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arXiv:2409.10130 · Physical review. B./Physical review. B

Quantum walks of correlated photons in non-Hermitian photonic lattices

Mingyuan Gao, Chong Sheng, Yule Zhao, Runqiu He, Liangliang Lu, Wei Chen, Kun Ding, Shining N. Zhu, Hui Liu

Published Sep 9, 2024• 15 citations
arXivHTMLPDF

Abstract

Quantum walks have demonstrated capabilities that surpass classical approaches across a range of applications, including quantum computing, quantum simulation, quantum information processing, etc. Recently, quantum walks in non-Hermitian systems have garnered significant attention. The authors experimentally realize here a non-Hermitian photonic lattice on a silicon chip, observing asymmetric quantum walks of single photons induced by the non-Hermitian skin effect. Notably, they investigate the entanglement dynamics of correlated photons, revealing a suppression of entanglement in these non-Hermitian systems.

DOI
10.1103/physrevb.110.094308

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Quantum walks have demonstrated capabilities that surpass classical approaches across a range of applications, including quantum computing, quantum simulation, quantum information processing, etc. Recently, quantum walks in non-Hermitian systems have garnered significant attention. The authors experimentally realize here a non-Hermitian photonic lattice on a silicon chip, observing asymmetric quantum walks of single photons induced by the non-Hermitian skin effect. Notably, they investigate the entanglement dynamics of correlated photons, revealing a suppression of entanglement in these non-Hermitian systems.
The non-Hermitian skin effect (NHSE), referring to the anomalous localization of eigenstates, has been widely discussed in single-particle systems. However, the interplay between the interacting NHSE and the quantum optical phenomena remains elusive. Here, We present the non-Hermitian quantum walks of strongly correlated photon pairs. Through studying the dynamic behavior of the photon pairs in the nonreciprocal Bose-Hubbard chain, we theoretically demonstrate the interplay between interactions and the NHSE. When launching two non-entangled photons, the photons exhibit the nonreciprocal bunching effect, which can be suppressed by the interactions. When launching two path-entangled photons, the interactions can not only suppress but reverse the nonreciprocal bunching. In stark contrast to the common wisdom that the NHSE suppresses the entanglement of the quantum many-body system, the entanglement of the photons here can be significantly enhanced. Our results reveal that many-body interactions and entanglement significantly restrain the non-Hermitian nonreciprocal quantum dynamics, offering insights into the interplay between many-body quantum entanglement and non-Hermitian physics. The non-Hermitian skin effect, which nonreciprocally accumulates particles at the boundary, generally suppresses entanglement by constraining global correlations. Here, the authors demonstrate that interactions can suppress nonreciprocal bunching, while entangled photons can reverse bunching direction, leading to enhanced entanglement.
Non-Hermitian systems can exhibit unique quantum phases without any Hermitian counterparts. For example, the latest theoretical studies predict a new surprising phenomenon that bulk bands can localize and dissipate prominently at the system boundary, which is dubbed the non-Hermitian edge burst effect. Here we realize a one-dimensional non-Hermitian Su-Schrieffer-Heeger lattice with bulk translation symmetry implemented with a photonic quantum walk. Employing time-resolved single-photon detection to characterize the chiral motion and boundary localization of bulk bands, we determine experimentally that the dynamics underlying the non-Hermitian edge burst effect is due to the interplay of non-Hermitian skin effect and imaginary band gap closing. This new non-Hermitian physical effect deepens our understanding of quantum dynamics in open quantum systems.
Quantum walks in an elaborately designed graph, is a powerful tool simulating physical and topological phenomena, constructing analog quantum algorithms and realizing universal quantum computing. Integrated photonics technology has emerged as a versatile platform to implement various quantum information tasks and a promising candidate to perform large-scale quantum walks. Both extending physical dimensions and involving more particles will increase the complexity of the evolving systems and the desired quantum resources. Pioneer works have demonstrated single particle walking on two-dimensional (2D) lattices and multiple walkers interfering on a one-dimensional structure. However, 2D multi-particle quantum walk, genuinely being not classically simulatable, has been a vacancy for nearly ten years. Here, we present a genuine 2D quantum walk with correlated photons on a triangular photonic lattice, which can be mapped to a state space up to 37X37 dimensions. This breaks through the physically restriction of single-particle evolution, which can encode information in a large space and constitute high-dimensional graphs indeed beneficial to quantum information processing. A site-by-site addressing between the chip facet and the 2D fanout interface enables an observation of over 600 non-classical interferences simultaneously, violating a classical limit up to 57 standard deviations. Our platform offers a promising prospect for multi-photon quantum walks in a large-scale 2D arrangement, paving the way for practical quantum simulation and quantum computation beyond classical regime.
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.
Quantum walks in an elaborately designed graph are a powerful tool for simulating physical and topological phenomena, constructing novel quantum algorithms, and realizing universal quantum computing. Integrated photonics technology has emerged as a versatile platform for implementing a variety of quantum information tasks and as a promising candidate for performing large-scale quantum walks. Both extending physical dimensions and involving more particles will increase the complexity of the evolving systems. Pioneering studies have demonstrated a single particle walking on two-dimensional lattices and multiple walkers interfering on a one-dimensional structure. However, multiple particles evolving in a genuine two-dimensional space in a scalable fashion has remained a vacancy for nearly 10 years. We present a genuine two-dimensional quantum walk with correlated photons on a triangular photonic lattice, which is mapped to a 37 × 37 high-dimensional state space. The genuine two-dimensional quantum walk breaks through the physical restrictions of single-particle evolution, allowing for the encoding of information in large spaces and construction of high-dimensional graphs, which are beneficial for quantum information processing. Between the chip and the two-dimensional fanout interface, site-by-site addressing enables simultaneous detection of over 600 nonclassical interferences and observation of quantum correlations that violate a classical limit by 57 standard deviations. Our implementation provides a paradigm for multi-photon quantum walks in a two-dimensional configuration on a large scale, paving the way for practical quantum simulation and computation beyond the classical regime.
We experimentally study the effect of the lattice topology on photonic quantum walks. We generate correlated photon pairs in an array of silicon nanowaveguides making use of the high-nonlinearity available in the system. By using single-photon measurements and propagation simulations we demonstrate the transition between the characteristic path entanglement in random quantum walks and topological localization of the quantum states. Further, we show that this topological localization is robust against disorder that preserves the chiral symmetry of the system.