Beating the Abbe Diffraction Limit in Confocal Microscopy via Nonclassical Photon Statistics

We experimentally demonstrate quantum enhanced resolution in confocal fluorescence microscopy exploiting the nonclassical photon statistics of single nitrogen-vacancy color centers in diamond. By developing a general model of superresolution based on the direct sampling of the $k$th-order autocorrelation function of the photoluminescence signal, we show the possibility to resolve, in principle, arbitrarily close emitting centers.

Figure 1

Setup of the experiment: (a) $XYZ$ closed-loop piezoelectric stage, (b) sample, (c) $100\times \text{oil}$ objective, (d) excitation light (532 nm), (e) laser source, (f) dichroic filter, (g) long-pass filters, (h) $50:50$ fiber beam splitter, (i) single-photon detectors, and (j) coincidence electronics.

Figure 2

Example of the super-resolution technique applied to a cluster of 3 NV centers. (a) Typical scan on a region of the sample obtained collecting the signals emitted by each center on a pixel-by-pixel basis via single-photon sensitive confocal microscope. (b) Magnification of the area of interest. (c) Map of $g^{(2)}$ function. (d) Map of $g^{(3)}$ function. (e) Super-resolved map for $k=2$. (f) Super-resolved map for $k=3$.

Figure 3

Plot of the measured FWHM values, characterizing the resolution of the confocal microscope, versus the order $k$ of the generalized $g$ function used, together with the fit of the data, showing their good agreement with the expected scaling of the resolution as $1/\sqrt{k}$.

Figure 4

(a) Direct mapping of the signal emitted by two NV centers, whose distance is below the FWHM of each peak, by the confocal microscope. (b) Map of the $g^{(2)}$ function. (c) Map obtained via the superresolution function for $k=2$. (d) Map obtained via the superresolution function for $k=3$. (e),(f) Maps derived, respectively, from Eq. (5) and Eq. (6) for $g^{(k)}=0$ for $k\ge 3$.