Ramsauer effect in a one-dimensional quantum walk with multiple defects

Experimental observations of quantum walks in one dimension have provided many exciting applications in quantum computing, while recent theoretical investigation of single-phase defect in these system points towards interesting phenomena associated with bound states. Here we obtain analytical solutions of a quantum walk with a general quantum coin in one dimension with multiple defects, with predictions on the condition for zero reflectance for scattering state and the existence of an analogy to the Ramsauer effect for multiple defects. We also show the transition from the zero-reflectance state to the bound state can provide a method for preparing the quantum walk in a bound state. Applications to systems similar to thin film optics are suggested.

Figure 1

Contour plot of the reflectance of Hadamard walk vs phase shift $\varphi$ and quasimomentum $k$. The darker color represents lower value of reflectance.

Figure 2

Reflectance of Hadamard walk vs the quasimomentum $k$ for different $\varphi$.

Figure 3

Reflectance for a quantum walk with different $\theta$ at the critical phase.

Figure 4

The amplitude of the wave function around a phase defect with phase shift $\varphi$ at position $N$.

Figure 5

Reflectance of a Hadamard walk going through two phase defects with the same phase shift $\varphi$ separated by distance $N$ vs the quasimomentum $k$.