Experimental Observation of Topologically Protected Bound States with Vanishing Chern Numbers in a Two-Dimensional Quantum Walk

Abstract

Quantum walks (QWs) provide a powerful tool as a quantum simulator to study and understand topological phases. Using such a quantum simulator, some topological phenomena have been discussed. However, all the experimental observations on the topological phenomena in QWs have been restricted to evolution in one dimension (1D) so far. The existing 2D experimental platforms cannot be applied to study topological phenomena due to lack of full control in the position space. Thus, some interesting topological phenomena in the 2D QW that do not exist in the 1D case, e.g., the edge-state-enhanced transport, have not been demonstrated experimentally. Here we report the experimental realization of 2D QW using spatial positions and orbital angular momentum of light. Based on our constructed experimental platform, we have observed 2D topological bound states with vanishing Chern numbers and confirmed the robustness of these bound states with respect to perturbations and disorder, which go beyond what has been known in static systems and are unique to periodically driven systems. Our studies not only represent an important advance in the study of topological phases, but also open up an avenue to explore topological properties in multidimensional QWs.

Two-dimensional topological quantum walks in the momentum space of structured light

“…By combining topology and our dynamical control of the system parameters, we could investigate dynamical quantum phase transitions in quantum walks [44][45][46]. The demonstration of a new platform for 2D quantum walks opens the door to the experimental study of this simple yet rich quantum dynamics in two spatial dimensions, with potential applications to diverse scenarios like the topological physics of 2D periodically-driven systems [29,30].…”

“…[14,18,29], where a 2D walk was cleverly simulated by folding a 2D lattice in a 1D chain, and in Ref. [30], where path and OAM encoding were combined. Very recently, a continuous-time walk has been realized in a 2D array of coupled-waveguides [31,32].…”

Experimental realization of a momentum-space quantum walk

“…Another future direction for this work is the creation of multi-dimensional QWs [36,37,64,75,76]. The obvious way to do this would be by using a multi-dimensional optical lattice produced by laser fields propagating in differ-ent spatial dimensions.…”

“…In contrast to several other QWs experimentally implemented in an assortment of walk spaces with a variety of possible walkers species [4,16,[24][25][26][27][28][29][30][31][32][33][34][35][36][37], we realize our walks in momentum space with a spinor Bose-Einstein condensate (BEC) of 87 Rb atoms. We demonstrate one of the characteristic signatures of a QW, with peaks in the walk distribution which propagate ballistically away from the origin, leading to a standard deviation of the walk distribution growing proportionally to the number of steps as the walk proceeds.…”

Long-lived quantum speedup based on plasmonic hot spot systems

“…quantum algorithms. One ideal theoretical scheme involving the long-lived quantum speedup is the quantum walk [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. In the quantum walk [2][3][4][5][6][7][8][9][10][11][12][13][14][15], a walker initially located at one site of a graph has a probability of reaching two adjacent sites, and then reaches each site of the graph as time passes.…”