Optical field characterization at the fundamental limit of spatial resolution with a trapped ion

TL;DR

This work introduces a trapped-ion sensor for sub-wavelength optical-field characterization, achieving spatial resolution set by the fundamental cross-section with a single $^{171}$Yb$^{+}$ ion confined to ~40 nm × 40 nm × 180 nm for a 370 nm field. It combines a parameter-free, eight-level ion–light interaction model with a graph-theoretic reduction to a time-independent Hamiltonian and validates it against extensive optical-pumping data. To enable field-scale mapping, the authors develop an inverse-physics approach using a neural-network to translate three pumping-curves (from different initial ion states) into local light parameters, reducing per-point readout time from hours to μs-scale and enabling practical high-resolution profiling, including synthetic high-NA focus scenarios. The approach promises rapid, field-deployable optical metrology for nanofabrication and quantum-information platforms, with potential extensions to off-resonant detection and multi-wavelength sensing to broaden applicability.

Abstract

Optical systems capable of generating fields with sub-wavelength spatial features have become standard in science and engineering research and industry. Pertinent examples include atom- and ion-based quantum computers and optical lithography setups. So far, no tools exist to characterize such fields - both intensity and polarization - at sub-wavelength length scales. We use a single trapped atomic ion, confined to approximately 40 nm X 40 nm X 180 nm to sense a laser light field at a wavelength of 370 nm. With its spatial extent smaller than the absorption cross-section of a resonant detector, the ion-sensor operates at the fundamental limit of spatial resolution. Our technique relies on developing an analytical model of the ion-light interaction and using the model to extract the intensity and polarization. An important insight provided in this work is also that the inverse of this model can be learned, in a restricted sense, on a deep neural network, speeding up the intensity and polarization readout by five orders of magnitude. This speed-up makes the technique field-deployable to characterize optical instruments by probing light at the sub-wavelength scale.

Figures (6)

• Figure 1: Cartoon schematic of the light-field sensing technique: A trapped $^{171}\mathrm{Yb}^{+}\space$ ion is moved to the field point where the light properties are to be measured and initialized in one of the sublevels of the $^2\mathrm{S}_{1/2}\space$$\ket{F=1}$ manifold (inset: Initial States) using a microwave horn antenna. The light that needs to be characterized pumps the population in $^2\mathrm{S}_{1/2}\space$$\ket{F=1}$ manifold to the $^2\mathrm{S}_{1/2}\space$$\ket{F=0}$ state (inset: Final State). The probability of pumping to $^2\mathrm{S}_{1/2}\space$$\ket{F=0}$ is a function of the initial state of the ion, the interaction time $\tau$, and the light intensity and polarization. The three measured probability decay curves, with the ion initialized in each of the three initial states, are fed to a deep neural network which then outputs the intensity and polarization of the light at the ion position.
• Figure 2: Validating the ion-light interaction model:a) Cartoon schematic of the experimental apparatus used to generate the 88 experimental optical pumping curves for validating our model (See section \ref{['sec:IonLightModelValidation']}). 76 curves were used to fit the data to the theoretical model and extracting the light parameters. b) Remaining 12 curves optical curves (not used for fitting) used for comparison with model predictions after extraction of light parameters. Here, $P_{\mathrm{aom}}$ is the RF drive power to the AOM and $\theta$ is the half-wave plate angle. c) Measured beam profile of the characterization beam in steps of 200 nm. The shaded regions represent the standard errors (200 experimental repetitions) and the green line is a Gaussian fit. The intensity at each point was estimated by recording probability of decay of the ion initialized in $^2\mathrm{S}_{1/2}\space$$\ket{F=1, \;m_F=0}$ to $^2\mathrm{S}_{1/2}\space$$\ket{F=0}$ after a fixed interaction time of $\tau = 30 \mu$s.
• Figure 3: Intelligent Sensing:Top: Simulated focal spot of a 0.8 NA objective lens assuming perfect reconstruction with a detector of cross-section $\lambda^2/2\pi$, at the wavelength $\lambda = 370$ nm. Here, just like our apparatus in Fig. \ref{['fig:SolverValidate']}, the z-axis is the direction of propagation of the beam at the input of the objective lens. The input light is x-polarized and $I_\mathrm{x}$, $I_\mathrm{z}$ and $I_{\mathrm{total}}$ represent normalized intensities. Middle: Reconstructed image plane field using intelligent reconstruction. Bottom: Reconstructed image plane field using intelligent reconstruction: Slice along y=0.
• Figure 4: Detailed Schematic of the experimental setup
• Figure 5: Labeling Scheme for energy levels in $^2\mathrm{S}_{1/2}\space$ and $^2\mathrm{P}_{1/2}\space$