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Physical Review A

Anderson localization and colocalization of spatially entangled photons

Ayman F. Abouraddy, Giovanni Di Giuseppe, Demetrios N. Christodoulides, Bahaa E. A. Saleh

Published Oct 10, 2012• 44 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.86.040302

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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.
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 demonstrate quantum walks of a photon pair in a spatially extended Einstein-Podolsky-Rosen state coupled into an on-chip multiport photonic lattice. By varying the degree of entanglement we observe Anderson localization for pairs in a separable state and Anderson colocalization for pairs in an Einstein-Podolsky-Rosen entangled state. In the former case, each photon localizes independently, while in the latter neither photon localizes, but the pair colocalizes--revealing unexpected survival of the spatial correlations through strong disorder.
We measure ensemble-averaged quantum correlations of path-entangled photons, propagating in a disordered lattice and undergoing Anderson localization. These result in intriguing patterns, which show that quantum interference leads to unexpected dependencies of the location of one particle on the location of the other. These correlations are shared between localized and nonlocalized components of the two-photon wave function, and, moreover, yield information regarding the nature of the disorder itself. Such effects cannot be reproduced with classical waves, and are undetectable without ensemble averaging.
We put forward an experimental configuration to observe transverse Anderson localization of partially coherent light beams with a tunable degree of first-order coherence. The scheme makes use of entangled photons propagating in disordered waveguide arrays and is based on the unique relationship between the degree of entanglement of a pair of photons and the coherence properties of the individual photons constituting the pair. The scheme can be readily implemented with current waveguide-on-a-chip technology, and surprisingly the tunability of the coherence properties of the individual photons is done at the measurement stage, without resorting to changes of the light source itself.