We propose here optical resonance imaging (ORI), a direct optical analog to magnetic resonance imaging (MRI). The proposed pulse sequence for ORI maps space to time and recovers an image from a heterodyne-detected third-order nonlinear photon echo measurement. As opposed to traditional photon echo measurements, the third pulse in the ORI pulse sequence has significant pulse-front tilt that acts as a temporal gradient. This gradient couples space to time by stimulating the emission of a photon echo signal from different lateral spatial locations of a sample at different times, providing a widefield ultrafast microscopy. We circumvent the diffraction limit of the optics by mapping the lateral spatial coordinate of the sample with the emission time of the signal, which can be measured to high precision using interferometric heterodyne detection. This technique is thus an optical analog of MRI, where magnetic-field gradients are used to localize the spin–echo emission to a point below the diffraction limit of the radio frequency wave used. We calculate the expected ORI signal using 15 fs pulses and 87° of pulse-front tilt, collected using f /2 optics, and find a two-point resolution of 275 nm using 800 nm light that satisfies the Rayleigh criterion. We also derive a general equation for resolution in optical resonance imaging that indicates that there is a possibility of superresolution imaging using this technique. The photon echo sequence also enables spectroscopic determination of the input and output energy. The technique thus correlates the input energy with the final position and energy of the exciton.
We propose here optical resonance imaging (ORI), a direct optical analog to magnetic resonance imaging (MRI). The proposed pulse sequence for ORI maps space to time and recovers an image from a heterodyne-detected third-order nonlinear photon echo measurement. As opposed to traditional photon echo measurements, the third pulse in the ORI pulse sequence has significant pulse-front tilt that acts as a temporal gradient. This gradient couples space to time by stimulating the emission of a photon echo signal from different lateral spatial locations of a sample at different times, providing a widefield ultrafast microscopy. We circumvent the diffraction limit of the optics by mapping the lateral spatial coordinate of the sample with the emission time of the signal, which can be measured to high precision using interferometric heterodyne detection. This technique is thus an optical analog of MRI, where magnetic-field gradients are used to localize the spin–echo emission to a point below the diffraction limit of the radio frequency wave used. We calculate the expected ORI signal using 15 fs pulses and 87° of pulse-front tilt, collected using f /2 optics, and find a two-point resolution of 275 nm using 800 nm light that satisfies the Rayleigh criterion. We also derive a general equation for resolution in optical resonance imaging that indicates that there is a possibility of superresolution imaging using this technique. The photon echo sequence also enables spectroscopic determination of the input and output energy. The technique thus correlates the input energy with the final position and energy of the exciton.
Scanning probe microscopy and gradient imaging are two techniques for imaging at sub-wavelength spatial resolution. Gradient imaging in the form of magnetic resonance imaging (MRI) has so far been demonstrated only in the radio- and microwave frequency domains [1]. An extension of MRI to optical frequencies for imaging (semi-) transparent objects is of interest because an optical photon detection process is inherently more sensitive than magnetic induction detection, potentially leading to increased spatial resolution. Rare-earth ions incorporated into a crystalline host are promising as a prototype system for demonstration of high spatial resolution OMRI.
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.
