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Journal of International Crisis and Risk Communication Research

Entangled Photon Pairs in Disordered Photonic Lattices

Lane Martin

Published Jan 1, 2014• 0 citations
OpenAlex

Abstract

Photonic lattices consisting of arrays of evanescently coupled waveguides fabricated with precisely controlled parameters have enabled the study of discrete optical phenomena, both classical and quantum, and the simulation of other physical phenomena governed by the same dynamics. In this dissertation, I have experimentally demonstrated transverse Anderson localization of classical light in arrays with off-diagonal coupling disorder and investigated theoretically and experimentally the propagation of entangled photon pairs through such disordered systems. I discovered a new phenomenon, Anderson co-localization, in which a spatially entangled photon pair in a correlated transversally extended state localizes in the correlation space, though neither photon localizes on its own. When the photons of a pair are in an anti-correlated state, they maintain their anti-correlation upon transmission through the disordered lattice, exhibiting Anderson anti-localization. These states were generated by use of parametric down conversion in a nonlinear crystal. The transition between the correlated and anti-correlated states was also explored by using a lens system in a configuration intermediate between imaging and Fourier transforming. In the course of this research, I discovered a curious aspect of light transmission through such disordered discrete lattices. An excitation wave of a single spatial frequency (transverse momentum) is transmitted through the system and is accompanied by another wave with the same spatial frequency but opposite sign, indicating some form of internal reflection facilitated by the disordered structure.

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Photonic lattices consisting of arrays of evanescently coupled waveguides fabricated with precisely controlled parameters have enabled the study of discrete optical phenomena, both classical and quantum, and the simulation of other physical phenomena governed by the same dynamics. In this dissertation, I have experimentally demonstrated transverse Anderson localization of classical light in arrays with off-diagonal coupling disorder and investigated theoretically and experimentally the propagation of entangled photon pairs through such disordered systems. I discovered a new phenomenon, Anderson co-localization, in which a spatially entangled photon pair in a correlated transversally extended state localizes in the correlation space, though neither photon localizes on its own. When the photons of a pair are in an anti-correlated state, they maintain their anti-correlation upon transmission through the disordered lattice, exhibiting Anderson anti-localization. These states were generated by use of parametric down conversion in a nonlinear crystal. The transition between the correlated and anti-correlated states was also explored by using a lens system in a configuration intermediate between imaging and Fourier transforming. In the course of this research, I discovered a curious aspect of light transmission through such disordered discrete lattices. An excitation wave of a single spatial frequency (transverse momentum) is transmitted through the system and is accompanied by another wave with the same spatial frequency but opposite sign, indicating some form of internal reflection facilitated by the disordered structure.
We explore the propagation of light in a two-photon state in disordered optical systems that induce Anderson localization. We show that entangled-photon pairs demonstrate a surprising behavior that we call Anderson colocalization: While neither photon exhibits Anderson localization, the spatial correlations of the pair remain intact. Furthermore, we show that entangled-photon pairs colocalize faster than classical light localizes in the same system. We also explore the propagation of anticorrelated and partially entangled photon pairs in such systems. The results are developed using a linear systems theory that extends the scope of quantum imaging to incorporate disordered systems.
We report on our latest findings on photonic Quantum Walks (QW) of entangled particles in several quantum transport regimes as for instance in photonic Bloch lattices or disordered lattices. Furthermore, the discrete fractional Fourier transform of quantum states is presented in the context of QWs. The propagation of a classical single walker on a random graph is an important field in statistics and can be applied on many domains in nature reaching from a foraging animals over Brownian molecular motion towards the evolution of lead changes in competitive team sports. Its quantum mechanical counterpart, the Quantum Walk (QW), features genuine quantum objects to walk on a random graph and hence, leading to non-classical quantum interference, in particular when considering two or more walkers. Their great potential lies i.a. in their ability to exponentially speed up a multitude of algorithms, as for instance the data bank search algorithm from L. Grover. In this regard, photonic lattices of evanescently coupled waveguides represent an ideal platform to study QW dynamics, since they feature advantages in stability, robustness and miniaturization. Our waveguide lattices were fabricated by means the direct laser inscription technique. In doing so, three dimensional waveguide geometries are realizable, enabling the implementation of various QW graphs. Along these lines, we study QWs of entangled photon pairs in disordered lattices. There we observe Anderson co-localization, meaning that neither the individual photons nor the pair localizes, rather their distance does. It turns out that both photons tend to bunch as they will be found together in the same lattice site, implying that their original correlation remains while performing a QW in a disordered lattice. Further, we investigate QWs of non-local two-photon EPR-states in Bloch-lattices. The experimental results reveal the strong dependence of the correlation output statistics (bosonic-, anyonicor fermionic-like) on the input states' symmetry. Finally, the discrete fractional Fourier transform of quantum states is realized through a discrete QW lattice. The results demonstrate the enormous potential of waveguide lattices in the field of quantum photonics and give rise to further investigations like the Fourier suppression law.
∗ both authors contributed equally Quantum entanglement, the non-separability of a multipartite wave function, became essential in understanding the non-locality of quantum mechanics. In optics, this non-locality can be demon-strated on impressively large length scales, as photons travel with the speed of light and interact only weakly with their environment. With the discovery of spontaneous parametric down-conversion (SPDC) in nonlinear crystals, an efficient source for entangled photon pairs, so-called biphotons, be-came available. It has recently been shown that SPDC can also be implemented in nonlinear arrays of evanescently coupled waveguides which allows the generation and the investigation of correlated quantum walks of such biphotons in an integrated device. Here, we analytically and experimentally demonstrate that the biphoton degrees of freedom are entailed in an additional spatial dimension, therefore the SPDC and the subsequent quantum random walk in one-dimensional (1D) arrays can be simulated through classical optical beam propagation in a two-dimensional (2D) photonic lattice. Thereby, the output intensity images directly represent the biphoton correlations and exhibit a clear violation of a Bell-type inequality. PACS numbers: 42.50.-p, 42.82.Et, 42.65.Lm