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Optical Lithography and Atom Localization beyond the Diffraction Limit via Rabi Gradient

Zeyang Liao

Published Jul 28, 2014• 0 citations
OpenAlex

Abstract

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.

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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.

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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 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.
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.
We evaluate the resonance-fluorescence spectrum of a bunch of two-level atoms driven by a gradient coherent laser field. The result shows that we can determine the positions of atoms from the spectrum even when the atoms locate within the subwavelength range and the dipole-dipole interaction is significant. This far-field resonance-fluorescence-localization microscopy method does not require point-by-point scanning, and it may be more time efficient. We also give a possible scheme to extract the position information in an extended region without requiring more peak power of the laser. Finally, we also briefly discuss how to perform two-dimensional imaging based on our scheme.
The resolution of imaging devices is ultimately limited by the diffraction of light. This limit can be circumvented by exploiting near-field phenomena, non-linearities of the sample or specific illumination schemes, which led to the recent explosion of optical super-resolution techniques. However, it would be desirable to reach the nanoscale in the most general way possible, with far-field linear imaging of uniformly illuminated samples. In the last few years, the answer to that came with the field of quantum-inspired super-resolution (QISR), where quantum metrological techniques were used to find novel measurement schemes that, beyond the conventional direct imaging of light, would achieve higher precisions. Interestingly, these ideas would always in some way or another involve transverse spatial modes of light. This thesis presents our work on the subject, with novel theoretical and experimental results. Firstly, we develop the traditional theory of QISR, with has mostly focused on either the estimation of separation of two point sources or on geometric moments of samples. Then, we introduce our own results on optical imaging of general distributions of point sources, in a step to take QISR from toy examples to real imaging scenarios. Secondly, we apply all the concepts studied on a experimental, proof-of-principle implementation of a QISR scheme dubbed Hermite-Gaussian Microscopy (HGM), which uses heterodyne detection with several Hermite-Gaussian modes as local oscillator in order to reconstruct the object sample and achieve super-resolution. We report the techniques necessary for the manipulation of spatial modes of light, as well as our results, where we demonstrated 2D imaging with twofold resolution enhancement beyond the diffraction limit.
Far-field optical microscopy beyond the Abbe diffraction limit, making use of nonlinear excitation (e.g. STED), or temporal fluctuations in fluorescence (PALM, STORM, SOFI) is already a reality. In contrast, overcoming the diffraction limit using non-classical properties of light is very difficult to achieve due to the fragility of quantum states of light. Here, we experimentally demonstrate superresolution microscopy based on quantum properties of light naturally emitted by fluorophores used as markers in fluorescence microscopy. Our approach is based on photon antibunching, the tendency of fluorophores to emit photons one by one rather than in bursts. Although a distinctively quantum phenomenon, antibunching is readily observed in most common fluorophores even at room temperature. This nonclassical resource can be utilized directly to enhance the imaging resolution, since the non-classical far-field intensity correlations induced by antibunching carry high spatial frequency information on the spatial distribution of emitters. Detecting photon statistics simultaneously in the entire field of view, we were able to detect non-classical correlations of the second and third order, and reconstructed images with resolution significantly beyond the diffraction limit. Alternatively, we demonstrate the utilization of antibunching for augmenting the capabilities of localization-based superresolution imaging in the presence of multiple emitters, using a novel detector comprised of an array of single photon detectors connected to a densely packed fiber bundle. These features allow us to enhance the spatial and temporal resolution with which multiple emitters can be imaged compared with other techniques that rely on CCD cameras.