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Applied Physics Letters

Direct measurement of sub-wavelength interference using thermal light and photon-number-resolved detection

Yanhua Zhai, F. E. Becerra, Jingyun Fan, Alan L. Migdall

Published Sep 8, 2014• 12 citations
Publisher

Abstract

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.

DOI
10.1063/1.4895101

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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.
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.
Abstract A method for correlating thermal light over a wide spectral range is proposed. A multi-wavelength pseudothermal source, prepared by projecting laser beams of multiple wavelengths (650 nm, 635 nm, 532 nm, and 473 nm) onto a moving thin ground glass plate, is employed in a double-slit interference experiment. The ground glass plate induces random phase differences between light beams of different wavelengths passing through it. This initial random phase difference significantly influences the high-order intensity correlation functions of multi-wavelength thermal beams. Experimentally, second-order correlated interference patterns, including subwavelength interference, of pseudothermal beams with different wavelengths are observed in the intensity correlation measurements. This method facilitates applications of correlated thermal photons in quantum information processing and quantum imaging.
The high-order intensity correlation function of NNN-photon interference with thermal light observed in a recent experiment [S. Oppel, T. B\"uttner, P. Kok, and J. von Zanthier, Phys. Rev. Lett. 109, 233603 (2012)] is analyzed. The terms in the expansion of the NthN\mathrm{th}Nth-order correlation function are put into three groups. One group contributes a homogeneous background. Both of the other two contribute $(N\ensuremath{-}1)$-fold super-resolving fringes. In principle they correspond to coherent and incoherent superpositions of classical optical fields, respectively. Therefore similar super-resolving fringes can be obtained without intensity-correlation measurements. We report the experimental results of the coherent and incoherent super-resolving diffraction fringes, which are observed directly in the intensity distribution. The $N\ensuremath{-}1$ sources in both the coherent and incoherent cases are set in certain definite positions. In the coherent case, moreover, the phase difference between two adjacent source fields is $\ensuremath{\pi}$. The fringe visibility is unity in the incoherent case, while it decreases as NNN increases in the incoherent case.
In this paper, we report an interference experiment in which a spatially incoherent light source illuminates two spatially separated apertures, whose superposition at the same place forms a double-slit. The experimental result exhibits a well-defined interference fringe solely through intensity measurements, in agreement with the theoretical analysis by means of the first-order spatial interference of the incoherent light. Consequently, the nonlocal double-slit interference with thermal light should be attributed to the first-order spatial correlation of incoherent field.