Abstract
Bringing optical microscopy to the shortest possible length and time scales has been a long-sought goal, connecting nanoscopic elementary dynamics with the macroscopic functionalities of condensed matter. Super-resolution microscopy has circumvented the far-field diffraction limit by harnessing optical nonlinearities1. By exploiting linear interaction with tip-confined evanescent light fields2, near-field microscopy3,4 has reached even higher resolution, prompting a vibrant research field by exploring the nanocosm in motion5,6,7,8,9,10,11,12,13,14,15,16,17,18,19. Yet the finite radius of the nanometre-sized tip apex has prevented access to atomic resolution20. Here we leverage extreme atomic nonlinearities within tip-confined evanescent fields to push all-optical microscopy to picometric spatial and femtosecond temporal resolution. On these scales, we discover an unprecedented and efficient non-classical near-field response, in phase with the vector potential of light and strictly confined to atomic dimensions. This ultrafast signal is characterized by an optical phase delay of approximately π/2 and facilitates direct monitoring of tunnelling dynamics. We showcase the power of our optical concept by imaging nanometre-sized defects hidden to atomic force microscopy and by subcycle sampling of current transients on a semiconducting van der Waals material. Our results facilitate access to quantum light–matter interaction and electronic dynamics at ultimately short spatio-temporal scales in both conductive and insulating quantum materials.
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Acknowledgements
We thank C. Bustamante, F. Bonafé, A. Rubio and F. J. Gießibl for discussions and M. Furthmeier for technical assistance. This work was supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – Project-ID, 314695032 – SFB 1277 (Subprojects A05 and B02), major instrumentation grant INST 89/505-1 FUGG and through research grants HU1598/8, HU1598/9-RE2669/8 and WI5664/3-1. We acknowledge the computing time provided on the high-performance computers Noctua 2 at the NHR Center PC2. These are funded by the Federal Ministry of Education and Research and the state governments participating on the basis of the resolutions of the GWK for the national high-performance computing at universities (www.nhr-verein.de/unsere-partner).
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T.S., M.A.H., Y.A.G. and R.H. conceived the study. T.S., J.H., F. Schiegl, F. Sandner, P.M., V.B., S.L., M.A.H. and Y.A.G. performed the experiments and analysed the data. T.S. and Y.A.G. fabricated the samples. T.S., J.H., F. Schiegl, F. Sandner, P.M., V.B., M.Z., S.N., S.L., J.R., J.W., M.A.H., Y.A.G. and R.H. contributed to the discussions of the experimental results. T.S., J.H., M.A.H., Y.A.G. and R.H. developed and computed the dipole emission model. J.W. developed and computed the ab initio quantum simulations. The paper was written by T.S., Y.A.G. and R.H. with input and contributions from all authors.
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After the final round of submission, the University of Regensburg applied for a German patent (no. 10 2024 108 203.8) on near-field optical tunnelling emission microscopy. The authors declare no further competing interests.
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Extended data figures and tables
Extended Data Fig. 1 Tip-sample distance dependence of the scattered transients for the first and third harmonic.
First (a) and third (b) harmonic, \({E}_{1}^{{\rm{scat}}}\) and \({E}_{3}^{{\rm{scat}}}\), of the scattered electric fields, measured simultaneously with the transients shown in Fig. 1b (peak far-field strength \({\hat{E}}_{{\rm{light}}}=1.3\) kV cm−1). For the closest tip-sample distance about 900 electrons are rectified per pulse on average. The colours correspond to the distances shown in Fig. 1c. The strong underlying nonlinearity is highlighted by the increased difference in signal strength for different tip-sample separations when going to higher demodulation orders.
