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.
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.
We experimentally investigate topological phenomena in one-dimensional discrete-time photonic quantum walks using a combination of methods. We first detect winding numbers of the quantum walk by directly measuring the average chiral displacement, which oscillates around quantized winding numbers for finite-step quantum walks. Topological phase transitions can be identified as changes in the center of oscillation of the measured chiral displacement. The position of topological phase transition is then confirmed by measuring the moments of the walker probability distribution. Finally, we observe localized edge states at the boundary of regions with different winding numbers. We also confirm the robustness of edge states against chiral-symmetry-preserving disorder.
What is the role of topology in the propagation of quantum light in photonic lattices? We address this question by studying the propagation of squeezed states in a topological one-dimensional waveguide array, benchmarking our results with those for a topologically trivial localized state, and studying their robustness against disorder. Specifically, we study photon statistics, one-mode and two-mode squeezing, and entanglement generation when the localized state is excited with squeezed light. These quantum properties inherit the shape of the localized state but, more interestingly, and unlike in the topologically trivial case, we find that propagation of squeezed light in a topologically protected state robustly preserves the phase of the squeezed quadrature as the system evolves. We show how this latter topological advantage can be harnessed for quantum information protocols.
We report on our latest findings on photonic Quantum Walks (QW) of entangled particles in several quantum transport regimes as for instance in photonic Bloch lattices or disordered lattices. Furthermore, the discrete fractional Fourier transform of quantum states is presented in the context of QWs. The propagation of a classical single walker on a random graph is an important field in statistics and can be applied on many domains in nature reaching from a foraging animals over Brownian molecular motion towards the evolution of lead changes in competitive team sports. Its quantum mechanical counterpart, the Quantum Walk (QW), features genuine quantum objects to walk on a random graph and hence, leading to non-classical quantum interference, in particular when considering two or more walkers. Their great potential lies i.a. in their ability to exponentially speed up a multitude of algorithms, as for instance the data bank search algorithm from L. Grover. In this regard, photonic lattices of evanescently coupled waveguides represent an ideal platform to study QW dynamics, since they feature advantages in stability, robustness and miniaturization. Our waveguide lattices were fabricated by means the direct laser inscription technique. In doing so, three dimensional waveguide geometries are realizable, enabling the implementation of various QW graphs. Along these lines, we study QWs of entangled photon pairs in disordered lattices. There we observe Anderson co-localization, meaning that neither the individual photons nor the pair localizes, rather their distance does. It turns out that both photons tend to bunch as they will be found together in the same lattice site, implying that their original correlation remains while performing a QW in a disordered lattice. Further, we investigate QWs of non-local two-photon EPR-states in Bloch-lattices. The experimental results reveal the strong dependence of the correlation output statistics (bosonic-, anyonicor fermionic-like) on the input states' symmetry. Finally, the discrete fractional Fourier transform of quantum states is realized through a discrete QW lattice. The results demonstrate the enormous potential of waveguide lattices in the field of quantum photonics and give rise to further investigations like the Fourier suppression law.
Abstract Entangled multiphoton states lie at the heart of quantum information, computing, and communications. In recent years, topology has risen as a new avenue to robustly transport quantum states in the presence of fabrication defects, disorder, and other noise sources. Whereas topological protection of single photons and correlated photons has been recently demonstrated experimentally, the observation of topologically protected entangled states has thus far remained elusive. Here, we experimentally demonstrate the topological protection of spatially entangled biphoton states. We observe robustness in crucial features of the topological biphoton correlation map in the presence of deliberately introduced disorder in the silicon nanophotonic structure, in contrast with the lack of robustness in non‐topological structures. The topological protection is shown to ensure the coherent propagation of the entangled topological modes, which may lead to robust propagation of quantum information in disordered systems.
We investigate one-dimensional (1D) discrete-time quantum walks (QWs) with spatially or temporally random defects as a consequence of interactions with random environments. We focus on the QWs with chiral symmetry in a topological phase, and reveal that chiral symmetry together with the bipartite nature of the QWs brings about intriguing behaviors such as coexistence of topologically protected edge states at zero energy and Anderson transitions in the 1D chiral class at nonzero energy in their dynamics. In contrast to results of previous studies, therefore, the spatially disordered QWs can avoid complete localization due to the Anderson transition. It is further confirmed that the edge states are robust to spatial disorder but not to temporal disorder.
Topological insulators are fascinating states of matter exhibiting protected edge states and robust quantized features in their bulk. Here, we propose and validate experimentally a method to detect topological properties in the bulk of one-dimensional chiral systems. We first introduce the mean chiral displacement, and we show that it rapidly approaches a multiple of the Zak phase in the long time limit. Then we measure the Zak phase in a photonic quantum walk, by direct observation of the mean chiral displacement in its bulk. Next, we measure the Zak phase in an alternative, inequivalent timeframe, and combine the two windings to characterize the full phase diagram of this Floquet system. Finally, we prove the robustness of the measure by introducing dynamical disorder in the system. This detection method is extremely general, as it can be applied to all one-dimensional platforms simulating static or Floquet chiral systems.