热光关联空间滤波与亚波长干涉
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摘要
关联成像与关联干涉首先在量子纠缠系统中实现的。然而近期一系列的研究证明,热光也可以实现关联成像和关联干涉。这打破了纠缠光源的局限性,同时也引发了热光关联成像的量子本质与经典本质之争。热光的光联干涉和关联成像逐渐成为研究的热点课题之一。本文在热光关联干涉实验中提出关联滤波的思想,用以提高关联干涉条纹的可见度。我们设计非相干双光子干涉仪,能够在双光子强度测量中获得亚波长干涉条纹。
可见度是衡量关联像的一个重要依据,实验中获得的像可见度越大,关联图像就越清晰,越能反应物体的细节,我们也就可以获得物体更多的信息。本文通过对关联干涉的研究,理论分析了影响关联干涉的一个重要因素——关联通光面积,并发现光场强度与关联通光面积成正比关系。我们根据理论分析的结果,利用空间关联滤波原理,在与双缝相对称位置的光路中放置光阑,适当减小光阑尺寸的大小,就可以获得较为理想可见度的关联干涉条纹。
纠缠双光子的亚波长干涉实验是量子纠缠超越经典瑞利分辨极限的验证,表明量子刻录的可行性。而热光源的亚波长干涉实验中,亚波长干涉条纹发生在相互关联光子处于相对的位置,不能实现量子刻录。因此研究一种不依赖于光束重合准直的亚波长干涉,将为热光量子刻录的开发应用奠定基础。本文中我们设计了一种非相干干涉仪,将相互关联的两路光波之一的波前反转,然后使二者传输到同一平面,在探测平面上进行(x,x)扫描获得亚波长干涉条纹。我们的研究进一步发现,本方案的亚波长干涉图样并不依赖于两关联光束的准直和重合情况。如果将两光束的中心偏移,仍然可以得到较为理想的亚波长干涉条纹,并且亚波长干涉条纹的中心与两光束的对称中心重合。由于并不需要严格的准直,我们的实验装置能够适应于并不苛刻的实验条件。
Correlated imaging and correlated interference were first realized with quantum entangled system. However, the recent studies showed that the thermal light sources can also realize correlated imaging and correlated interference, and thus brake the limitation of quantum entangled source. The inquiry that correlated imaging concerns quantum entanglement or classical correlation was evoked. From that on, correlated interference and correlated imaging became a hot topic. We propose the idea of correlated filtering in the correlated interference experiment in this thesis. Correlated filtering can increase the visibility degree of the correlated interference fringes. We design an incoherent two-photon interferometer to obtain sub-wavelength interference fringes by two-photon intensity measurement.
Visibility is one of the important quality parameter for optical imaging. If the visibility of the correlated images in the experiment becomes larger, the correlated images become clearer, and more details of the objects can be reflected, we finally can find more information of the objects. We theoretically analyze an important factor, the correlated area of the light beam, in correlated imaging and correlated interference experiment. We find that the field intensity is proportional to the correlated area of the light beam. Following with the theoretical analysis and correlated filtering, we insert an optical diagraph into the empty arm, in accordance with the symmetrical position of the object. By diminishing the size of the optical diagraph, we can obtain the correlated interference fringes with good visibility.
Sub-wavelength interference experiment with entangled two-photons verified quantu-m lithography, which can surpass the classical diffraction limit. The sub-wavelength interference with thermal light, which occurs at symmetrical positions, can not be used in quantum lithography. In the thesis we design an incoherent interferometer to obtain the sub-wavelength interference fringes by two-photon intensity measurement at the same position. In the interferometer, the field wave front in the input plane is inverted in one arm to the output plane. We also find in the sub-wavelength interference experiment that the sub-wavelength interference fringes are independent of the alignment and super-position of the two correlated beams. If the centers of the two beams are not overlapped, we can still obtain the sub-wavelength interference fringes. The center of the fringes is positioned at the center of the two beams. Therefore, our experiment design can fit for rough conditions.
