# Measuring geometric phases with a dynamical quantum Zeno effect in a Bose-Einstein condensate

## TL;DR

This paper demonstrates a method to measure geometric phases in a Bose-Einstein condensate by employing a dynamical quantum Zeno effect to isolate the geometric component without needing detailed control of the Hamiltonian.

## Contribution

It introduces a novel approach combining the dynamical quantum Zeno effect with measurement-free evolution to extract geometric phases in quantum systems.

## Key findings

- Successfully measured geometric phases in a BEC using the proposed method.
- Showed that the dynamical quantum Zeno effect can inhibit geometric phase formation.
- Provided a way to determine the geometric Aharonov-Anandan phase without Hamiltonian control.

## Abstract

A closed-trajectory evolution of a quantum state generally imprints a phase that contains both dynamical and geometrical contributions. While dynamical phases depend on the reference system, geometric phase factors are uniquely defined by the properties of the outlined trajectory. Here, we generate and measure geometric phases in a Bose-Einstein condensate of $^{87}$Rb using a combination of dynamical quantum Zeno effect and measurement-free evolution. We show that the dynamical quantum Zeno effect can inhibit the formation of a geometric phase without altering the dynamical phase. This can be used to extract the geometric Aharonov-Anandan phase from any closed-trajectory evolution without requiring knowledge or control of the Hamiltonian.