Implementing Quantum Walks Using Orbital Angular Momentum of Classical Light

We present an implementation scheme for a quantum walk in the orbital angular momentum space of a laser beam. The scheme makes use of a ring interferometer, containing a quarter-wave plate and a $q$ plate. This setup enables one to perform an arbitrary number of quantum walk steps. In addition, the classical nature of the implementation scheme makes it possible to observe the quantum walk evolution in real time. We use nonquantum entanglement of the laser beam’s polarization with its orbital angular momentum to implement the quantum walk.

Figure 1

A typical evolution of the probability in a quantum walk on a one-dimensional lattice. The initial coin state of the particle is $(|\uparrow ⟩+i|\downarrow ⟩)/\sqrt{2}$.

Figure 2

Diagrammatic representation of the optical setup of a quantum walk. A laser beam passes through a $q$ plate, followed by a quarter-wave plate. The loop corresponds to a single iteration of a quantum walk process.