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Proceedings of the Steklov Institute of Mathematics

Tunneling in Double-Layer Optical Waveguides as Quantum Walks on Graphs

Alexey A. Melnikov, A. P. Alodjants, Leonid Evgenevich Fedichkin

Published Jul 1, 2021• 2 citations
Publisher

Abstract

Abstract Modern integrated photonic quantum technologies are based on optical waveguides. The propagation of light in optical waveguides allows one to implement quantum computation and bosonic quantum simulation. Nevertheless, to further develop photonic quantum devices, one needs a precise mathematical description of quantum dynamics in waveguides. In this paper, we consider a double-layer array of optical waveguides and find exact analytical expressions for the Hamiltonian of the system and its parameters. The results are obtained both in the ideal waveguide approximation and in the case of photon loss in the waveguides.

DOI
10.1134/s0081543821020140

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Abstract Modern integrated photonic quantum technologies are based on optical waveguides. The propagation of light in optical waveguides allows one to implement quantum computation and bosonic quantum simulation. Nevertheless, to further develop photonic quantum devices, one needs a precise mathematical description of quantum dynamics in waveguides. In this paper, we consider a double-layer array of optical waveguides and find exact analytical expressions for the Hamiltonian of the system and its parameters. The results are obtained both in the ideal waveguide approximation and in the case of photon loss in the waveguides.
Quantum simulation is one of the core areas in the development of quantum technologies. Among the various simulation platforms, integrated waveguides have proven to be a powerful and versatile tool. One important aspect of quantum simulation is the analysis of open quantum systems. In most practical applications it is in fact essential to understand and control the dynamics between the quantum system and its environment. Typical effects of interest for example involve decoherence or memory effects, which lead to non-Markovian behavior. In this work we establish integrated waveguides as a tool for the simulation of open quantum systems. Using polarization as well as a photon's path degree of freedom, we implement the coupling of a qubit with a low dimensional discrete environment. Based on a measure of non-Markovianity, we define and quantify specific types of information and information transfer between system and environment. Experimentally we implement and verify non-Markovian evolution in an optical waveguide array and analyze types of information flow between system and environment realizable through integrated photonics.
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In this work is presented a macroscopic quantum-mechanical analysis of quantum light progression in different kinds of integrated photonic waveguide structures with coupled modes, and therefore with validity, for instance, for integrated optical waveguides (conventional integrated optics), photonic crystal waveguides, nano-optical waveguides (plasmonic modes) and so on. The main goal of the work is to give a consistent and explicit derivation of the quantum Momentum operator, and therefore to calculate the corresponding Heisenberg's Equations. Quantum propagation of nonclassical light states are analyzed in different linear and nonlinear integrated devices.
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