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arXiv:2109.08314 · Physical Review Letters

Superresolution Microscopy of Optical Fields Using Tweezer-Trapped Single Atoms

Emma Deist, Justin A. Gerber, Yue-Hui Lu, Johannes Zeiher, Dan Stamper-Kurn

Published Feb 22, 2022• 46 citations
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Abstract

We realize a scanning probe microscope using single trapped ^{87}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.

DOI
10.1103/physrevlett.128.083201

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We realize a scanning probe microscope using single trapped ^{87}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.
Sub-micrometer light patterns play a pivotal role in biology, biophysics, and AMO physics, yet their in situ characterization is limited in spatial resolution and sensitivity. Here, we present an atom camera with a single ultracold atom in an optical tweezer as a scanning probe. Measuring the energy shift on the spin states with the long coherence time and polarization-sensitive transitions yields highly sensitive, high-resolution 2D imaging of both intensity and polarization ellipticity. We characterize the polarization of a tightly-focused beam, observing its non-trivial profile. The spatial resolution is fundamentally limited by the atom’s position uncertainty, suppressed down to quantum fluctuations (~25 nm) in the motional ground state of the tweezer, with an experimentally obtained upper bound of σ ≤ 96(4) nm. This method enables imaging beyond the diffraction limit, surpassing previous approaches limited by thermal fluctuations of the atom, and provides a powerful tool for designing and analyzing submicron-scale light patterns. In situ super-resolution imaging of light has inherent limitations when applied to the polarization profile. Here, the authors introduce an “atom camera” approach by means of a single tweezer-trapped 87Rb atom measuring the field-induced shifts at sub-micrometer steps, achieving resolution beyond the optical diffraction limit.
The paper summarizes on the results of several experiments on single trapped ions which have been used to map optical fields. In these experiments, the ion was placed either in front of a (distant) mirror or in an optical cavity. Sub-wavelength resolution is achieved because the position of the ion relative to the mirror(s) is well-controlled and the ion's spatial wavefunction is confined to a region much smaller than the optical wavelength (400 to 800 nm). This strong localization is due to the trapping potential of a Paul-type ion trap, and laser cooling. In the three experiments the ions were Doppler-cooled, and a resolution between about 10 and 50 nm was achieved. With this resolution, the spatial variation of an optical standing-wave field was detected by shifting the single ion through the field structure.
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.
We measure the ac Stark shifts of the $5{S}_{1/2},F=2\ensuremath{\rightarrow}5{P}_{3/2},{F}^{\ensuremath{'}}=3$ transitions of individual optically trapped 87{}^{87}87Rb atoms using a nondestructive detection technique that allows us to measure the fluorescent signal of one and the same atom for over 60 s. These measurements allow the efficient and rapid characterization of single-atom traps that is required for many coherent quantum information protocols. Although this method is demonstrated using a single-atom trap, the concept is readily extended to resolvable atomic arrays.
The center-of-mass position of a single trapped atomic ion is measured and tracked in time with high precision. Employing a near-resonant radio frequency field of wavelength 2.37 cm and a static magnetic field gradient of 19 T/m, the spatial location of the ion is determined with an unprecedented wavelength-relative resolution of 5 ×\times× 10−9^{-9}−9, corresponding to an absolute precision of 0.12 nm. Measurements of an electrostatic force on a single ion demonstrate a sensitivity of 2.2 ×\times× 10−23 N/Hz^{-23} ~\text{N}/\sqrt{\text{Hz}}−23 N/Hz​. The real-time measurement of an atom's position complements the well-established technique of scanning near-field radio frequency transmission microscopy and opens up a novel route to using this method with path breaking spatial and force resolution.
A scanning optical microscope whose active element (the tip) consists of a crystal containing impurity ions or color centers, which are excited by laser radiation, is proposed. The excitation energy from a single impurity center located at the point of the tip is transferred to the fluorescence centers of the experimental sample by the mechanism of resonant dipole-dipole exchange. It is shown that this approach can give nanometer spatial resolution with high sensitivity, which in many cases is much higher than the sensitivity of the “standard” near-field fluorescence microscopy.