The Quantum Foucault Modes

TL;DR

This paper explores a non-Hermitian, PT-symmetric driven quantum harmonic oscillator, revealing a surprising analogy to the classical Foucault pendulum and uncovering novel quantum dynamics with no classical counterpart.

Contribution

It introduces a new quantum dynamics regime under PT-symmetric driving, linking quantum trajectories to classical pendulum motion and identifying unique quantum behaviors.

Findings

Quantum trajectories mirror classical Foucault pendulum paths.

Discovery of quantum oscillators with evolving momentum but fixed position.

Identification of dynamics forbidden in classical physics.

Abstract

The driven quantum harmonic oscillator is fundamental to a number of important physical systems. Here, we consider the quantum harmonic oscillator under non-Hermitian, PT-symmetric driving, showing that the resulting set of Wigner-space trajectories of an initial coherent state is identical to the set of real-space trajectories of the classical Foucault pendulum. Remarkably, in the case mapped from the trivial 1D pendulum, the corresponding quantum dynamics are those of an oscillator with periodically evolving momentum but fixed position, a novel type of dynamics which are forbidden in classical systems.