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Journal of Optics

Photon-number correlations in waveguide lattices with second order coupling

Qi Fan, Zhen Feng, Y. F. Wang, Ping Xu, Shining N. Zhu, Wanhua Zheng

Published Oct 22, 2014• 10 citations
Publisher

Abstract

We introduce second-order coupling into the transport and coupling of photons in waveguide lattices. Second-order coupling, as well as high-order couplings, can be significant in long, compact or some special lattices, and is important for large-scale quantum circuits. Photon-number correlations with various amounts of second-order couplings are calculated. Some distinctive and interesting effects arise, and these are helpful for our comprehension of quantum walks in waveguide lattices.

DOI
10.1088/2040-8978/16/12/125007

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We introduce second-order coupling into the transport and coupling of photons in waveguide lattices. Second-order coupling, as well as high-order couplings, can be significant in long, compact or some special lattices, and is important for large-scale quantum circuits. Photon-number correlations with various amounts of second-order couplings are calculated. Some distinctive and interesting effects arise, and these are helpful for our comprehension of quantum walks in waveguide lattices.
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Abstract Quantum walks (QWs) are one of the fundamental concepts in quantum information science, being an essential component for various new applications. Implementing QWs using integrated photonic waveguide lattices allows for realizing long evolution times, for exploring novel lattice geometries, and even for controllable coupling to the environment. This tutorial gives an introduction to the field of on-chip QWs of single photons and photon pairs featuring non-classical two-photon correlations.
For a one-dimensional (1D) waveguide coupled to two or three qubits, we show that the photon-photon correlations have a wide variety of behavior, with structure that depends sensitively on the frequency and on the qubit-qubit separation L. We study the correlations by calculating the second-order correlation function in which the interference among the photons multiply scattered from the qubits causes rich structure. In one case, for example, transmitted and reflected photons are both bunched initially, but then become strongly anti-bunched for a long time interval. We first calculate the correlation function including non-Markovian effects and then show that a much simpler Markovian treatment, which can be solved analytically, is accurate for small qubit separation. As a result, the non-classical properties of microwaves in a 1D waveguide coupled to many superconducting qubits with experimentally accessible separation L could be readily explored with our approach.