wölk, Ch. Wunderlich

Published Jul 26, 2024• 0 citations
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Abstract

The center-of-mass position of a single trapped atomic ion is measured and tracked in time with high precision. Employing a near-resonant radio frequency field of wavelength 2.37 cm and a static magnetic field gradient of 19 T/m, the spatial location of the ion is determined with an unprecedented wavelength-relative resolution of 5 $\times$ 10$^{-9}$, corresponding to an absolute precision of 0.12 nm. Measurements of an electrostatic force on a single ion demonstrate a sensitivity of 2.2 $\times$ 10$^{-23} ~\text{N}/\sqrt{\text{Hz}}$. The real-time measurement of an atom's position complements the well-established technique of scanning near-field radio frequency transmission microscopy and opens up a novel route to using this method with path breaking spatial and force resolution.

DOI
10.48550/arxiv.2407.18670

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The center-of-mass position of a single trapped atomic ion is measured and tracked in time with high precision. Employing a near-resonant radio frequency field of wavelength 2.37 cm and a static magnetic field gradient of 19 T/m, the spatial location of the ion is determined with an unprecedented wavelength-relative resolution of 5 ×\times× 10−9^{-9}−9, corresponding to an absolute precision of 0.12 nm. Measurements of an electrostatic force on a single ion demonstrate a sensitivity of 2.2 ×\times× 10−23 N/Hz^{-23} ~\text{N}/\sqrt{\text{Hz}}−23 N/Hz​. The real-time measurement of an atom's position complements the well-established technique of scanning near-field radio frequency transmission microscopy and opens up a novel route to using this method with path breaking spatial and force resolution.
Single-atom quantum sensors offer high spatial resolution and high sensitivity to electric and magnetic fields. Among them, trapped ions offer exceptional performance in sensing electric fields, which has been used in particular to probe these in the proximity of metallic surfaces. However, the flexibility of previous work was limited by the use of radio-frequency trapping fields, which has restricted spatial scanning to linear translations, and calls into question whether observed phenomena are connected to the presence of the radio-frequency fields. Here, using a Penning trap instead, we demonstrate a single ion probe which offers three-dimensional position scanning at distances between 505050 μmμ\mathrm{m}μm and 450450450 μmμ\mathrm{m}μm from a metallic surface and above a 200×200200\times200200×200 μm2μ\mathrm{m}^{2}μm2 area, allowing us to reconstruct static and time-varying electric as well as magnetic fields. We use this to map charge distributions on the metallic surface and noise stemming from it. The methods demonstrated here allow similar probing to be carried out on samples with a variety of materials, surface constitutions and geometries, providing a new tool for surface science.
We report a calibrated measurement of 174 yoctonewton (1× 10−24 N = 1 yN), using a cloud of 60 Be ion confined in a Penning ion trap. These measurements suggest that ion traps may form the basis of a new class of ultra-sensitive deployable force sensors. 1. Summary Measurement of extremely small forces is of interest in a variety of fields ranging from atomic-force-microscopy, to electron spin resonance, to tests of fundamental principles. State-of-the-art small force detection relies on using thin cantilevers of which the resonant vibrational response is probed in reaction to an external force. Such systems have achieved force sensitivities on the order of attonewtons [1]. It has been suggested that single trapped ions could achieve force sensitivities on the order of ∼ 1 yn and consequently be used as a new class of force sensor [2]. Here we demonstrate a calibrated, yoctonewton scale force measurement using 60 Be ions confined in a Penning ion trap. The ions are subjected to a small oscillating electric field and their resonant response is probed using phase sensitive detection of modulations in the fluorescence intensity of a probe beam near-resonant with the S1/2 −→ P3/2 transition. We detect forces as small as 174 yn corresponding to a force sensitivity of 390±150 yn/ √ Hz. Extrapolated sensitivities are consistent with ∼ 1.7 yn/√Hz in the single ion limit [3]. Figure 1: Resonant response of Be ions under the influence of weak, oscillating electric fields. Left-most column Experiment, modulations in fluorescence intensity as a function of driving force simulation for different drive times (indicated in right-most column). Central column Theoretical simulation corresponding to left column. Right-most column cross sections through data in left-most column with theoretical fits.
We realize a scanning probe microscope using single trapped ^{87}Rb atoms to measure optical fields with subwavelength spatial resolution. Our microscope operates by detecting fluorescence from a single atom driven by near-resonant light and determining the ac Stark shift of an atomic transition from other local optical fields via the change in the fluorescence rate. We benchmark the microscope by measuring two standing-wave Gaussian modes of a Fabry-Pérot resonator with optical wavelengths of 1560 and 781 nm. We attain a spatial resolution of 300 nm, which is superresolving compared to the limit set by the 780 nm wavelength of the detected light. Sensitivity to short length scale features is enhanced by adapting the sensor to characterize an optical field via the force it exerts on the atom.
We are currently developing Raman-induced resonance-imaging techniques for ultrahigh-resolution position measurement and localization of moving atoms.1 We obtain transit-time-limited frequency resolution in intense spatially varying potentials, which correlate the atomic position with the Raman resonance frequency. The use of optical fields for the Raman region permits easy application to very small interaction volumes where extremely large spatially varying Zeeman shifts or light shifts (109-1012 Hz/cm) can be employed to achieve position resolution as high as 7 nm. This leads to quantum-mechanical limitations on the measurement accuracy.
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.
The paper summarizes on the results of several experiments on single trapped ions which have been used to map optical fields. In these experiments, the ion was placed either in front of a (distant) mirror or in an optical cavity. Sub-wavelength resolution is achieved because the position of the ion relative to the mirror(s) is well-controlled and the ion's spatial wavefunction is confined to a region much smaller than the optical wavelength (400 to 800 nm). This strong localization is due to the trapping potential of a Paul-type ion trap, and laser cooling. In the three experiments the ions were Doppler-cooled, and a resolution between about 10 and 50 nm was achieved. With this resolution, the spatial variation of an optical standing-wave field was detected by shifting the single ion through the field structure.