# Fast state and trap rotation of a particle in an anisotropic potential

## TL;DR

This paper develops a method to rapidly rotate the state of a particle in a 2D anisotropic harmonic trap by transforming the system into normal modes, enabling efficient state manipulation.

## Contribution

It introduces a symplectic transformation approach to decouple the dynamics and design fast trap-rotation protocols for arbitrary initial states.

## Key findings

- Normal modes are decoupled via symplectic transformations.
- Fast trap-rotation processes are feasible when normal frequencies are commensurate.
- The method applies to both quantum and classical particles.

## Abstract

We study the dynamics of a quantum or classical particle in a two-dimensional rotating anisotropic harmonic potential. By a sequence of symplectic transformations for constant rotation velocity we find uncoupled normal generalized coordinates and conjugate momenta in which the Hamiltonian takes the form of two independent harmonic oscillators. The decomposition into normal-mode dynamics enables us to design fast trap-rotation processes to produce a rotated version of an arbitrary initial state, when the two normal frequencies are commensurate.