Nanoscale resolution fluorescence microscopy using electromagnetically induced transparency

We suggest a type of scanning fluorescence microscope that is capable of resolving nanometer-size objects in the far field. The key idea is to use the spatial sensitivity of the dark state of electromagnetically induced transparency and localize an atomic excitation to a spot much smaller than the wavelength of light.

Figure 1

(Color online) Energy level diagram and simplified schematic of the suggested technique. The probe and the coupling laser beams form a traditional $\Lambda$ scheme and drive the atoms into the dark state. The sensitive spatial dependence of the dark state on the intensities of the two laser beams can be used to localize the population of state $\mid 2⟩$ to a spot much smaller than the diffraction limit. The fluorescence laser that scatters photons only when the atom is in state $\mid 2⟩$ may then be used to detect the tightly localized population. By scanning the focusing lens, a fluorescence shadow image of the embedded object at the nanometer scale is obtained.

Figure 2

(Color online) Localization of atomic excitation to a spot much smaller than the diffraction limit. (a) shows the atomic excitation $\mathbf{\mid }⟨2\mid {\psi }_{dark}⟩{\mathbf{\mid }}^2$, assuming that the atomic system is in the dark state given by Eq. (1). (b) shows the spatial distribution of the Rabi frequencies for the probe laser ${\Omega }_p$ and the coupling laser ${\Omega }_c$, which results in the localization of (a). These distributions are calculated numerically by taking into account vectorial properties of light near a tight focus. (c) is a zoom on (a) detailing the spatial structure of the excitation. The excitation has a full width at half maximum (FWHM) of $51.1\mathrm{nm}$, which is about 15 times smaller than the wavelength of light.

Figure 3

(Color online) Numerical calculation that demonstrates localization with pulsed excitation. The inset shows the assumed temporal profiles for the intensities of the probe (solid) and coupling (dashed) laser beams. Starting from the ground state $\mid 1⟩$, we numerically integrate the Schrödinger equation at each spatial point along the profiles of the probe and coupling laser beams of Fig. 2b. The data points are the fractional population $\mathbf{\mid }⟨2\mid \psi ⟩{\mathbf{\mid }}^2$ at $t=0.2\mathrm{\mu }\mathrm{s}$ (shown with a tick mark in the inset) at each spatial point. The solid line is a replot of Fig. 2c. There is good agreement between the results of the exact numerical simulation and the idealized calculation of Fig. 2.

Figure 4

(Color online) Numerical simulations that demonstrate the robust nature of our scheme. For the open squares, the intensity of the coupling laser beam fluctuates by $\pm 10\%$ at each scanning point. For the solid squares, a timing jitter of $\pm 0.01\mathrm{\mu }\mathrm{s}$ is assumed between the probe and coupling laser pulses. All the other parameters are identical to those of Fig. 3. The solid line is a replot of the numerical simulation of Fig. 3.