可见度是衡量关联像的一个重要依据,实验中获得的像可见度越大,关联图像就越清晰,越能反应物体的细节,我们也就可以获得物体更多的信息。本文通过对关联干涉的研究,理论分析了影响关联干涉的一个重要因素——关联通光面积,并发现光场强度与关联通光面积成正比关系。我们根据理论分析的结果,利用空间关联滤波原理,在与双缝相对称位置的光路中放置光阑,适当减小光阑尺寸的大小,就可以获得较为理想可见度的关联干涉条纹。
纠缠双光子的亚波长干涉实验是量子纠缠超越经典瑞利分辨极限的验证,表明量子刻录的可行性。而热光源的亚波长干涉实验中,亚波长干涉条纹发生在相互关联光子处于相对的位置,不能实现量子刻录。因此研究一种不依赖于光束重合准直的亚波长干涉,将为热光量子刻录的开发应用奠定基础。本文中我们设计了一种非相干干涉仪,将相互关联的两路光波之一的波前反转,然后使二者传输到同一平面,在探测平面上进行(x,x)扫描获得亚波长干涉条纹。我们的研究进一步发现,本方案的亚波长干涉图样并不依赖于两关联光束的准直和重合情况。如果将两光束的中心偏移,仍然可以得到较为理想的亚波长干涉条纹,并且亚波长干涉条纹的中心与两光束的对称中心重合。由于并不需要严格的准直,我们的实验装置能够适应于并不苛刻的实验条件。
Correlated imaging and correlated interference were first realized with quantum entangled system. However, the recent studies showed that the thermal light sources can also realize correlated imaging and correlated interference, and thus brake the limitation of quantum entangled source. The inquiry that correlated imaging concerns quantum entanglement or classical correlation was evoked. From that on, correlated interference and correlated imaging became a hot topic. We propose the idea of correlated filtering in the correlated interference experiment in this thesis. Correlated filtering can increase the visibility degree of the correlated interference fringes. We design an incoherent two-photon interferometer to obtain sub-wavelength interference fringes by two-photon intensity measurement.
Visibility is one of the important quality parameter for optical imaging. If the visibility of the correlated images in the experiment becomes larger, the correlated images become clearer, and more details of the objects can be reflected, we finally can find more information of the objects. We theoretically analyze an important factor, the correlated area of the light beam, in correlated imaging and correlated interference experiment. We find that the field intensity is proportional to the correlated area of the light beam. Following with the theoretical analysis and correlated filtering, we insert an optical diagraph into the empty arm, in accordance with the symmetrical position of the object. By diminishing the size of the optical diagraph, we can obtain the correlated interference fringes with good visibility.
Sub-wavelength interference experiment with entangled two-photons verified quantu-m lithography, which can surpass the classical diffraction limit. The sub-wavelength interference with thermal light, which occurs at symmetrical positions, can not be used in quantum lithography. In the thesis we design an incoherent interferometer to obtain the sub-wavelength interference fringes by two-photon intensity measurement at the same position. In the interferometer, the field wave front in the input plane is inverted in one arm to the output plane. We also find in the sub-wavelength interference experiment that the sub-wavelength interference fringes are independent of the alignment and super-position of the two correlated beams. If the centers of the two beams are not overlapped, we can still obtain the sub-wavelength interference fringes. The center of the fringes is positioned at the center of the two beams. Therefore, our experiment design can fit for rough conditions.
引文
[1]A. Einstein, B. Podolsky, and N. Rosen, "Can Quantum-Mechanical Discription of Physical Reality Be Considered Complete?" [J], Phys. Rev.,47,777 (1935).
[2]B. R. Brown, and R. Q. Twiss, "Correlation between photons in two coherent beans of light" [J], Nature,177,27(1956).
[3]B. R. Brown, and R. Q. Twiss, "A test of a new type of stellar interferometer on Sirius" [J], Nature,178,1046, (1956).
[4]T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko. "Optical imaging by means of two-photon quantum entanglement" [J], Phys. Rev. A,52, R3429 (1995).
[5]M. D'Angelo, M. V. Chekhova, Y. H. Shih, Phys. Rev. Lett.,87,013602 (2001).
[6]A. F. Abouraddy, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, "Role of entanglement in two-photon imaging", Phys. Rev. Lett.,87,123602 (2001).
[7]R. S. Bennink, S. J. Bentley, and R. W. Boyd, "Two-Photon Coincidence Imaging with a Classical Source" [J], Phys. Rev. Lett.,89,113601(2002).
[8]D. Zh. Cao and K. G. Wang, "Sub-wavelength interference in macroscopic observation" [J], Phys. Lett. A,333,23 (2004).
[9]R. S. Bennink, S. J. Bentley, R. W. Boyd, and J. C. Howell, "Quantum and Classical Coincidence Imaging" [J]. Phys. Rev. Lett.,92,033601(2004).
