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Journal of Physics Conference Series

Quantum walks of photon pairs in twisted waveguide arrays

Dmitrii N. Vavulin, Andrey A. Sukhorukov

Published Nov 2, 2015• 1 citation
Publisher

Abstract

We consider an array of closely spaced optical waveguides, which are twisted around a central axis along the propagation direction. We derive Schrodinger-type equation of the biphoton wavefunction, taking into account the waveguide bending through the appearance of additional phase in the coupling coefficients. We present an example of the evolution of quantum photon-pair state.

DOI
10.1088/1742-6596/643/1/012050

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We consider an array of closely spaced optical waveguides, which are twisted around a central axis along the propagation direction. We derive Schrodinger-type equation of the biphoton wavefunction, taking into account the waveguide bending through the appearance of additional phase in the coupling coefficients. We present an example of the evolution of quantum photon-pair state.
This work reveals that linear propagation of classical light beams can be used to simulate the nonlinear effect of SPDC leading to photon pair generation and quantum random walks of the generated biphotons. In particular, the authors demonstrate that the quantum correlations of biphotons generated in a quadratically nonlinear 1D waveguide array can be mapped onto a linear beam propagation in specially designed 2D array of coupled optical waveguides. This analogy enables us to simulate, with classical light, the quantum coincidence counts for biphotons including the regime of breaking a 1D Bell like inequality as indicated by positve values of the non-classicality.
We describe the generation of photon pairs entangled in optical angular momentum through spontaneous four-wave mixing in circular arrays of nonlinear waveguides. We show that the incorporation of the array twist along the waveguides can enable robust generation even in the presence of defects and inhomogeneities. We present analytical results and numerical simulations based on coupled-mode equations for the classical pump field and a discrete Schr\"odinger equation for the biphoton wave function.
Arrays of coupled optical waveguides provide a flexible platform for manipulation of optical beams and pulses. Recently, the propagation of non-classical light in waveguide arrays has shown a surging attention. It was shown that quantum walks of correlated photon pairs realized through propagation in waveguide arrays can lead to nontrivial quantum correlations at the array output. However, all currently used schemes for quantum walks utilise correlated photon pairs generated externally to the array. Here, we propose and demonstrate numerically a novel scheme enabling simultaneous generation of correlated photon pair through spontaneous parametric downconversion (SPDC) and quantum walks inside a single photonic element an array of quadratic nonlinear waveguides. This scheme avoids entirely the need for complex interfaces between the different photonic elements and enables novel ways for control of the quantum correlations.
A quantum walk in an ordered medium exhibits ballistic propagation. A related process is the driven quantum walk, in which the number of walkers varies along the propagation. In this work, we show that a driven quantum walk of biphoton states in an array of nonlinear waveguides does not propagate ballistically, but instead presents two transport regimes: superballistic and superdiffusive. We also study the effects of off-diagonal and diagonal disorder. In addition to the observation of Anderson localization, both types of disorder lead to the disappearance of the superballistic regime.