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arXiv:2406.08424 · Nature Physics

Ultrasensitive single-ion electrometry in a magnetic field gradient

F. Bonus, C. Knapp, Christophe H. Valahu, M. Mironiuc, Sebastian Weidt, W. K. Hensinger

Published Jun 11, 2025• 6 citations
arXivHTMLPDF

Abstract

Hyperfine energy levels in trapped ions offer long-lived spin states. In addition, the motion of these charged particles couples strongly to electric field perturbations. These characteristics make trapped ions attractive platforms for the quantum sensing of electric fields. However, the spin states do not exhibit a strong intrinsic coupling to electric fields, lim iting the achievable sensitivity. Here, we amplify the coupling between electric field perturbations and the spin states by using a static magnetic field gradient. Displacements of the trapped ion resulting from the applied electric field perturbations are thereby mapped to an instantaneous change in the energy-level splitting of the internal spin states. This gradient-mediated coupling of the electric field to the spin enables the use of well-established magnetometry protocols for electrometry, making it possible to achieve extremely sensitive measurements of d.c. and a.c. electric fields. We also employ a rotating-frame relaxometry technique and demonstrate the use of our quantum sensor as an electric field noise spectrum analyser. Finally, we describe a set of hardware modifications that are capable of achieving a further improvement in sensitivity by up to six orders of magnitude.

DOI
10.1038/s41567-025-02887-9

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Hyperfine energy levels in trapped ions offer long-lived spin states. In addition, the motion of these charged particles couples strongly to electric field perturbations. These characteristics make trapped ions attractive platforms for the quantum sensing of electric fields. However, the spin states do not exhibit a strong intrinsic coupling to electric fields, lim iting the achievable sensitivity. Here, we amplify the coupling between electric field perturbations and the spin states by using a static magnetic field gradient. Displacements of the trapped ion resulting from the applied electric field perturbations are thereby mapped to an instantaneous change in the energy-level splitting of the internal spin states. This gradient-mediated coupling of the electric field to the spin enables the use of well-established magnetometry protocols for electrometry, making it possible to achieve extremely sensitive measurements of d.c. and a.c. electric fields. We also employ a rotating-frame relaxometry technique and demonstrate the use of our quantum sensor as an electric field noise spectrum analyser. Finally, we describe a set of hardware modifications that are capable of achieving a further improvement in sensitivity by up to six orders of magnitude.
Today's most sensitive experiments for detecting CP-violating permanent electric dipole moments (EDM) rely on molecular spectroscopy. The high sensitivity arises from large internal electric fields that interact with the constituents of the molecule. For molecular ions it has long been assumed that experiments with static polarization from dc electric fields are infeasible, as the ion's charge would either shift it to a field free region or eject it from the trap. This constraint appears to make single ion quantum-logic clocks, among the most precise measurement devices available, incompatible with EDM measurements. Here, we demonstrate that, under typical trapping conditions, heavy molecular ions with small Ω/ΛΩ/ΛΩ/Λ-doubling can be polarized by a static electric field while remaining confined in the Paul trap. This effect arises from a cancellation between the electrostatic force and the trap's ponderomotive force, resulting in an equilibrium position where the ion experiences a dc electric field component. Dynamic decoupling allows to implement co-magnetometry schemes in a single molecule and provides long interrogation times. This will allow the operation of a quantum-logic molecular radio-frequency clock in static electric fields, providing sensitivity to EDMs. Working with only a few ions and non-destructive detection techniques opens the door to the use of highly sensitive, rare, and radioactive molecular species as well as quantum-enhanced metrology schemes to achieve unprecedented levels of accuracy and precision.
This thesis describes an ion trap magnetometer, in which experimental hardware and theory for trapped ion magnetometry has been developed and demonstrated. Quantum magnetometry has been a fast expanding field in recent years due to the plethora of military, medical and security applications. The current quantum magnetometer literature has shown great improvements on the standard magnetometer success metrics such as sensitivity, spacial resolution, frequency tuneability, noise shielding and vector field resolution. Ion trap magnetometry could potentially boast several advantages over some of the better established methods such as, nano-meter spatial resolution, broadband tuneability over radio-frequency (RF) and microwave frequencies, and magnetic field noise shielding and sensitivity improvements through dynamic decoupling methods; all in room temperature environments. The experimental setup discussed uses a micro-fabricated Paul trap for ion confinement due to the scalability of this technology. The method for sensing that was demonstrated utilises long-wavelength radiation dressed states to extend the coherence time of a single 171Yb+ ion beyond the bare states and to allow for a high level of frequency tuneability. The coherence times measured were T2 = 0:645 s for RF field sensing at 15.616 MHz and T2 = 1.153 s for microwave field sensing at 12.658466 GHz. Sensitivities of SB = 125.857 ± 26.155 pT/ vHz for RF magnetic fields and SB = 102.054 ± 11.046 pT/ vHz for microwave magnetic fields were achieved experimentally. A novel micro-fabricated Paul trap for trapping multiple ion clusters was developed to improve sensitivity values by increasing the total number of trapped ions. The design confines ions over a two-dimensional surface spanning 0.65 x 1.00 mm which would also allow for magnetic field gradient measurements. Efforts have been made to miniaturise certain experimental hardware to further the development of portable trapped ion experiments. For this, a miniaturised RF resonator that could be used for radial confinement of ions within Paul traps has been developed. At the current stage of development it is capable of applying a peak RF voltage of 114.9 V with a Q value of 70 at a resonant frequency of O/2p = 12.65 MHz.
In the current landscape of quantum technologies, great efforts are being made to overcome the technical challenges of realising robust and scalable devices for use in a wide variety of potentially impactful applications. This thesis therefore describes the design considerations and assembly of a purpose-built vacuum system for the realisation of high-fidelity quantum logic operations on a microfabricated surface ion trap device. The device consists of an X-junction structure with embedded current-carrying wires, which will allow for the demonstration of scalable, laser-free, magnetic field gradient-based quantum logic. Initial characterisation experiments and observations pertaining to this novel microchip design are presented, as well as demonstrations of coherent quantum operations using the 171Yb+ qubit both with and without the current-carrying wire generated magnetic field gradient. In addition, this work also shows how this static magnetic field gradient design for scalable quantum computing may be leveraged for use in metrology. By utilising the inherent gradient-induced coupling of the trapped ion qubit’s transition frequency to it’s position in this architecture, the ion becomes extremely sensitive to electric field perturbations, enabling the implementation of many well-established quantum electric and magnetic field sensing techniques. Furthermore, the nature of this novel sensing scheme permits high sensitivities within the unique DC − kHz bandwidth, which many current quantum electrometers are unable to reach. Measurements of DC and AC electric fields yield unprecedented sensitivities for the sensing of phase coherent electric fields in a linear Paul trap. In addition, an implementation of a common magnetometry technique to measure electric field noise is also exhibited. Finally, it is shown that a purpose built system for the implementation of this scheme has the potential to improve sensitivities by up to six orders of magnitude, enabling the possibility of utilising this scheme for a wide variety of applications'
mechanical oscillator, and the collective electronic spin serves as the measurement device. By entangling the oscillator and collective spin and controlling the coherent dynamics via a many-body echo, a displacement is mapped into a spin rotation while avoiding quantum back-action and thermal noise. We achieve a sensitivity to displacements of 8.8 ± 0.4 decibels below the standard quantum limit and a sensitivity for measuring electric fields of 240 ± 10 nanovolts per meter in 1 second. Feasible improvements should enable the use of trapped ions in searches for dark matter.
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.
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.