[10]M. D. Angelo, Y. H. Kim, S. P. Kulik, and Y. H. Shih, "Identifying Entanglement Using Quantum Ghost Interference and Imaging" [J], Phys. Rev. Lett.,92,233601 (2004).
[11]J. C. Howell, R. S. Bennink, S. J. Bentley and R. W. Boyd, "Realization of the Einstein-Podolsky-Rosen Paradox Using Momentum and Position Entangled Photons from Spontaneous Parametric Down Conversion" [J], Phys. Rev. Lett.,92,210403 (2004).
[12]J. Cheng and S. Han, "Incoherent Coincidence Imaging and Its Applicability in X-ray Diffraction" [J], Phys. Rev. Lett.,92,093903 (2004).
[13]A. Valencia, G. Scarcelli, M. D'Angelo, and Y. H. Shih, Arxiv:quant-ph/0408001.
[14]A. Gatti, E. Brambilla, M. Bache and L. A. Lugiato, "Ghost imaging with thermal light comparing entanglement and classical correlation " [J], Phys. Rev. Lett.93,093602 (2004).
[15]A. Gatti, E. Brambilla, M. Bache and L. A. Lugiato, "Correlated imaging, quantum and classical" [J], Phys. Rev. A.70,013802 (2004).
[16]Y. Cai, and S. Zhu, "Ghost interference with partially coherent radiation" [J], Opt. Lett.,29,2716 (2004).
[17]M.O. Scully, M. S. Zubairy, Quantum Optics [M], Cambridge University press,1997.
[18]D. Zhang, X. H. Chen, Y. H. Zhai, and L. A. Wu, "Correlated two-photon imaging with true thermal light" [J], Arxiv:quant-ph/0503122.
[19]翟艳华,热光的双光子特性[M],博士学位论文,北京：中国科学院研究生院,2007.
[20]A. Valencia, G. Scarcelli, M. D'Angelo, and Y. H. Shih, Phys. Rev. Lett.,94,063601 (2005).
[21]姚启钧,光学教程(第二版)[M],北京：高等教育出版社,1989.
[22]T. B. Pittman, D. V. Strekalov, A. Migdall, M. H. Rubin, A. V. Sergienko, and Y. H. Shih, "Can Two-Photon Interference be Considered the Interference of Two Photons?" [J]. Phys. Rev. Lett.,77,1917-1920 (1996).
[23]M. D'Angelo, A. Valencia, M. H. Rubin, and Y. H. Shih, "Resolution of quantum and classical ghost imaging" [J], Phys. Rev. A,72,013810 (2005).
[24}E. K. Tan, J. Jeffers, S. M. Barnett and D. T. Pegg, "Retrodictive states and two-photon quantum imaging" [J], Arxiv:quant-ph/0303099.
[25]彭金生,李高翔.近代量子光学导论[M].北京：科学出版社,148,1996.
[26]K. Wang and D. Z. Cao, "Sub-wavelength coincidence interference with classical thermal light, " Phys. Rev. A,70,041801R (2004).
[27]D. V. Strekalov, A. V. Sergienko,. D. N. Klyshko, and Y. H. Shih, "Obervation of two-Photon "ghost" interference and diffraction" [J], Phys. Rev. Lett.,74,3600 (1995).
[28]J. W. Goodman, Statistical Optics[M], Wiley, New York,1985.
[29]J. Jacobson, G. Bjork, I. Chuang, Y. Yamamoto, Phys. Rev. Lett.,74,4835 (1995).
[30]E. J. S. Fonseca, C. H. Monken, S. Padua, Phys. Rev. Lett.,82,2868(1999).
[31]A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, J. Pbowling, Phys. Rev. Lett.85,2733 (2000).
[32]M. Zhang, Q. Wei, X. Shen, Y. Liu, H. Liu, J. Cheng, and S. Han, Phys. Rev. A,75, 021803R (2007).
[2]B. R. Brown, and R. Q. Twiss, "Correlation between photons in two coherent beans of light" [J], Nature,177,27(1956).
[3]B. R. Brown, and R. Q. Twiss, "A test of a new type of stellar interferometer on Sirius" [J], Nature,178,1046, (1956).
[4]T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko. "Optical imaging by means of two-photon quantum entanglement" [J], Phys. Rev. A,52, R3429 (1995).
[5]M. D'Angelo, M. V. Chekhova, Y. H. Shih, Phys. Rev. Lett.,87,013602 (2001).
[6]A. F. Abouraddy, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, "Role of entanglement in two-photon imaging", Phys. Rev. Lett.,87,123602 (2001).
