Topological Phases with Quantum Walks
Topological Phases with Quantum Walks
This Demonstration simulates a quantum dynamical protocol for a single spin-1/2 particle in a one-dimensional lattice, called a (split-step) discrete-time quantum walk. The dynamics generated through the quantum walk realize intriguing dynamical phases called topological phases. These phases are characterized by an integer (winding number), which can be controlled by changing the parameters of the protocols corresponding to the first and second rotation angles, and (see Details for the description of the protocol). The topological phase diagram of the quantum walk is drawn on the right.
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A unique signature of these topological phases is the existence of topologically protected bound states at the boundary of regions belonging to two distinct topological phases. One can create such a boundary by implementing the (spatially inhomogeneous) quantum walk with different first rotation angles on the left and right of the origin (here we choose the same rotation for the second rotation ). Now this Demonstration initializes the particle at the origin (boundary) with either spin up or spin down, and simulates the inhomogeneous quantum walk. The resulting probability distribution of the particle is plotted on the left. When the right and left regions correspond to the quantum walk protocols of distinct topological phases, one can confirm the existence of a bound state by observing that there is a finite probability of finding a particle near the phase boundary after many steps of the quantum walk.
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