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 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.
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.
We present a theoretical investigation of coherent anti-Stokes Raman scattering (CARS) that is modulated by periodically depleting the ground-state population through Rabi oscillations driven by an additional control laser. We find that such a process generates optical sidebands in the CARS spectrum and that the frequency of the sidebands depends on the intensity of the control laser light field. We show that analyzing the sideband frequency upon scanning the beams across the sample allows one to spatially resolve emitter positions where a spatial resolution of 65 nm, which is well below the diffraction limit, can be obtained.
In theoretical investigations, we review several nonlinear optical approaches towards subdiffraction-limited resolution in label-free imaging via coherent anti-Stokes Raman scattering (CARS). Using a density matrix model and numerical integration, we investigate various level schemes and combinations of the light fields that induce CARS along with additional control laser fields. As the key to techniques that gain far-field resolution below the diffraction limit, we identify the inhibition of the buildup of vibrational molecular coherence via saturation or depletion of population (Beeker et al. Opt Express 17:22632–22638, 2009) or the generation of Stark broadening and spatially dependent Rabi sideband generation (Beeker et al. Phys Rev A 81(1), 2010). Depending on the coherence and population decay rates offered by a particular molecular energy level scheme, we identify various different regimes. In the first case, where an additional state (called the control state) and a vibrational state are able to rapidly exchange population via incoherent processes, a prepopulation of the upper vibrational state inhibits the buildup of vibrational coherence. With increasing control laser intensity, this suppresses CARS emission via an incoherent, saturation type of nonlinear process. Using an intense, donut-shaped control laser beam, similar to stimulated emission depletion (STED) microscopy, this can suppress CARS emission from all sample locations except within a subdiffraction-sized range around the central node. Scanning the control beams across the sample provides subdiffraction-limited resolution imaging. An alternative, which does not require a rapid exchange of population with the control state, applies a control beam that only partially depletes the vibrational ground state. Thereby, a CARS point spread function containing a subdiffraction-limited component is generated. Subdiffraction images can then be retrieved through deconvolution. Further approaches are based on the coherent, nonlinear, resonant response of the sample. In this case, CARS signal depletion by Stark splitting of the weakly populated upper vibrational state or the observation of spatially dependent Rabi oscillation may increase the resolution beyond the diffraction limit.
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 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.