Synthetic forces induce complex dynamics in a photonic quantum walk

Classical kinematics tells us that free objects accelerate under the influence of a constant force. But for particles in periodic potentials, such as electrons in crystals, the application of a constant force causes them to follow oscillating trajectories known as Bloch oscillations.

While these oscillations are usually observed in solid-state systems, D’Errico et al. use a photonic setup to model this behavior in a 1D quantum walk, a quantum analogue of the classical random walk.

The team implemented the quantum walk using a helium-neon laser and a system of lenses, liquid-crystal polarization gratings and waveplates; the synthetic force was created by lateral displacement of liquid crystal plates.

“Our setup is engineered so that the laser beam suffers the analog of a constant force, displaying Bloch oscillations and even more intriguing evolutions,” said author Filippo Cardano. “As this system is extremely controllable, we can tune the force strength and show, for instance, how these regular trajectories turn into complex patterns when the force is ‘too’ large.”

The team also describes the dynamics of one-dimensional quantum walks using a numerical simulation. They find that the applied force can be tuned such that the interplay between Bloch oscillations and state transitions predicted by Landau-Zener theory reconstitutes the initial distribution of the walker wave packet after dispersal. They confirm this result experimentally.

Using their setup, the researchers “plan to extend these studies to more complex quantum walks. Complexity could be introduced by considering the evolution of multi-photon states, quantum walks on higher-dimensional lattices or by using non-unitary optical elements, as those featuring gain and losses,” Cardano said.

Source: “Bloch-Landau-Zener dynamics induced by a synthetic field in a photonic quantum walk,” by Alessio D’Errico, Raouf Barboza, Rebeca Tudor, Alexandre Dauphin, Pietro Massignan, Lorenzo Marrucci, and Filippo Cardano, APL Photonics (2021). The article can be accessed at https://doi.org/10.1063/5.0037327 .

This paper is part of the Synthetic Gauge Field Photonics collection, learn more here .