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Scientific Reports

Flexible Two-Photon Interference Fringes with Thermal Light

De-Zhong Cao, Cheng Ren, Jin-Yang Ni, Yan Zhang, Su-Heng Zhang, Kaige Wang

Published May 9, 2017• 3 citations
Publisher

Abstract

Flexible interference patterning is an important tool for adaptable measurement precisions. We report on experimental results of controllable two-photon interference fringes with thermal light in an incoherent rotational shearing interferometer. The two incoherent beams in the interferometer are orthogonally polarized, and their wavefront distributions differ only in an angle of rotation. The spacings and directions of the two-photon interference fringes vary with the rotation angle, as illustrated in three cases of two-photon correlation measurements in experiment.

DOI
10.1038/s41598-017-02119-y

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Flexible interference patterning is an important tool for adaptable measurement precisions. We report on experimental results of controllable two-photon interference fringes with thermal light in an incoherent rotational shearing interferometer. The two incoherent beams in the interferometer are orthogonally polarized, and their wavefront distributions differ only in an angle of rotation. The spacings and directions of the two-photon interference fringes vary with the rotation angle, as illustrated in three cases of two-photon correlation measurements in experiment.
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.
The interferometer is one of the most important devices for revealing the nature of light and for precision optical metrology. Although many experiments were performed for probing photon behavior in various configurations, a complete study of photon behavior in a birefringent interferometer has not been performed, to our knowledge. By using an environmental turbulence immune Mach-Zehnder interferometer, we observe tunable photonic beatings by rotating a birefringent crystal versus the temperature of the crystal for both the single photon and two photons. Furthermore, the two-photon interference fringes beat 2 times faster than the single-photon interference fringes. This beating effect is used to determine the thermal dispersion coefficients of the two principal refractive axes with a single measurement: the two-photon interference shows superresolution and high sensitivity. Obvious differences between two-photon and single-photon interference are also revealed in unbalanced situations. In addition, the influence of the photon bandwidth on the beating behaviors that come from polarization-dependent decoherence is also investigated. Our findings will be important for better understanding the behavior of two-photon interference in a birefringent interferometer and for precision optical metrology with quantum enhancement.
We propose an experimental scheme in which two orthogonally polarized thermal light beams with antisymmetrical wavefronts are overlapped. The experimental results demonstrate that this setup can focus the beam in two-photon and multiphoton correlation measurements. The focused ``two-photon'' spot possesses subwavelength resolution, surpassing the classical diffraction limit. Since the experimental setup consists of only two right-angle-mirror devices without the help of lenses, the two-photon focusing effect does not apparently rely on the beam focusing. Physically, the phenomenon signifies that the photon bunching can be localized within a very small region through two-photon interference in contrast to the conventional Hanbury Brown--Twiss effect of thermal light. In the higher-order intensity correlation measurement, the multiphoton bunching can be limited within a very small central region while the background is greatly suppressed.
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.
The distinguishing of the multiphoton quantum interference effect from the classical one forms one of the most important issues in modern quantum mechanics and experimental quantum optics. For a long time, the two-photon interference (TPI) of correlated photons has been recognized as a pure quantum effect that cannot be simulated with classical lights. In the meantime, experiments have been carried out to investigate the classical analogues of the TPI. In this study, we conduct TPI experiments with uncorrelated photons with different center frequencies from a luminescent light source, and we compare our results with the previous ones of correlated photons. The observed TPI fringe can be expressed in the form of three phase terms related to the individual single-photon and two-photon states, and the fringe pattern is strongly affected by the two single-photon-interference fringes and also by their visibilities. With the exception of essential differences such as valid and accidental coincidence events within a given resolving time and the two-photon spectral bandwidth, the interference phenomenon itself exhibits the same features for both correlated and uncorrelated photons in the single-photon counting regime.