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Journal of Physics B Atomic Molecular and Optical Physics

Coherent Rabi oscillations in a molecular system and sub-diffraction-limited pattern generation

Zeyang Liao, M. Al-Amri, Muhammad Suhail Zubairy

Published Apr 14, 2015• 3 citations
Publisher

Abstract

Abstract The resolution of a photolithography and optical imaging system is restricted by the diffraction limit. Coherent Rabi oscillations have been shown to be able to overcome the diffraction limit in a simple two-level atomic system (Z Liao, M Al-amri, and M S Zubairy 2010 Phys. Rev. Lett. 105 183601 ). In this paper, we numerically calculate the wave packet dynamics of a molecular system interacting with an ultrashort laser pulse and show that coherent Rabi oscillations in a molecular system are also possible. Moreover, a sub-diffraction-limited pattern can be generated in this system by introducing spatially modulated Rabi oscillations. We also discuss several techniques to improve the visibility of the sub-diffraction-limited pattern. Our result may have important applications in super-resolution optical lithography and optical imaging.

DOI
10.1088/0953-4075/48/10/105101

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Abstract The resolution of a photolithography and optical imaging system is restricted by the diffraction limit. Coherent Rabi oscillations have been shown to be able to overcome the diffraction limit in a simple two-level atomic system (Z Liao, M Al-amri, and M S Zubairy 2010 Phys. Rev. Lett. 105 183601 ). In this paper, we numerically calculate the wave packet dynamics of a molecular system interacting with an ultrashort laser pulse and show that coherent Rabi oscillations in a molecular system are also possible. Moreover, a sub-diffraction-limited pattern can be generated in this system by introducing spatially modulated Rabi oscillations. We also discuss several techniques to improve the visibility of the sub-diffraction-limited pattern. Our result may have important applications in super-resolution optical lithography and optical imaging.
The resolutions of the optical microscope and the optical lithography are both limited by the well-known Rayleigh limit. Rabi oscillation is a coherent nonlinear process that can modulate the population distribution between two energy states and also modulate the resonant fluorescence spectrum. If we have a gradient electric field amplitude in the space, the Rabi frequency for different position is also different. The spatial distribution of the population in the excited state can be modulated and the spatial information of the atoms can also be encoded in the resonant fluorescence spectrum. If the gradient of the field is large enough, the pattern generated can be subwavlength and the atoms with subwavelength distances can also be extracted. Here we present a review on both the subwavelength photolithography and microscopy via Rabi oscillations.
The resolutions of the optical lithography is limited by the well-known Rayleigh limit. Although the atom lithography can generate features smaller than this limit, the spacing of the pattern is still limited by the optical wavelength. Here, we proposed two atom lithography methods, both of which used the coherent Rabi oscillation to break the diffraction limit. One is in the microwave regime where the Rydberg atom is used and micrometer resolution can be achieved. The other is in the optical regime where sub-10 nanometer resolution is possible.
Abbe’s diffraction limit restricts the resolution of an optical imaging and lithography system. A coherent Rabi oscillation is shown to be able to overcome the diffraction limit in both optical and atom lithography. In previous studies, semiclassical theory is applied, where the driving field is treated as a classical light, and quantum fluctuation is neglected. Here, we show that the quantum fluctuation may reduce the visibility of the superresolution pattern. However, by squeezing the photon number fluctuation, we are able to significantly increase its visibility.
The resolution of traditional optical microscope and optical lithography is limited by about half wavelength of the light source, which is well known as the diffraction limit or Abbe limit. The resolution limit is due to the missing of high spatial frequency components in the far-field. One way to achieve high resolution is to move the detector into the near-field region where the evanescent wave can be collected. However, these methods are surface-bound and usually very slow which have limited applications. It has long been an interesting and important question about how to overcome the diffraction limit in the far-field.\n\nFor optical lithography, a number of methods have been proposed to overcome the diffraction limit such as multi-photon scanning, quantum entanglement, quantum inspired process (e.g., dopperlon), and quantum dark state. However, these methods either require multi-photon absorber, quantum entanglement, or multi-energy levels, which restrict them from extending to higher resolution in practice. In this thesis, we showed that sub-diffraction-limited resolution can be generated by the coherent Rabi gradient. This method does not require multi-photon absorber or quantum entanglement but just quantum coherence of the medium. Extension from lower resolution to higher resolution is very straightforward where we just need to increase the pulse intensity or pulse duration. We also proposed two atom lithography experiments based on the Rabi gradient. The first one uses Rubidium Rydberg atom and microwave where we showed that sub-micrometer line spacing is possible. The second one uses Chromium atom and optical field where we showed that sub-10nm line spacing is possible while the wavelength of the light is about 400nm.\n\nFor optical imaging, a number of methods have also been proposed to achieve super-resolution such as multi-photon microscope, stimulated-emission-depletion, structured illumination microscopy, centroid-based techniques and metamaterial-based lens. Here, we will show a new method to achieve resolution beyond the diffraction limit which we called it resonance fluorescence microscopy. Resonance fluorescence has been proposed to localize a single atom with resolution beyond the diffraction limit. The separation between two atoms can also be extracted from the resonance\nfluorescence spectrum. To develop it as microscopy, we need to evaluate the resonance fluorescence spectrum of multiple-atom system. We analytically solved the general feature of the spectrum when the Rabi frequency is much larger than the dipole-dipole interaction and showed how to extract the spatial information of the atoms with resolution far beyond the diffraction limit. This method is entirely based on far-field techniques and it does not require point-by-point scanning.
The resolution of optical lithography and the spacing of atom lithography are limited by about half of the wavelength due to the Rayleigh limit. Here we propose a coherent atom lithography experiment which can print nanometer structures. In this proposal, we show that subwavelength spatial distribution of the atoms in the excited state can be achieved by inducing spatially modulated Rabi oscillations in two-level atoms. We use the internal energy of the atoms to excite the photoresist and it can then print the subwavelength structure into the photoresist. For the peak Rabi frequency of about 2 GHz and the recoil limited collimation, we show that sub-10-nm10\text{-nm}10-nm spacing in both one- and two-dimensional space is possible.
We propose a scheme for microscopy with resolution far beyond the diffraction limit by using coherent Rabi oscillations. When the sample is illuminated by a gradient laser field, Rabi oscillations will be induced which can lead to a sinusoidal excitation in the sample. This is similar to the structured illumination microscopy (SIM) which can recover high-spatial-frequency components in the far field. However, different from linear SIM, the sinusoidal pattern here can have a spatial frequency much higher than that of the linear standing wave. Due to this property, we can achieve extremely high resolution, as in the nonlinear saturated SIM, but keep the reconstruction algorithm as simple as the linear one.