Extended Data Fig. 2 Decay of the NOTE signal at large tip-tapping amplitudes.
a, Electro-optically detected scattered THz transients demodulated at the second harmonic of the tip-tapping frequency (\({E}_{2}^{{\rm{scat}}}\)) with A = 5 nm and \({\hat{E}}_{{\rm{light}}}=1.1\) kV cm−1. For the transient acquired at the closest tip-sample distance \(\langle \,{J}_{{\rm{lw}}}\,\rangle =-180\) pA, on average about 80 rectified electrons per pulse. b, Peak of the THz transient (\({\hat{E}}_{2}^{{\rm{scat}}}\)) at t = 0 fs, measured at a tip-tapping amplitude A = 5 nm for increasing tip-sample separation \(\Delta z\). c, Logarithmic-scale plot of the data shown in Fig. 2b: \({\hat{E}}_{2}^{{\rm{scat}}}\) measured at the second harmonic of the tip-tapping frequency (A = 200 pm, \({\hat{E}}_{{\rm{light}}}=0.8\) kV cm−1), alongside the time-integrated lightwave tunnelling current \(\langle \,{J}_{{\rm{lw}}}\,\rangle \) measured for increasing tip-sample separation (on average about 200 electrons per pulse are rectified for the closest tip-sample distance).
Extended Data Fig. 3 NOTE transients sampled on Au(111).
Electro-optically detected scattered THz transients measured at the first three harmonics of the tip-tapping frequency (A = 1 nm). In each panel, the red curve shows the case of an approached tip, where tunnelling currents can flow (\(\langle \,{J}_{{\rm{lw}}}\,\rangle =-300\,{\rm{pA}}\), on average about 140 rectified electrons per pulse, Δν = −4.8 Hz, \({\hat{E}}_{{\rm{light}}}=1.3\) kV cm−1). The blue curve shows the case where the tip is retracted away from the tunnelling barrier.
Extended Data Fig. 4 Steady-state tunnelling spectrum of Au(111) and optical detection bandwidth.
a, Experimental tunnelling spectrum, measured with steady-state STM on the surface of Au(111). b, Amplitude and phase of the response of the EOS detection, including the detector response of gallium phosphide and focusing conditions of the parabolic mirrors.
Extended Data Fig. 5 Distribution of tunnelled charges at the tip apex.
a, Distribution of charges on the surface of a sphere with radius r = 100 Å at distance d = 5 Å from a large sphere with radius R. The local strength of the surface charge is indicated by the diameter of the blue circles. b, Surface charge density around the surface of the sphere as a function of the polar angle θ shown in a.
Extended Data Fig. 6 Numerical model of the tip-transfer function.
a, Spatial distribution of the electric field magnitude on a cross-section of the STM tip. The inset shows the near fields in the vicinity of the nanoscale apex. b, Magnitude and phase of the field enhancement at the tip apex as a function of frequency.
Extended Data Fig. 7 Atomic-scale decay of the NOTE signal in the quantum simulation.
a, Amplitude of the simulated NOTE dipoles (A = 1 Å) evaluated at t = 0 fs, for increasing average tip-sample separation \(\left\langle z\right\rangle \). b, Simulated peak of the ultrafast tunnelling current (\({\hat{J}}_{{\rm{l}}{\rm{w}}}\)) for a static tip as a function of the tip-sample separation z. The angstrom-scale decay of the NOTE dipole in panel a closely follows that of the ultrafast tunnelling current.
Extended Data Fig. 8 Bias spectroscopy of mono- and trilayer WSe2 on Au(111).
Normalized steady-state differential conductance of WSe2 mono- and trilayer on Au(111). In the monolayer, some electrons tunnel directly from tip to Au(111), resulting in a measurable current within the gap. The additional tunnelling barriers introduced by the trilayer remove this current pathway.
Extended Data Fig. 9 Far-field THz transient and spectrum.
a, Incident THz transient sampled in the far field. b, Corresponding spectrum of the incident THz field.
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Siday, T., Hayes, J., Schiegl, F. et al. All-optical subcycle microscopy on atomic length scales. Nature 629, 329–334 (2024). https://doi.org/10.1038/s41586-024-07355-7
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DOI: https://doi.org/10.1038/s41586-024-07355-7
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