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arXiv:2110.01146 · Physical Review Applied

Phonon-Laser Ultrasensitive Force Sensor

Zhi-Chao Liu, Ya-Qi Wei, Liang Chen, Ji Li, S.-Q. Dai, Fei Zhou, Mang Feng

Published Oct 7, 2021• 36 citations
arXivHTMLPDF

Abstract

Developing nanomechanical oscillators for ultrasensitive force detection is very useful in exploring science. We report our achievement of ultrasensitive detection of the external force regarding the radiofrequency electric field by a nanosensor made of a single trapped ${}^{40}{\mathrm{Ca}}^{+}$ ion under injection locking, where squeezing is additionally applied to detection of the smallest force in the ion trap. The employed ion is confined stably in a surface electrode trap and works as a phonon laser that is very sensitive to the external disturbance. The injection locking drove the ion's oscillation with phase synchronization, yielding the force detection with sensitivity of 347 $\ifmmode\pm\else\textpm\fi{}50\phantom{\rule{0.2em}{0ex}}\mathrm{yN}/\sqrt{\mathrm{Hz}}$. Further with 3-dB squeezing applied on the oscillation phase variance, we achieve a successful detection of the smallest force to be $86.5\ifmmode\pm\else\textpm\fi{}70.1$ yN.

DOI
10.1103/physrevapplied.16.044007

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Developing nanomechanical oscillators for ultrasensitive force detection is very useful in exploring science. We report our achievement of ultrasensitive detection of the external force regarding the radiofrequency electric field by a nanosensor made of a single trapped 40Ca+{}^{40}{\mathrm{Ca}}^{+}40Ca+ ion under injection locking, where squeezing is additionally applied to detection of the smallest force in the ion trap. The employed ion is confined stably in a surface electrode trap and works as a phonon laser that is very sensitive to the external disturbance. The injection locking drove the ion's oscillation with phase synchronization, yielding the force detection with sensitivity of 347 \ifmmode±\else\textpm\fi50yN/Hz\ifmmode\pm\else\textpm\fi{}50\phantom{\rule{0.2em}{0ex}}\mathrm{yN}/\sqrt{\mathrm{Hz}}\ifmmode±\else\textpm\fi50yN/Hz​. Further with 3-dB squeezing applied on the oscillation phase variance, we achieve a successful detection of the smallest force to be 86.5\ifmmode±\else\textpm\fi70.186.5\ifmmode\pm\else\textpm\fi{}70.186.5\ifmmode±\else\textpm\fi70.1 yN.
Precision measurement of low-frequency electric field (LFEF) signals with frequency from 30 to 300 kHz is crucial for advancing both fundamental science and practical applications owing to their unique frequency regime. For conventional electromagnetic antennas, the long wavelength (i.e., several kilometers) of the LFEF leads to a severe size constraint because efficient radiation becomes challenging to achieve when the antenna size is much smaller than the long wavelength of the LFEF signals, which in turn results in a reduction of measurement sensitivity and compromises antenna's performance. By exploiting the high intrinsic sensitivity of cold trapped ions to weak alternating electric signals via Coulomb interaction, we demonstrate a single-ion phonon laser sensor based on an injection-locked 40Ca+ ion confined in a surface-electrode trap. Combining the beat frequency technique with the injection-locked phonon laser oscillation, we demonstrate a practical and efficient approach for simultaneous extraction of the frequency, phase, and amplitude from a single measurement, without the need for sideband cooling. This approach achieves precision detection for LFEF signals with a sensitivity of 403.8 μV/(m Hz1/2) and a detection limit of 61.5 μV/m. In addition, this approach also shows remarkable robustness against noise. Our study helps realize practical single-atom sensors in the low-frequency regime, opening avenues for applications in subsurface communication, precision metrology, mass spectrometry, and biomedical monitoring.
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The phonon laser realized in a trapped ion, i.e., a self-sustained mechanical oscillator, has demonstrated the unique characteristics in practically detecting externally applied electric signals without the prerequisite of sideband cooling. Entering the quantum regime via sideband cooling is expected to further improve its sensing performance. Here we report the first experimental realization of a quantum-regime single-ion phonon laser (nˉ<10\bar{n}<10nˉ<10) using a trapped 40Ca+^{40}\mathrm{Ca}^+40Ca+ ion and demonstrate electrometry based on its phase-space symmetry-breaking response to weak resonant electric fields. By tuning the phonon-laser parameters, we reveal that the sensing performance is fundamentally governed by the finite-time relaxation dynamics of the underlying open quantum system. We find that a slow Liouvillian relaxation, correlated with the finite experimental interaction window, effectively enhances the dynamic susceptibility while maintaining the structural robustness of the limit cycle. This regime, when applied to the detection of electric fields, produces a shot-noise-limited peak sensitivity of 14.15±0.77 μV/m/Hz14.15 \pm 0.77~μ\mathrm{V/m}/\sqrt{\mathrm{Hz}}14.15±0.77 μV/m/Hz​ and a minimum detectable field variation of δEmin≈1.83 μV/mδE_{\mathrm{min}} \approx 1.83~μ\mathrm{V/m}δEmin​≈1.83 μV/m. Our results establish quantum phonon lasers as a practical platform for advanced sensing and highlight the central role of Liouvillian dynamics in non-equilibrium electrometry.
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.
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.
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.