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Physical Review Letters

Ensemble-Averaged Quantum Correlations between Path-Entangled Photons Undergoing Anderson Localization

Yehonatan Gilead, Mor Verbin, Yaron R. Silberberg

Published Sep 24, 2015• 30 citations
Publisher

Abstract

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.

DOI
10.1103/physrevlett.115.133602

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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 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 study the quantum correlation of path-entangled states of two photons in coupled one-dimensional waveguide arrays with lattice defects. Both off-diagonal and diagonal defects are considered, which show different effects on the quantum correlation of path-entangled two-photon states. Two-photon bunching or anti-bunching effects can be observed and controlled. The two photons are found to have a tendency to bunch at the side lobes with a repulsive off-diagonal defect, and the path-entanglement of the input two-photon state can be preserved during the propagation. We also found that defect modes may play an important role on the two-photon correlation of path-entangled states in the waveguide arrays. Due to the quantum interference effect, intriguing evolution dynamics of the two-photon correlation matrix elements with oscillation frequencies being either twice of or the same as that of a classical light wave, depending on the position of the correlation matrix element, is observed. Our results show that it is possible to manipulate the two-photon correlation properties of path-entangled states in waveguide arrays with lattice defects.
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 predict quantum correlations between noninteracting particles evolving simultaneously in a disordered medium. While the particle density follows the single-particle dynamics and exhibits Anderson localization, the two-particle correlation develops unique features that depend on the quantum statistics of the particles and their initial separation. On short time scales, the localization of one particle becomes dependent on whether or not the other particle is localized. On long time scales, the localized particles show oscillatory correlations within the localization length. These effects can be observed in Anderson localization of nonclassical light and ultracold atoms.
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.