Imaginary geometric phases of quantum trajectories

TL;DR

This paper introduces the concept of imaginary geometric phases in quantum trajectories, linking geometric phases to quantum diffusion and demonstrating their effects on light polarization in a specific material system.

Contribution

It reveals that quantum trajectory diffusion can have a geometric origin, extending the traditional understanding of geometric phases to include their imaginary parts.

Findings

Imaginary geometric phase causes polarization ellipticity in terahertz sidebands.

Real geometric phase results in Faraday rotation of polarized light.

Quantum diffusion can be characterized by an imaginary geometric phase.

Abstract

A quantum object can accumulate a geometric phase when it is driven along a trajectory in a parameterized state space with non-trivial gauge structures. Inherent to quantum evolutions, a system can not only accumulate a quantum phase but may also experience dephasing, or quantum diffusion. Here we show that the diffusion of quantum trajectories can also be of geometric nature as characterized by the imaginary part of the geometric phase. Such an imaginary geometric phase results from the interference of geometric phase dependent fluctuations around the quantum trajectory. As a specific example, we study the quantum trajectories of the optically excited electron-hole pairs, driven by an elliptically polarized terahertz field, in a material with non-zero Berry curvature near the energy band extremes. While the real part of the geometric phase leads to the Faraday rotation of the linearly polarized light that excites the electron-hole pair, the imaginary part manifests itself as the polarization ellipticity of the terahertz sidebands. This discovery of geometric quantum diffusion extends the concept of geometric phases.