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arXiv:quant-ph/0404078

Coincidence Subwavelength Interference by a Classical Thermal Light

Kaige Wang, De-Zhong Cao

Published Apr 13, 2004• 3 citations
arXivHTMLPDF

Abstract

We show that a thermal light random in transverse direction can perform subwavelength double slit interference in a joint-intensity measurement. This is the classical version of quantum lithography, and it can be explained with the correlation of rays instead of the entanglement of photons.
DOI
10.48550/arxiv.quant-ph/0404078

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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.
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.
We propose a two-photon subwavelength interference scheme for classical light in which multiple quantum-like entangled two-photon paths play an essential role. These entangled two-photon paths are introduced through a specially designed source composed of many point sources jjj with jjj's complex amplitude being a superposition of modes ${e}^{i{\ensuremath{\phi}}_{j}}$ and ${e}^{i{\ensuremath{\phi}}_{j}^{(1)}}$, where ${\ensuremath{\phi}}_{j}$ and ${\ensuremath{\phi}}_{j}^{(1)}$ are temporally random phases but satisfying ${\ensuremath{\phi}}_{j}+{\ensuremath{\phi}}_{j}^{(1)}={\ensuremath{\phi}}_{0}$, with ${\ensuremath{\phi}}_{0}$ being either a constant or a random phase in time. Interference between the entangled two-photon paths could lead to second-order subwavelength interference of an object put in front of the source plane. In a proof-of-principle experiment, by using a spatial light modulator to modulate the wave front of a coherent light, we have generated such a source and observed subwavelength interference of a double-slit mask via two-photon measurement.