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Optics and Photonics News

Observing Anderson Co-Localization of Entangled Photon Pairs

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

Published Dec 1, 2013• 0 citations
Publisher

Abstract

In 1958, Philip Anderson suggested that a quantum mechanical wave function may undergo localization in a disordered lattice as a result of interference between different paths arising from multiple scattering. While direct evidence of this localization remains elusive in solid state physics, its optical analogue may be realized in random arrays of coupled waveguides.

DOI
10.1364/opn.24.12.000047

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In 1958, Philip Anderson suggested that a quantum mechanical wave function may undergo localization in a disordered lattice as a result of interference between different paths arising from multiple scattering. While direct evidence of this localization remains elusive in solid state physics, its optical analogue may be realized in random arrays of coupled waveguides.
In 1958, P.W. Anderson predicted the exponential localization of electronic wave functions in disordered solids, and the resulting absence of diffusion. It has been realized later that Anderson localization is ubiquitous in wave physics as it originates from the interference between multiple scattering paths, and this has prompted an intense activity to observe it with light waves, microwaves, sound waves, and electron gases, but there was no direct observation of exponential spatial localization of matterwaves (electrons or others).
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 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.
Summary form only given. In 1958 P.W. Anderson predicted that the wave-function of a quantum particle can be localized in the presence of a static disordered potential [1]. This phenomenon arises from the destructive interference of waves propagating in static disordered media. As a consequence, in these conditions, particle and energy transport through a disordered medium are expected to be strongly suppressed and an initially localized wave packet does not spread out with time. In this work we experimentally study the localization properties of a pair of non-interacting particles obeying bosonic/fermionic statistics by simulating a one-dimensional QW of a two-photon polarization-entangled state in a disordered medium. Quantum walk is the quantum counterpart of classical random walk: a walker jumping between different sites of a lattice with a given probability. In the quantum case the walker is a quantum system, whose quantum properties affect the transport. When multi-particle walkers travel within the QW their bosonic or fermionic nature strongly affects the transport. Here we implement different quantum statistics by exploiting of the polarization-entangled bi-photon input state. The QW circuit has been experimentally realized by femtosecond laser writing which provides a perfect phase stability [2]. In particular, we realized an 8-step quantum walk circuit composed by an array of polarization independent beam splitters arranged in a cascade configuration of Mach-Zehnder (MZ) interferometers (see Fig.1a).