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Physical Review Letters

Einstein-Podolsky-Rosen Spatial Entanglement in Ordered and Anderson Photonic Lattices

Giovanni Di Giuseppe, Lane Martin, Armando Pérez-Leija, Robert Keil, Felix Dreisow, Stefan Nolte, Alexander Szameit, Ayman F. Abouraddy, Demetrios N. Christodoulides, Bahaa E. A. Saleh

Published Apr 10, 2013• 82 citations
Publisher

Abstract

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.

DOI
10.1103/physrevlett.110.150503

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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 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.
The Einstein-Podolsky-Rosen (EPR) pair of qubits plays a critical role in many quantum protocol applications such as quantum communication and quantum teleportation. Due to interactions with the environment, an EPR pair can lose its entanglement and no longer serve as a useful quantum resource. On the other hand, it has been suggested that introducing disorder into environment might help prevent thermalization and improve the preservation of entanglement. Here, we theoretically investigate the time evolution of quantum entanglement of an EPR pair in a random-field XXZ spin chain model in the Anderson localized (AL) and many-body localized (MBL) phase. We find that the entanglement between qubits decreases and approaches a plateau in the AL phase, but shows a power-law decrease after some critical time determined by the interaction strength in the MBL phase. Our findings shed light on applying AL/MBL to improve quantum information storage, and can be used as a practical indicator to distinguish the AL and MBL phase.
The Einstein–Podolsky–Rosen (EPR) pair of qubits plays a critical role in many quantum protocol applications such as quantum communication and quantum teleportation. Due to interactions with the environment, an EPR pair can lose its entanglement and no longer serve as a useful quantum resource. On the other hand, it has been suggested that introducing disorder into environment might help prevent thermalization and improve the preservation of entanglement. Here, we theoretically investigate the time evolution of quantum entanglement of an EPR pair in a random-field XXZ spin chain model in the Anderson localized (AL) and many-body localized (MBL) phase. We find that the entanglement between qubits decreases and approaches a plateau in the AL phase, but shows a power-law decrease after some critical time determined by the interaction strength in the MBL phase. Our findings shed light on applying AL/MBL to improve quantum information storage, and can be used as a practical indicator to distinguish the AL and MBL phase.