[7]R. S. Bennink, S. J. Bentley, and R. W. Boyd, "Two-Photon Coincidence Imaging with a Classical Source" [J], Phys. Rev. Lett.,89,113601(2002).
[8]D. Zh. Cao and K. G. Wang, "Sub-wavelength interference in macroscopic observation" [J], Phys. Lett. A,333,23 (2004).
[9]R. S. Bennink, S. J. Bentley, R. W. Boyd, and J. C. Howell, "Quantum and Classical Coincidence Imaging" [J]. Phys. Rev. Lett.,92,033601(2004).
[10]M. D. Angelo, Y. H. Kim, S. P. Kulik, and Y. H. Shih, "Identifying Entanglement Using Quantum Ghost Interference and Imaging" [J], Phys. Rev. Lett.,92,233601 (2004).
[11]J. C. Howell, R. S. Bennink, S. J. Bentley and R. W. Boyd, "Realization of the Einstein-Podolsky-Rosen Paradox Using Momentum and Position Entangled Photons from Spontaneous Parametric Down Conversion" [J], Phys. Rev. Lett.,92,210403 (2004).
[12]J. Cheng and S. Han, "Incoherent Coincidence Imaging and Its Applicability in X-ray Diffraction" [J], Phys. Rev. Lett.,92,093903 (2004).
[13]A. Valencia, G. Scarcelli, M. D'Angelo, and Y. H. Shih, Arxiv:quant-ph/0408001.
[14]A. Gatti, E. Brambilla, M. Bache and L. A. Lugiato, "Ghost imaging with thermal light comparing entanglement and classical correlation " [J], Phys. Rev. Lett.93,093602 (2004).
[15]A. Gatti, E. Brambilla, M. Bache and L. A. Lugiato, "Correlated imaging, quantum and classical" [J], Phys. Rev. A.70,013802 (2004).
[16]Y. Cai, and S. Zhu, "Ghost interference with partially coherent radiation" [J], Opt. Lett.,29,2716 (2004).
[17]M.O. Scully, M. S. Zubairy, Quantum Optics [M], Cambridge University press,1997.
[18]D. Zhang, X. H. Chen, Y. H. Zhai, and L. A. Wu, "Correlated two-photon imaging with true thermal light" [J], Arxiv:quant-ph/0503122.
[19]翟艳华,热光的双光子特性[M],博士学位论文,北京：中国科学院研究生院,2007.
[20]A. Valencia, G. Scarcelli, M. D'Angelo, and Y. H. Shih, Phys. Rev. Lett.,94,063601 (2005).
[21]姚启钧,光学教程(第二版)[M],北京：高等教育出版社,1989.
[22]T. B. Pittman, D. V. Strekalov, A. Migdall, M. H. Rubin, A. V. Sergienko, and Y. H. Shih, "Can Two-Photon Interference be Considered the Interference of Two Photons?" [J]. Phys. Rev. Lett.,77,1917-1920 (1996).
[23]M. D'Angelo, A. Valencia, M. H. Rubin, and Y. H. Shih, "Resolution of quantum and classical ghost imaging" [J], Phys. Rev. A,72,013810 (2005).
[24}E. K. Tan, J. Jeffers, S. M. Barnett and D. T. Pegg, "Retrodictive states and two-photon quantum imaging" [J], Arxiv:quant-ph/0303099.
[25]彭金生,李高翔.近代量子光学导论[M].北京：科学出版社,148,1996.
[26]K. Wang and D. Z. Cao, "Sub-wavelength coincidence interference with classical thermal light, " Phys. Rev. A,70,041801R (2004).
[27]D. V. Strekalov, A. V. Sergienko,. D. N. Klyshko, and Y. H. Shih, "Obervation of two-Photon "ghost" interference and diffraction" [J], Phys. Rev. Lett.,74,3600 (1995).
[28]J. W. Goodman, Statistical Optics[M], Wiley, New York,1985.
[29]J. Jacobson, G. Bjork, I. Chuang, Y. Yamamoto, Phys. Rev. Lett.,74,4835 (1995).
[30]E. J. S. Fonseca, C. H. Monken, S. Padua, Phys. Rev. Lett.,82,2868(1999).
[31]A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, J. Pbowling, Phys. Rev. Lett.85,2733 (2000).
[32]M. Zhang, Q. Wei, X. Shen, Y. Liu, H. Liu, J. Cheng, and S. Han, Phys. Rev. A,75, 021803R (2007).