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arXiv:2203.00919 · Applied Physics Letters

A single-atom mechano-optical transducer for sensing sub-attonewton vector DC force

Yang Liu, Pengfei Lu, Xinxin Rao, Hao Wu, Kunxu Wang, Qifeng Lao, Ji Bian, Feng Zhu, Le Luo

Published Dec 19, 2022• 2 citations
arXivHTMLPDF

Abstract

Mechano-optical transducers are devices that convert a force or displacement signal to an optical one, enabling ultrasensitive mechanical detection. Currently, ultraweak DC force sensors with high spatial resolution are in high demand for the search of possible exotic spin-dependent interactions beyond the standard model in sub-millimeter scale. Here, we demonstrate a mechano-optical transducer of a single trapped ion with the force sensitivity about 600 zN/Hz for the DC force. This method utilizes the Doppler shift of the time-resolved fluorescence to detect the ion's micromotion that is coupled to a vector force. By alternating the directions of the detection laser beams, the vector DC forces can be precisely measured. Such a mechano-optical transducer provides sub-attonewton sensitivity with the spatial resolution in single-atom level, enabling various uses for both scientific and industrial purposes.

DOI
10.1063/5.0125600

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Mechano-optical transducers are devices that convert a force or displacement signal to an optical one, enabling ultrasensitive mechanical detection. Currently, ultraweak DC force sensors with high spatial resolution are in high demand for the search of possible exotic spin-dependent interactions beyond the standard model in sub-millimeter scale. Here, we demonstrate a mechano-optical transducer of a single trapped ion with the force sensitivity about 600 zN/Hz for the DC force. This method utilizes the Doppler shift of the time-resolved fluorescence to detect the ion's micromotion that is coupled to a vector force. By alternating the directions of the detection laser beams, the vector DC forces can be precisely measured. Such a mechano-optical transducer provides sub-attonewton sensitivity with the spatial resolution in single-atom level, enabling various uses for both scientific and industrial purposes.
Forces drive all physical interactions. High-sensitivity measurement of the effect of forces enables the quantitative investigation of physical phenomena. Laser-cooled trapped atomic ions are a well-controlled quantum system whose low mass, strong Coulomb interaction, and readily detectable fluorescence signal make them a favorable platform for precision metrology. We demonstrate a three-dimensional sub-attonewton sensitivity force sensor based on a super-resolution imaging of a single trapped ion. The force is detected by measuring the ion's displacement in three dimensions with nanometer precision. Observed sensitivities were 372 ± 9, 347 ± 18, and 808 ± 51 zN/[Formula: see text], corresponding to 24×, 87×, and 21× above the quantum limit. We verified this technique by measuring a 95-zN light pressure force, an important systematic effect in optically based sensors.
Abstract Force sensors are at the heart of different technologies such as atomic force microscopy or inertial sensing. These sensors often rely on the measurement of the displacement amplitude of mechanical oscillators under applied force. The best sensitivity is typically achieved when the force is alternating at the mechanical resonance frequency of the oscillator, thus increasing its response by the mechanical quality factor. The measurement of low-frequency forces, that are below resonance, is a more difficult task as the resulting oscillation amplitudes are significantly lower. Here we use a single-trapped 88Sr+ ion as a force sensor. The ion is electrically driven at a frequency much lower than the trap resonance frequency. We measure small amplitude of motion by measuring the periodic Doppler shift of an atomic optical clock transition, enhanced using the quantum lock-in technique. We report frequency force detection sensitivity as low as 2.8 × 10−20 NHz−1/2.
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.
In this paper, direct observation of micromotion for multiple ions in a laser-cooled trapped ion crystal is discussed along with a measurement technique for micromotion amplitude. Micromotion is directly observed using a time-resolving, single-photon-sensitive camera that provides both fluorescence and position data for each ion on the nanosecond time scale. Micromotion amplitude and phase for each ion in the crystal are measured, allowing this method to be sensitive to tilts and shifts of the ion chain from the null of the radio-frequency quadrupole potential in the linear trap. Spatial resolution makes this micromotion detection technique suitable for complex ion configurations, including two-dimensional geometries. It does not require any additional equipment or laser beams, and the modulation of the cooling lasers or trap voltages is not necessary for detection as it is in other methods.
The ability to detect extremely small forces is vital for a variety of disciplines including precision spin-resonance imaging, microscopy, and tests of fundamental physical phenomena. Current force-detection sensitivity limits have surpassed 1 aN/HzaN/\sqrt{Hz}aN/Hz​ (atto =10−18=10^{-18}=10−18) through coupling of micro or nanofabricated mechanical resonators to a variety of physical systems including single-electron transistors, superconducting microwave cavities, and individual spins. These experiments have allowed for probing studies of a variety of phenomena, but sensitivity requirements are ever-increasing as new regimes of physical interactions are considered. Here we show that trapped atomic ions are exquisitely sensitive force detectors, with a measured sensitivity more than three orders of magnitude better than existing reports. We demonstrate detection of forces as small as 174 yNyNyN (yocto =10−24=10^{-24}=10−24), with a sensitivity 390±150\pm150±150 yN/HzyN/\sqrt{Hz}yN/Hz​ using crystals of n=60n=60n=60 9^{9}9Be+^{+}+ ions in a Penning trap. Our technique is based on the excitation of normal motional modes in an ion trap by externally applied electric fields, detection via and phase-coherent Doppler velocimetry, which allows for the discrimination of ion motion with amplitudes on the scale of nanometers. These experimental results and extracted force-detection sensitivities in the single-ion limit validate proposals suggesting that trapped atomic ions are capable of detecting of forces with sensitivity approaching 1 yN/HzyN/\sqrt{Hz}yN/Hz​. We anticipate that this demonstration will be strongly motivational for the development of a new class of deployable trapped-ion-based sensors, and will permit scientists to access new regimes in materials science.
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.