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

The quantum Zeno effect offers a robust method to extract the geometric phase from any closed-trajectory evolution of a quantum state. We exploit the exquisite control coming from an atom chip to perform optimal manipulation of internal-state quantum dynamics of a Bose-Einstein condensate of ${}^{87}Rb$ atoms. In this presentation I will show how we generate and measure the geometric Aharonov-Anandan phase without requiring knowledge or control of the Hamiltonian, but only exploiting the dynamical quantum Zeno effect.