Superresolution Microscopy of Optical Fields Using Tweezer-Trapped Single Atoms

We realize a scanning probe microscope using single trapped ${}^{87}\mathrm{Rb}$ atoms to measure optical fields with subwavelength spatial resolution. Our microscope operates by detecting fluorescence from a single atom driven by near-resonant light and determining the ac Stark shift of an atomic transition from other local optical fields via the change in the fluorescence rate. We benchmark the microscope by measuring two standing-wave Gaussian modes of a Fabry-Pérot resonator with optical wavelengths of 1560 and 781 nm. We attain a spatial resolution of 300 nm, which is superresolving compared to the limit set by the 780 nm wavelength of the detected light. Sensitivity to short length scale features is enhanced by adapting the sensor to characterize an optical field via the force it exerts on the atom.

Figure 1

Overview of the experiment. (a) Atoms are loaded from an optical dipole trap into an array of optical tweezers, centered within an optical cavity. The radial ($y$) position of tweezers along the array is controlled using an acousto-optical deflector (AOD), while the axial ($x$) position is controlled using a piezoactuated mirror. Atomic fluorescence is imaged through a $\mathrm{NA}=0.5$ objective (used also to focus tweezer light) onto a scientific CMOS (sCMOS) camera. (b) Single-shot (top) and averaged (bottom) fluorescence images of ten-atom tweezer array. (c) ac Stark shifts are applied to the ${}^{87}\mathrm{Rb}$ $5S_{1/2}$ to $5P_{3/2}$ imaging transition at 780 nm by light at wavelengths of 1560 nm (LW, green arrow) and 781 nm (SW, dark red arrow), both supported by the optical cavity. LW light reduces the imaging transition frequency, due to the dominant downward shift of the excited state caused by the proximity of the $5P_{3/2}$ to $4D$ transitions near 1529 nm. SW light increases the imaging transition frequency and exerts a strong potential on ground-state atoms.

Figure 2

Demonstration of sensor operation. (a) Background-subtracted integrated photon counts for fluorescence images (exposure 500 ms) of single atoms at imaging detunings $\mathrm{\Delta }/2\pi =-64.8,-23.7,-10.0,-3.2\mathrm{MHz}$ (lightening shades of blue). Near atomic resonance, single-atom fluorescence is easily distinguished from camera noise (gray), allowing us to detect an atom with 99.99% fidelity. For far-detuned probing, the photon-count distributions for zero- and one-atom images overlap ($\mathrm{\Delta }/2\pi =-64.8\mathrm{MHz}$ data shown together in inset, gray). However, postselection (inset, blue) based on a later near-resonant image frame identifies single-atom images. (b) Detected photon counts vs $\mathrm{\Delta }$ for an atom held in an optical tweezer of depth $k_B\times 1.5(2)\mathrm{mK}$ (blue) and subject to increasing intensities of LW cavity field (lightening shades of red). Error bars indicate estimated single-shot uncertainty based on photon detection noise. Solid lines are fits to Eq. (1). The inset compares ${\delta }_{\mathrm{ac}}$ from LW light measured at $\mathrm{\Delta }/2\pi =-37\mathrm{MHz}$ [gray line in Fig. 2] with a prediction that is based on the estimated cavity circulating intensity, with a correction factor of 0.7 applied to account for a reduction in the ac Stark shift measured at the LW antinode due to spatial averaging by the finite temperature atomic distribution.

Figure 3

Superresolution imaging of LW cavity field. (a) Several atoms trapped in tweezers of depth $k_B\times 1.5(2)\mathrm{mK}$ are arrayed in a direction nearly perpendicular to the cavity axis, spaced to probe the cavity mode at several radial positions. The calculated intensity profile of the cavity mode is shown in gray scale. The array is translated in 100 nm steps along the cavity axis (trajectory shown). ${\delta }_{\mathrm{ac}}$ is measured for each tweezer at every position along this trajectory. (b) Axial dependence of ac Stark shift measurements for four tweezers whose radial positions are indicated in (c). Modulation with a periodicity of the LW lattice ($d=780\mathrm{nm}$) is clearly visible with contrasts between 0.30 and 0.47. Error bars indicate standard error on the mean of repeated measurements. (c) Radial profile of the LW ${\mathrm{TEM}}_{00}$ mode, determined from axial average ${\overline{\delta }}_{\mathrm{ac}}$ of data in (b). Error bars are smaller than the data points. Solid line is a fit to a Gaussian with a waist of $25.9(3)\mu \mathrm{m}$.

Figure 4

Force sensing measurement of SW cavity lattice through distortion of LW measurement. (a) Optical trapping potential (green) and thermal atomic distribution (orange) due to the tweezer (left) and the sum of the tweezer and SW cavity field (right). The SW lattice narrows and displaces the atomic distribution. (b) Axial ac Stark shift due to the LW cavity field measured with a single atom trapped in a tweezer of depth $k_B\times 0.34(3)\mathrm{mK}$ in the absence (presence) of SW light, shown in light (dark) green. The axial variation at the LW periodicity gains an overall offset, increases in amplitude, and is shifted axially upon imposition of the SW potential. Error bars indicate standard error on the mean of repeated measurements. (c) Axially-averaged offset of the LW ac Stark shift due to the SW cavity field measured at different radial positions. Solid line is a fit to a Gaussian with a waist of $20(3)\mu \mathrm{m}$. Starred point indicates the tweezer used for (b).