Abstract: The one-dimensional coinless discrete-time quantum walk is realized in optical waveguides by utilizing directional couplers between waveguides in this work, then the topological diagram of this system is obtained and the corresponding dynamic evolution behavior affected by topological edge states is studied.The results show that when the number of the lattice sites is even, there are three different topological phases, corresponding to the topological edge states with zero-energy, π-energy, zero-energy and π-energy coexistence, respectively. Whereas, when the number of the lattice sites is odd, there are only two different topological phases, corresponding to the topological edge states with zero-energy,zeroenergy and π-energy coexistence, respectively. By choosing the appropriate parameter and initial state, the walkers, i.e. particles, can only be localized at the boundary of the system or oscillate on the two lattice sites of the boundary. The localization behavior of the walkers during the walking process provides a feasible scheme to realize nondestructive quantum state transmission and quantum information transmission.

Key words: quantum optics, optical waveguide, coinless discrete-time quantum walks, topological phase diagram, topological edge states, dynamic evolution