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arXiv:1306.0276 · Scientific Reports

Super sub-wavelength patterns in photon coincidence detection

Ruifeng Liu, Pei Zhang, Yu Zhou, Hong Gao, Fuli Li

Published Feb 17, 2014• 11 citations

Abstract

High-precision measurements implemented with light are desired in all fields of science. However, light acts as a wave, and the Rayleigh criterion in classical optics yields a diffraction limit that prevents obtaining a resolution smaller than the wavelength. Sub-wavelength interference has potential application in lithography because it beats the classical Rayleigh resolution limit. Here, we carefully study second-order correlation theory to establish the physics behind sub-wavelength interference in photon coincidence detection. A Young's double slit experiment with pseudo-thermal light is performed to test the second-order correlation pattern. The results show that when two point detectors are scanned in different ways, super sub-wavelength interference patterns can be obtained. We then provide a theoretical explanation for this surprising result, and demonstrate that this explanation is also suitable for the results found for entangled light. Furthermore, we discuss the limitations of these types of super sub-wavelength interference patterns in quantum lithography.

DOI: 10.1038/srep04068

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High-precision measurements implemented with light are desired in all fields of science. However, light acts as a wave, and the Rayleigh criterion in classical optics yields a diffraction limit that prevents obtaining a resolution smaller than the wavelength. Sub-wavelength interference has potential application in lithography because it beats the classical Rayleigh resolution limit. Here, we carefully study second-order correlation theory to establish the physics behind sub-wavelength interference in photon coincidence detection. A Young's double slit experiment with pseudo-thermal light is performed to test the second-order correlation pattern. The results show that when two point detectors are scanned in different ways, super sub-wavelength interference patterns can be obtained. We then provide a theoretical explanation for this surprising result, and demonstrate that this explanation is also suitable for the results found for entangled light. Furthermore, we discuss the limitations of these types of super sub-wavelength interference patterns in quantum lithography.

In classical optics, Young's double-slit experiment with colored coherent light gives rise to individual interference fringes for each light frequency, referring to single-photon interference. However, two-photon double-slit interference has been widely studied only for wavelength-degenerate biphoton, known as subwavelength quantum lithography. In this work, we report double-slit interference experiments with two-color biphoton. Different from the degenerate case, the experimental results depend on the measurement methods. From a two-axis coincidence measurement pattern we can extract complete interference information about two colors. The conceptual model provides an intuitional picture of the in-phase and out-of-phase photon correlations and a complete quantum understanding about the which-path information of two colored photons.

Classically, the spatial resolution of the image of an object is usually determined by the Rayleigh criterion. However, quantum properties of light have been exploited to form images with resolutions exceeding this criterion and beating the standard quantum limit, which allow high measurement sensitivity. We found that it is possible to super-resolve a distributed object made of two parts that are spatially separated but when superposed over each other form an object. A coincidence interference pattern of a nonlocal two-photon system with periodicity proportional to $\ensuremath{\lambda}/2$ was measured even when each photon, with wavelength of $\ensuremath{\lambda}$, has been scattered by different parts of an object, none of them being the object itself.

The resolution of optical interference is ultimately limited by the wavelength of light, which is known as Rayleigh criterion. Interestingly, this limitation could be surpassed by considering photonic de Broglie wave, and the resulting subwavelength interference is useful for lithography and super-resolving phase measurementsuper-resolving phase measurement. Usually, quantum entangled state is necessary to realize photonic de Broglie wave. Recent advances show that subwavelength interference could also be realized with a classical light through post-selected operation or by considering light-matter interaction. In this work, a new classical source is designed to achieve subwavelength interference without any post-selected operation in a linear scheme.

We examine thermal light diffracted through a double slit using photon-number-resolved detection to directly measure high-order spatial correlations, and we see sinusoidal modulations of those correlations. The fringe width can, in principal, be made arbitrarily small, and we have experimentally obtained fringe widths as small as 30 nm with 800 nm wavelength light. This extreme sub-wavelength resolution, along with this direct detection technique, offers potential for high precision measurement applications.

We propose an incoherent interferometer which can partly modify the spatial correlation property of thermal light. Applying the interferometer to the two-photon double-slit interference with thermal light, we find that the subwavelength interference patterns appear in the intensity correlation not only between two same polarized photons at different positions but also between two orthogonally polarized photons at the same position. The latter can correspond to the two-photon double-slit interference using a two-photon entangled source. Our experimental result suggests that a thermal light source is capable of accomplishing subwavelength lithography technique to surpass the Rayleigh resolution limit.