This thesis presents a novel magnetic resonance imaging (MRI) technique for spinor Bose-Einstein condensates (BEC) with the paramagnetic Faraday effect. This quantum-photon interface couples the spin of the BEC to the polarisation of an off-resonant laser, which in a magnetic field gradient allows a 1D density profile of the BEC to be reconstructed. As opposed to conventional imaging techniques that are destructive or diffraction limited, this technique is minimally destructive to the BEC and not diffraction limited. Multishot in situ imaging of a single condensate is therefore possible, paving the way for time-resolved studies and 2D/3D reconstructions. A theoretical model for Faraday imaging is developed using the tensor polarisability formalism for the atom-light interaction, and the signal-to-noise ratio is derived. Resolution limits induced by Stern-Gerlach separation are considered, encouraging rapid measurements with strong magnetic field gradients. Analysing the trapping potential reveals that the `magic-zero' wavelength 790nm produces no dipole force and enables a tightly focused probe laser to be used without perturbing the trap. Polarisation-maintaining fibers were seen to impart large fluctuations depending on the incident polarisation, which were minimised. The broad diode laser emission background is seen to reduce the lifetime of the BEC, which was corrected with an interference filter. Short-time Fourier transforms are used to process the photodetected signal, showing the evolution of the polarisation rotation frequency and amplitude. Frequency-modulation is observed at the power line frequency, corresponding to magnetic field fluctuations induced by nearby equipment. Birefringence of optical elements results in elliptical polarisation of the probe and an effective magnetic field, which is cancelled using a quarter-waveplate. The quadratic Zeeman effect causes rapid amplitude modulation, and is eliminated by applying a microwave dressing field. Radiative spin echo is achieved in a magnetic field gradient, proving that dephasing is coherent, and that multishot imaging possible. Magnetic resonance imaging (MRI) is performed on a partially-evaporated atom cloud, distinguishing the thermal and condensed fractions. A split dipole trap is used to create two spatially separated BECs, which are individually resolved during MRI. The resolution is only limited by the strength of the applied magnetic field gradient, and is not subject to the diffraction limit. Custom coils will enable MRI of condensates at the sub-micron scale.
We present a theoretical study of optical magnetic-resonance imaging (OMRI), an extension of magnetic-resonance imaging to the optical frequency domain. OMRI images the spatial distribution of centers with field-dependent optical transitions by projection reconstruction from multiple tomographic scans. Spatial resolution is limited by magnetic-field gradient strengths and transition linewidths. These restrict the choice of systems accessible to OMRI, and rare-earth ions are identified as possible candidates. High-resolution laser spectroscopic techniques that overcome the effect of inhomogeneous broadening of electronic transitions are discussed. OMRI by transient hole-burning spectroscopy is presented as one approach for subwavelength spatial imaging, and its sensitivity is calculated. Submicrometer spatial resolution is possible by employing very-high-field gradients (>10 T/cm) and centers exhibiting megahertz linewidths.
Abstract Magnetic resonance imaging is a three-dimensional imaging technique, where a gradient of the magnetic field is used to interrogate spin resonances with spatial resolution. The application of this technique to probe the coherence of atoms with good three-dimensional resolution is a challenging application. We propose and demonstrate an optical method to probe spin resonances via a two-photon Raman transition, reconstructing the 3D-structure of an atomic ensemble’s coherence, which is itself subject to external fields. Our method relies on a single time-and-space resolved heterodyne measurement, allowing the reconstruction of a complex 3D coherence profile. Owing to the optical interface, we reach a tomographic image resolution of 14 × 14 × 36 μm3. The technique allows to probe any transparent medium with a resonance structure and provides a robust diagnostic tool for atom-based quantum information protocols. As such, it is a viable technique for application to magnetometry, electrometry, and imaging of electromagnetic fields.
The resolution of optical imaging devices is ultimately limited by the diffraction of light. To circumvent this limit, modern superresolution microscopy techniques employ active interaction with the object by exploiting its optical nonlinearities, nonclassical properties of the illumination beam, or near field probing. Thus, they are not applicable whenever such interaction is not possible, for example, in astronomy or noninvasive biological imaging. Far field, linear optical superresolution techniques based on passive analysis of light coming from the object would cover these gaps. In this Letter, we present the first proof-of-principle demonstration of such a technique for 2D imaging. It works by accessing information about spatial correlations of the image optical field and, hence, about the object itself via measuring projections onto Hermite-Gaussian transverse spatial modes. With a basis of 21 spatial modes in both transverse dimensions, we perform two-dimensional imaging with twofold resolution enhancement beyond the diffraction limit.