The characterization of externally applied signals is essential in order to improve performance and design appropriate engineering strategies in cold-atom experiments. Here, we present a practical technique to detect the artificially introduced electric signals by an exquisite sensor made of a single ${}^{40}$$\mathrm{Ca}$${}^{+}$ ion behaving as the phonon laser. The sensor can work as an oscilloscope, detecting spectra of the signals in the time domain, and also as a frequency spectrograph for the signal probe with respect to the frequency. The high precision of such an atomic sensor relies on the unique characteristics of the phonon laser. In particular, the sensor is practical since it works without the prerequisite of sideband cooling and the performance of the sensor can be further improved depending on better trapping conditions and a higher collection efficiency of the spontaneous emission fluorescence.
The characterization of externally applied signals is essential in order to improve performance and design appropriate engineering strategies in cold-atom experiments. Here, we present a practical technique to detect the artificially introduced electric signals by an exquisite sensor made of a single {}^{40}$$\mathrm{Ca}$${}^{+} ion behaving as the phonon laser. The sensor can work as an oscilloscope, detecting spectra of the signals in the time domain, and also as a frequency spectrograph for the signal probe with respect to the frequency. The high precision of such an atomic sensor relies on the unique characteristics of the phonon laser. In particular, the sensor is practical since it works without the prerequisite of sideband cooling and the performance of the sensor can be further improved depending on better trapping conditions and a higher collection efficiency of the spontaneous emission fluorescence.
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.
Precision measurement of low-frequency electric field (LFEF) signals with frequency from 30 kHz 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 that 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 acted by 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 the sensitivity of 404 uV/(m * Hz1/2) and the detection limit of 61.5 uV/m. Besides, this approach also shows remarkable robustness against noise. Our study helps realizing practical single-atom sensors in the low-frequency regime, opening avenues for applications in subsurface communication, precision metrology, mass spectrometry, and biomedical monitoring.
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) using a trapped 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±0.77μV/m/Hz and a minimum detectable field variation of δEmin≈1.83μV/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.
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+ 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.
Abstract A single-ion reservoir has been tested, and characterized in order to be used as a highly sensitive optical detector of electric signals arriving at the trapping electrodes. Our system consists of a single laser-cooled40Ca+ion stored in a Paul trap with rotational symmetry. The performance is observed through the axial motion of the ion, which is equivalent to an underdamped and forced oscillator. Thus, the results can be projected also to Penning traps. We have found that, for an ion oscillator temperatureTaxial ≲ 10 mK in the forced-frequency rangeωz = 2π × (80,200 kHz), the reservoir is sensitive to a time-varying electric field equivalent to an electric force of 5.3(2) neV/μm, for a measured quality factorQ = 3875(45), and a decay time constantγz = 88(2) s−1. This method can be applied to measure optically the strength of an oscillating field or induced (driven) charge in this frequency range within times of tens of milliseconds. Furthermore the ion reservoir has been proven to be sensitive to electrostatic forces by measuring the ion displacement. Since the heating rate is below 0.3 μeV/s, this reservoir might be used as optical detector for any ion or bunch of charged particles stored in an adjacent trap.
Rydberg atoms have emerged as a versatile and efficient platform for high-sensitivity quantum sensing of free-space electric fields, with remarkable progress in detecting low-frequency signals. To date, low-frequency Rydberg receivers have relied on a constant bias field, typically realized via intra-cell electrodes or Rydberg plasmas generated by photoelectric effects or inter-atomic interactions. While these approaches improve sensitivity, they suffer from inherent challenges in calibration, long-term stability, and robustness, hindering practical deployment. Here, we propose, design, and experimentally demonstrate a quantum sensing scheme for low-frequency electric signals using modulated auxiliary fields in Rydberg atoms. Unlike conventional methods that employ external DC electric fields that are often fully shielded by adsorbed atom layers on the cell walls, we introduce an AC-field modulation strategy. The incoming low-frequency signal mixes with the auxiliary field, and together they induce Stark shifts of the Rydberg level. These shifts are mapped onto the probe laser via electromagnetically induced transparency (EIT), in a manner analogous to heterodyne detection. We demonstrate a sensitivity of 7.5±2.6μV/(cm⋅Hz1/2) at 5 kHz and a minimal detectable field of 0.26±0.04μV/cm with an integration time of 1000 s. Furthermore, we extend this approach to systematically analyze the performance of generalized auxiliary fields containing multiple frequency components. By virtue of modulated auxiliary field and quantum frequency mixing, our results establish a robust and systematic framework for quantum sensing of low-frequency electric fields with Rydberg atoms, offering improved sensitivity, stability, and immunity to environmental drifts.