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Photonics Research

Photonic two-particle quantum walks in Su–Schrieffer–Heeger lattices

Friederike Klauck, Matthias Heinrich, Alexander Szameit

Published Nov 18, 2020• 30 citations
Publisher

Abstract

We report on the experimental demonstration of two-photon quantum walks at the edge of a photonic Su–Schrieffer–Heeger lattice and compare them to those observed when launching photons at the edge of a homogeneous lattice. Whereas at the topological edge, one of the photons primarily remains close to the edge, both photons penetrate freely from the trivial edge into the bulk. This behavior manifests also in the average inter-particle distance, which is significantly larger at the topological edge. Hence, for a given propagation length, the entangled two-photon state launched at the topological edge extends over a wider domain of the lattice.

DOI
10.1364/prj.409005

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We report on the experimental demonstration of two-photon quantum walks at the edge of a photonic Su–Schrieffer–Heeger lattice and compare them to those observed when launching photons at the edge of a homogeneous lattice. Whereas at the topological edge, one of the photons primarily remains close to the edge, both photons penetrate freely from the trivial edge into the bulk. This behavior manifests also in the average inter-particle distance, which is significantly larger at the topological edge. Hence, for a given propagation length, the entangled two-photon state launched at the topological edge extends over a wider domain of the lattice.
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.
Topological protection of quantum correlations opens new horizons and opportunities in quantum technologies. A variety of topological effects has recently been observed in qubit networks. However, the experimental identification of the topological phase still remains challenging, especially in the entangled many-body case. Here, we propose an approach to independently probe single- and two-photon topological invariants from the time evolution of the two-photon state in a one-dimensional array of qubits. Extending the bulk-boundary correspondence to the two-photon scenario, we show that an appropriate choice of the initial state enables the retrieval of the topological invariant for the different types of the two-photon states in the interacting Su-Schrieffer-Heeger model. Our analysis of the Zak phase reveals additional facets of topological protection in the case of collapse of bound photon pairs.
The interplay of quantum light with non-Hermitian topological systems is a novel field showing surprising dynamics (1, 2). Here, we study quantum walks of photon pairs of different characteristics, i.e. distinguishable vs. indistinguishable photons, in passive non-Hermitian Su-Schrieffer-Heeger lattices. Using the robustness of topological protection, we study how quantum states can systematically avoid losses in passive systems. To probe this behaviour, we launch distinguishable and indistinguishable photon pairs in symmetric and antisymmetric input states into the lattice and record the respective probability of both photons to survive the loss and be detected at the output, a quantity we call the two-photon “survival rate”.
We study two-particle states in a Su-Schrieffer-Heeger (SSH) chain with periodic boundary conditions and nearest-neighbor (NN) interactions. The system is mapped into a problem of a single particle in a two-dimensional (2D) SSH lattice with potential walls along specific edges. The 2D SSH model has a trivial Chern number but a non-trivial Zak's phase, the one-dimensional (1D) topological invariant, along specific directions of the lattice, which allow for the presence of topological edge states. Using center-of-mass and relative coordinates, we calculate the energy spectrum of these two-body states for strong interactions and find that, aside from the expected appearance of doublon bands, two extra in-gap bands are present. These are identified as bands of topological states localized at the edges of the internal coordinate, the relative distance between the two particles. As such, the topological states reported here are intrinsically many-body in what concerns their real space manifestation, having no counterpart in single-particle states derived from effective models. Finally, we compare the effect of Hubbard interactions with that of NN interactions to show how the presence of the topological bound states is specific to the latter case.
Photonic quantum walks (PQWs), realized in lattices of evanescently coupled waveguides, are a powerful platform for demonstrating quantum [1], topological [2] and localization phenomena [3]. The PQW dynamics are captured with a tight-binding Hamiltonian, whose parameters can be engineered with the geometry of the waveguide array. It has been proposed that the two-qubit controlled-NOT (CNOT) gate can be implemented by quantum interference of two-photons in a carefully engineered PQW [4]. Whereas photonic quantum logic gates typically rely on a network of beamsplitters [5], the PQW implements the quantum logic in a single step. While multi-photon experiments in PQWs have been demonstrated [1]–[3], where photon-photon bunching governs the dynamics, the controlled preparation of entangling logic gates is yet to be experimentally explored.